Statistics By Jim

Making statistics intuitive

## What is a Null Hypothesis?

The null hypothesis in statistics states that there is no difference between groups or no relationship between variables. It is one of two mutually exclusive hypotheses about a population in a hypothesis test.

• Null Hypothesis H 0 : No effect exists in the population.
• Alternative Hypothesis H A : The effect exists in the population.

In every study or experiment, researchers assess an effect or relationship. This effect can be the effectiveness of a new drug, building material, or other intervention that has benefits. There is a benefit or connection that the researchers hope to identify. Unfortunately, no effect may exist. In statistics, we call this lack of an effect the null hypothesis. Researchers assume that this notion of no effect is correct until they have enough evidence to suggest otherwise, similar to how a trial presumes innocence.

In this context, the analysts don’t necessarily believe the null hypothesis is correct. In fact, they typically want to reject it because that leads to more exciting finds about an effect or relationship. The new vaccine works!

You can think of it as the default theory that requires sufficiently strong evidence to reject. Like a prosecutor, researchers must collect sufficient evidence to overturn the presumption of no effect. Investigators must work hard to set up a study and a data collection system to obtain evidence that can reject the null hypothesis.

Related post : What is an Effect in Statistics?

## Null Hypothesis Examples

Null hypotheses start as research questions that the investigator rephrases as a statement indicating there is no effect or relationship.

 Does the vaccine prevent infections? The vaccine does not affect the infection rate. Does the new additive increase product strength? The additive does not affect mean product strength. Does the exercise intervention increase bone mineral density? The intervention does not affect bone mineral density. As screen time increases, does test performance decrease? There is no relationship between screen time and test performance.

After reading these examples, you might think they’re a bit boring and pointless. However, the key is to remember that the null hypothesis defines the condition that the researchers need to discredit before suggesting an effect exists.

Let’s see how you reject the null hypothesis and get to those more exciting findings!

## When to Reject the Null Hypothesis

So, you want to reject the null hypothesis, but how and when can you do that? To start, you’ll need to perform a statistical test on your data. The following is an overview of performing a study that uses a hypothesis test.

The first step is to devise a research question and the appropriate null hypothesis. After that, the investigators need to formulate an experimental design and data collection procedures that will allow them to gather data that can answer the research question. Then they collect the data. For more information about designing a scientific study that uses statistics, read my post 5 Steps for Conducting Studies with Statistics .

After data collection is complete, statistics and hypothesis testing enter the picture. Hypothesis testing takes your sample data and evaluates how consistent they are with the null hypothesis. The p-value is a crucial part of the statistical results because it quantifies how strongly the sample data contradict the null hypothesis.

When the sample data provide sufficient evidence, you can reject the null hypothesis. In a hypothesis test, this process involves comparing the p-value to your significance level .

## Rejecting the Null Hypothesis

Reject the null hypothesis when the p-value is less than or equal to your significance level. Your sample data favor the alternative hypothesis, which suggests that the effect exists in the population. For a mnemonic device, remember—when the p-value is low, the null must go!

## Failing to Reject the Null Hypothesis

Conversely, when the p-value is greater than your significance level, you fail to reject the null hypothesis. The sample data provides insufficient data to conclude that the effect exists in the population. When the p-value is high, the null must fly!

Note that failing to reject the null is not the same as proving it. For more information about the difference, read my post about Failing to Reject the Null .

That’s a very general look at the process. But I hope you can see how the path to more exciting findings depends on being able to rule out the less exciting null hypothesis that states there’s nothing to see here!

Let’s move on to learning how to write the null hypothesis for different types of effects, relationships, and tests.

Related posts : How Hypothesis Tests Work and Interpreting P-values

## How to Write a Null Hypothesis

The null hypothesis varies by the type of statistic and hypothesis test. Remember that inferential statistics use samples to draw conclusions about populations. Consequently, when you write a null hypothesis, it must make a claim about the relevant population parameter . Further, that claim usually indicates that the effect does not exist in the population. Below are typical examples of writing a null hypothesis for various parameters and hypothesis tests.

Related posts : Descriptive vs. Inferential Statistics and Populations, Parameters, and Samples in Inferential Statistics

## Group Means

T-tests and ANOVA assess the differences between group means. For these tests, the null hypothesis states that there is no difference between group means in the population. In other words, the experimental conditions that define the groups do not affect the mean outcome. Mu (µ) is the population parameter for the mean, and you’ll need to include it in the statement for this type of study.

For example, an experiment compares the mean bone density changes for a new osteoporosis medication. The control group does not receive the medicine, while the treatment group does. The null states that the mean bone density changes for the control and treatment groups are equal.

• Null Hypothesis H 0 : Group means are equal in the population: µ 1 = µ 2 , or µ 1 – µ 2 = 0
• Alternative Hypothesis H A : Group means are not equal in the population: µ 1 ≠ µ 2 , or µ 1 – µ 2 ≠ 0.

## Group Proportions

Proportions tests assess the differences between group proportions. For these tests, the null hypothesis states that there is no difference between group proportions. Again, the experimental conditions did not affect the proportion of events in the groups. P is the population proportion parameter that you’ll need to include.

For example, a vaccine experiment compares the infection rate in the treatment group to the control group. The treatment group receives the vaccine, while the control group does not. The null states that the infection rates for the control and treatment groups are equal.

• Null Hypothesis H 0 : Group proportions are equal in the population: p 1 = p 2 .
• Alternative Hypothesis H A : Group proportions are not equal in the population: p 1 ≠ p 2 .

## Correlation and Regression Coefficients

Some studies assess the relationship between two continuous variables rather than differences between groups.

In these studies, analysts often use either correlation or regression analysis . For these tests, the null states that there is no relationship between the variables. Specifically, it says that the correlation or regression coefficient is zero. As one variable increases, there is no tendency for the other variable to increase or decrease. Rho (ρ) is the population correlation parameter and beta (β) is the regression coefficient parameter.

For example, a study assesses the relationship between screen time and test performance. The null states that there is no correlation between this pair of variables. As screen time increases, test performance does not tend to increase or decrease.

• Null Hypothesis H 0 : The correlation in the population is zero: ρ = 0.
• Alternative Hypothesis H A : The correlation in the population is not zero: ρ ≠ 0.

For all these cases, the analysts define the hypotheses before the study. After collecting the data, they perform a hypothesis test to determine whether they can reject the null hypothesis.

The preceding examples are all for two-tailed hypothesis tests. To learn about one-tailed tests and how to write a null hypothesis for them, read my post One-Tailed vs. Two-Tailed Tests .

Related post : Understanding Correlation

Neyman, J; Pearson, E. S. (January 1, 1933).  On the Problem of the most Efficient Tests of Statistical Hypotheses .  Philosophical Transactions of the Royal Society A .  231  (694–706): 289–337.

January 11, 2024 at 2:57 pm

January 10, 2024 at 1:23 pm

Hi Jim, In your comment you state that equivalence test null and alternate hypotheses are reversed. For hypothesis tests of data fits to a probability distribution, the null hypothesis is that the probability distribution fits the data. Is this correct?

January 10, 2024 at 2:15 pm

Those two separate things, equivalence testing and normality tests. But, yes, you’re correct for both.

Hypotheses are switched for equivalence testing. You need to “work” (i.e., collect a large sample of good quality data) to be able to reject the null that the groups are different to be able to conclude they’re the same.

With typical hypothesis tests, if you have low quality data and a low sample size, you’ll fail to reject the null that they’re the same, concluding they’re equivalent. But that’s more a statement about the low quality and small sample size than anything to do with the groups being equal.

So, equivalence testing make you work to obtain a finding that the groups are the same (at least within some amount you define as a trivial difference).

For normality testing, and other distribution tests, the null states that the data follow the distribution (normal or whatever). If you reject the null, you have sufficient evidence to conclude that your sample data don’t follow the probability distribution. That’s a rare case where you hope to fail to reject the null. And it suffers from the problem I describe above where you might fail to reject the null simply because you have a small sample size. In that case, you’d conclude the data follow the probability distribution but it’s more that you don’t have enough data for the test to register the deviation. In this scenario, if you had a larger sample size, you’d reject the null and conclude it doesn’t follow that distribution.

I don’t know of any equivalence testing type approach for distribution fit tests where you’d need to work to show the data follow a distribution, although I haven’t looked for one either!

February 20, 2022 at 9:26 pm

Is a null hypothesis regularly (always) stated in the negative? “there is no” or “does not”

February 23, 2022 at 9:21 pm

Typically, the null hypothesis includes an equal sign. The null hypothesis states that the population parameter equals a particular value. That value is usually one that represents no effect. In the case of a one-sided hypothesis test, the null still contains an equal sign but it’s “greater than or equal to” or “less than or equal to.” If you wanted to translate the null hypothesis from its native mathematical expression, you could use the expression “there is no effect.” But the mathematical form more specifically states what it’s testing.

It’s the alternative hypothesis that typically contains does not equal.

There are some exceptions. For example, in an equivalence test where the researchers want to show that two things are equal, the null hypothesis states that they’re not equal.

In short, the null hypothesis states the condition that the researchers hope to reject. They need to work hard to set up an experiment and data collection that’ll gather enough evidence to be able to reject the null condition.

February 15, 2022 at 9:32 am

Dear sir I always read your notes on Research methods.. Kindly tell is there any available Book on all these..wonderfull Urgent

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• Null and Alternative Hypotheses | Definitions & Examples

## Null and Alternative Hypotheses | Definitions & Examples

Published on 5 October 2022 by Shaun Turney . Revised on 6 December 2022.

The null and alternative hypotheses are two competing claims that researchers weigh evidence for and against using a statistical test :

• Null hypothesis (H 0 ): There’s no effect in the population .
• Alternative hypothesis (H A ): There’s an effect in the population.

The effect is usually the effect of the independent variable on the dependent variable .

Answering your research question with hypotheses, what is a null hypothesis, what is an alternative hypothesis, differences between null and alternative hypotheses, how to write null and alternative hypotheses, frequently asked questions about null and alternative hypotheses.

The null and alternative hypotheses offer competing answers to your research question . When the research question asks “Does the independent variable affect the dependent variable?”, the null hypothesis (H 0 ) answers “No, there’s no effect in the population.” On the other hand, the alternative hypothesis (H A ) answers “Yes, there is an effect in the population.”

The null and alternative are always claims about the population. That’s because the goal of hypothesis testing is to make inferences about a population based on a sample . Often, we infer whether there’s an effect in the population by looking at differences between groups or relationships between variables in the sample.

You can use a statistical test to decide whether the evidence favors the null or alternative hypothesis. Each type of statistical test comes with a specific way of phrasing the null and alternative hypothesis. However, the hypotheses can also be phrased in a general way that applies to any test.

The null hypothesis is the claim that there’s no effect in the population.

If the sample provides enough evidence against the claim that there’s no effect in the population ( p ≤ α), then we can reject the null hypothesis . Otherwise, we fail to reject the null hypothesis.

Although “fail to reject” may sound awkward, it’s the only wording that statisticians accept. Be careful not to say you “prove” or “accept” the null hypothesis.

Null hypotheses often include phrases such as “no effect”, “no difference”, or “no relationship”. When written in mathematical terms, they always include an equality (usually =, but sometimes ≥ or ≤).

## Examples of null hypotheses

The table below gives examples of research questions and null hypotheses. There’s always more than one way to answer a research question, but these null hypotheses can help you get started.

 ( ) Does tooth flossing affect the number of cavities? Tooth flossing has on the number of cavities. test: The mean number of cavities per person does not differ between the flossing group (µ ) and the non-flossing group (µ ) in the population; µ = µ . Does the amount of text highlighted in the textbook affect exam scores? The amount of text highlighted in the textbook has on exam scores. : There is no relationship between the amount of text highlighted and exam scores in the population; β = 0. Does daily meditation decrease the incidence of depression? Daily meditation the incidence of depression.* test: The proportion of people with depression in the daily-meditation group ( ) is greater than or equal to the no-meditation group ( ) in the population; ≥ .

*Note that some researchers prefer to always write the null hypothesis in terms of “no effect” and “=”. It would be fine to say that daily meditation has no effect on the incidence of depression and p 1 = p 2 .

The alternative hypothesis (H A ) is the other answer to your research question . It claims that there’s an effect in the population.

Often, your alternative hypothesis is the same as your research hypothesis. In other words, it’s the claim that you expect or hope will be true.

The alternative hypothesis is the complement to the null hypothesis. Null and alternative hypotheses are exhaustive, meaning that together they cover every possible outcome. They are also mutually exclusive, meaning that only one can be true at a time.

Alternative hypotheses often include phrases such as “an effect”, “a difference”, or “a relationship”. When alternative hypotheses are written in mathematical terms, they always include an inequality (usually ≠, but sometimes > or <). As with null hypotheses, there are many acceptable ways to phrase an alternative hypothesis.

## Examples of alternative hypotheses

The table below gives examples of research questions and alternative hypotheses to help you get started with formulating your own.

 Does tooth flossing affect the number of cavities? Tooth flossing has an on the number of cavities. test: The mean number of cavities per person differs between the flossing group (µ ) and the non-flossing group (µ ) in the population; µ ≠ µ . Does the amount of text highlighted in a textbook affect exam scores? The amount of text highlighted in the textbook has an on exam scores. : There is a relationship between the amount of text highlighted and exam scores in the population; β ≠ 0. Does daily meditation decrease the incidence of depression? Daily meditation the incidence of depression. test: The proportion of people with depression in the daily-meditation group ( ) is less than the no-meditation group ( ) in the population; < .

Null and alternative hypotheses are similar in some ways:

• They’re both answers to the research question
• They both make claims about the population
• They’re both evaluated by statistical tests.

However, there are important differences between the two types of hypotheses, summarized in the following table.

 A claim that there is in the population. A claim that there is in the population. Equality symbol (=, ≥, or ≤) Inequality symbol (≠, <, or >) Rejected Supported Failed to reject Not supported

To help you write your hypotheses, you can use the template sentences below. If you know which statistical test you’re going to use, you can use the test-specific template sentences. Otherwise, you can use the general template sentences.

The only thing you need to know to use these general template sentences are your dependent and independent variables. To write your research question, null hypothesis, and alternative hypothesis, fill in the following sentences with your variables:

Does independent variable affect dependent variable ?

• Null hypothesis (H 0 ): Independent variable does not affect dependent variable .
• Alternative hypothesis (H A ): Independent variable affects dependent variable .

## Test-specific

Once you know the statistical test you’ll be using, you can write your hypotheses in a more precise and mathematical way specific to the test you chose. The table below provides template sentences for common statistical tests.

 ( ) test  with two groups The mean dependent variable does not differ between group 1 (µ ) and group 2 (µ ) in the population; µ = µ . The mean dependent variable differs between group 1 (µ ) and group 2 (µ ) in the population; µ ≠ µ . with three groups The mean dependent variable does not differ between group 1 (µ ), group 2 (µ ), and group 3 (µ ) in the population; µ = µ = µ . The mean dependent variable of group 1 (µ ), group 2 (µ ), and group 3 (µ ) are not all equal in the population. There is no correlation between independent variable and dependent variable in the population; ρ = 0. There is a correlation between independent variable and dependent variable in the population; ρ ≠ 0. There is no relationship between independent variable and dependent variable in the population; β = 0. There is a relationship between independent variable and dependent variable in the population; β ≠ 0. Two-proportions test The dependent variable expressed as a proportion does not differ between group 1 ( ) and group 2 ( ) in the population; = . The dependent variable expressed as a proportion differs between group 1 ( ) and group 2 ( ) in the population; ≠ .

Note: The template sentences above assume that you’re performing one-tailed tests . One-tailed tests are appropriate for most studies.

The null hypothesis is often abbreviated as H 0 . When the null hypothesis is written using mathematical symbols, it always includes an equality symbol (usually =, but sometimes ≥ or ≤).

The alternative hypothesis is often abbreviated as H a or H 1 . When the alternative hypothesis is written using mathematical symbols, it always includes an inequality symbol (usually ≠, but sometimes < or >).

A research hypothesis is your proposed answer to your research question. The research hypothesis usually includes an explanation (‘ x affects y because …’).

A statistical hypothesis, on the other hand, is a mathematical statement about a population parameter. Statistical hypotheses always come in pairs: the null and alternative hypotheses. In a well-designed study , the statistical hypotheses correspond logically to the research hypothesis.

## Cite this Scribbr article

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Turney, S. (2022, December 06). Null and Alternative Hypotheses | Definitions & Examples. Scribbr. Retrieved 10 July 2024, from https://www.scribbr.co.uk/stats/null-and-alternative-hypothesis/

## Shaun Turney

Other students also liked, levels of measurement: nominal, ordinal, interval, ratio, the standard normal distribution | calculator, examples & uses, types of variables in research | definitions & examples.

## Null Hypothesis Definition and Examples, How to State

What is the null hypothesis, how to state the null hypothesis, null hypothesis overview.

## Why is it Called the “Null”?

The word “null” in this context means that it’s a commonly accepted fact that researchers work to nullify . It doesn’t mean that the statement is null (i.e. amounts to nothing) itself! (Perhaps the term should be called the “nullifiable hypothesis” as that might cause less confusion).

## Why Do I need to Test it? Why not just prove an alternate one?

The short answer is, as a scientist, you are required to ; It’s part of the scientific process. Science uses a battery of processes to prove or disprove theories, making sure than any new hypothesis has no flaws. Including both a null and an alternate hypothesis is one safeguard to ensure your research isn’t flawed. Not including the null hypothesis in your research is considered very bad practice by the scientific community. If you set out to prove an alternate hypothesis without considering it, you are likely setting yourself up for failure. At a minimum, your experiment will likely not be taken seriously.

• Null hypothesis : H 0 : The world is flat.
• Alternate hypothesis: The world is round.

Several scientists, including Copernicus , set out to disprove the null hypothesis. This eventually led to the rejection of the null and the acceptance of the alternate. Most people accepted it — the ones that didn’t created the Flat Earth Society !. What would have happened if Copernicus had not disproved the it and merely proved the alternate? No one would have listened to him. In order to change people’s thinking, he first had to prove that their thinking was wrong .

## How to State the Null Hypothesis from a Word Problem

You’ll be asked to convert a word problem into a hypothesis statement in statistics that will include a null hypothesis and an alternate hypothesis . Breaking your problem into a few small steps makes these problems much easier to handle.

Step 2: Convert the hypothesis to math . Remember that the average is sometimes written as μ.

H 1 : μ > 8.2

Broken down into (somewhat) English, that’s H 1 (The hypothesis): μ (the average) > (is greater than) 8.2

Step 3: State what will happen if the hypothesis doesn’t come true. If the recovery time isn’t greater than 8.2 weeks, there are only two possibilities, that the recovery time is equal to 8.2 weeks or less than 8.2 weeks.

H 0 : μ ≤ 8.2

Broken down again into English, that’s H 0 (The null hypothesis): μ (the average) ≤ (is less than or equal to) 8.2

## How to State the Null Hypothesis: Part Two

But what if the researcher doesn’t have any idea what will happen.

Example Problem: A researcher is studying the effects of radical exercise program on knee surgery patients. There is a good chance the therapy will improve recovery time, but there’s also the possibility it will make it worse. Average recovery times for knee surgery patients is 8.2 weeks.

Step 1: State what will happen if the experiment doesn’t make any difference. That’s the null hypothesis–that nothing will happen. In this experiment, if nothing happens, then the recovery time will stay at 8.2 weeks.

H 0 : μ = 8.2

Broken down into English, that’s H 0 (The null hypothesis): μ (the average) = (is equal to) 8.2

Step 2: Figure out the alternate hypothesis . The alternate hypothesis is the opposite of the null hypothesis. In other words, what happens if our experiment makes a difference?

H 1 : μ ≠ 8.2

In English again, that’s H 1 (The  alternate hypothesis): μ (the average) ≠ (is not equal to) 8.2

That’s How to State the Null Hypothesis!

Check out our Youtube channel for more stats tips!

Gonick, L. (1993). The Cartoon Guide to Statistics . HarperPerennial. Kotz, S.; et al., eds. (2006), Encyclopedia of Statistical Sciences , Wiley.

## 9.1 Null and Alternative Hypotheses

The actual test begins by considering two hypotheses . They are called the null hypothesis and the alternative hypothesis . These hypotheses contain opposing viewpoints.

H 0 , the — null hypothesis: a statement of no difference between sample means or proportions or no difference between a sample mean or proportion and a population mean or proportion. In other words, the difference equals 0.

H a —, the alternative hypothesis: a claim about the population that is contradictory to H 0 and what we conclude when we reject H 0 .

Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample data.

After you have determined which hypothesis the sample supports, you make a decision. There are two options for a decision. They are reject H 0 if the sample information favors the alternative hypothesis or do not reject H 0 or decline to reject H 0 if the sample information is insufficient to reject the null hypothesis.

Mathematical Symbols Used in H 0 and H a :

equal (=) not equal (≠) greater than (>) less than (<)
greater than or equal to (≥) less than (<)
less than or equal to (≤) more than (>)

H 0 always has a symbol with an equal in it. H a never has a symbol with an equal in it. The choice of symbol depends on the wording of the hypothesis test. However, be aware that many researchers use = in the null hypothesis, even with > or < as the symbol in the alternative hypothesis. This practice is acceptable because we only make the decision to reject or not reject the null hypothesis.

## Example 9.1

H 0 : No more than 30 percent of the registered voters in Santa Clara County voted in the primary election. p ≤ 30 H a : More than 30 percent of the registered voters in Santa Clara County voted in the primary election. p > 30

A medical trial is conducted to test whether or not a new medicine reduces cholesterol by 25 percent. State the null and alternative hypotheses.

## Example 9.2

We want to test whether the mean GPA of students in American colleges is different from 2.0 (out of 4.0). The null and alternative hypotheses are the following: H 0 : μ = 2.0 H a : μ ≠ 2.0

We want to test whether the mean height of eighth graders is 66 inches. State the null and alternative hypotheses. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

• H 0 : μ __ 66
• H a : μ __ 66

## Example 9.3

We want to test if college students take fewer than five years to graduate from college, on the average. The null and alternative hypotheses are the following: H 0 : μ ≥ 5 H a : μ < 5

We want to test if it takes fewer than 45 minutes to teach a lesson plan. State the null and alternative hypotheses. Fill in the correct symbol ( =, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

• H 0 : μ __ 45
• H a : μ __ 45

## Example 9.4

An article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third of the students pass. The same article stated that 6.6 percent of U.S. students take advanced placement exams and 4.4 percent pass. Test if the percentage of U.S. students who take advanced placement exams is more than 6.6 percent. State the null and alternative hypotheses. H 0 : p ≤ 0.066 H a : p > 0.066

On a state driver’s test, about 40 percent pass the test on the first try. We want to test if more than 40 percent pass on the first try. Fill in the correct symbol (=, ≠, ≥, <, ≤, >) for the null and alternative hypotheses.

• H 0 : p __ 0.40
• H a : p __ 0.40

## Collaborative Exercise

Bring to class a newspaper, some news magazines, and some internet articles. In groups, find articles from which your group can write null and alternative hypotheses. Discuss your hypotheses with the rest of the class.

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## AP®︎/College Statistics

Course: ap®︎/college statistics   >   unit 10.

• Idea behind hypothesis testing

## Examples of null and alternative hypotheses

• Writing null and alternative hypotheses
• P-values and significance tests
• Comparing P-values to different significance levels
• Estimating a P-value from a simulation
• Estimating P-values from simulations
• Using P-values to make conclusions

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null hypothesis

## Definition of null hypothesis

Examples of null hypothesis in a sentence.

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'null hypothesis.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

## Word History

1935, in the meaning defined above

Nullarbor Plain

## Cite this Entry

“Null hypothesis.” Merriam-Webster.com Dictionary , Merriam-Webster, https://www.merriam-webster.com/dictionary/null%20hypothesis. Accessed 12 Jul. 2024.

## More from Merriam-Webster on null hypothesis

Britannica.com: Encyclopedia article about null hypothesis

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• Indian J Crit Care Med
• v.23(Suppl 3); 2019 Sep

## An Introduction to Statistics: Understanding Hypothesis Testing and Statistical Errors

Priya ranganathan.

1 Department of Anesthesiology, Critical Care and Pain, Tata Memorial Hospital, Mumbai, Maharashtra, India

2 Department of Surgical Oncology, Tata Memorial Centre, Mumbai, Maharashtra, India

The second article in this series on biostatistics covers the concepts of sample, population, research hypotheses and statistical errors.

Ranganathan P, Pramesh CS. An Introduction to Statistics: Understanding Hypothesis Testing and Statistical Errors. Indian J Crit Care Med 2019;23(Suppl 3):S230–S231.

Two papers quoted in this issue of the Indian Journal of Critical Care Medicine report. The results of studies aim to prove that a new intervention is better than (superior to) an existing treatment. In the ABLE study, the investigators wanted to show that transfusion of fresh red blood cells would be superior to standard-issue red cells in reducing 90-day mortality in ICU patients. 1 The PROPPR study was designed to prove that transfusion of a lower ratio of plasma and platelets to red cells would be superior to a higher ratio in decreasing 24-hour and 30-day mortality in critically ill patients. 2 These studies are known as superiority studies (as opposed to noninferiority or equivalence studies which will be discussed in a subsequent article).

## SAMPLE VERSUS POPULATION

A sample represents a group of participants selected from the entire population. Since studies cannot be carried out on entire populations, researchers choose samples, which are representative of the population. This is similar to walking into a grocery store and examining a few grains of rice or wheat before purchasing an entire bag; we assume that the few grains that we select (the sample) are representative of the entire sack of grains (the population).

The results of the study are then extrapolated to generate inferences about the population. We do this using a process known as hypothesis testing. This means that the results of the study may not always be identical to the results we would expect to find in the population; i.e., there is the possibility that the study results may be erroneous.

## HYPOTHESIS TESTING

A clinical trial begins with an assumption or belief, and then proceeds to either prove or disprove this assumption. In statistical terms, this belief or assumption is known as a hypothesis. Counterintuitively, what the researcher believes in (or is trying to prove) is called the “alternate” hypothesis, and the opposite is called the “null” hypothesis; every study has a null hypothesis and an alternate hypothesis. For superiority studies, the alternate hypothesis states that one treatment (usually the new or experimental treatment) is superior to the other; the null hypothesis states that there is no difference between the treatments (the treatments are equal). For example, in the ABLE study, we start by stating the null hypothesis—there is no difference in mortality between groups receiving fresh RBCs and standard-issue RBCs. We then state the alternate hypothesis—There is a difference between groups receiving fresh RBCs and standard-issue RBCs. It is important to note that we have stated that the groups are different, without specifying which group will be better than the other. This is known as a two-tailed hypothesis and it allows us to test for superiority on either side (using a two-sided test). This is because, when we start a study, we are not 100% certain that the new treatment can only be better than the standard treatment—it could be worse, and if it is so, the study should pick it up as well. One tailed hypothesis and one-sided statistical testing is done for non-inferiority studies, which will be discussed in a subsequent paper in this series.

## STATISTICAL ERRORS

There are two possibilities to consider when interpreting the results of a superiority study. The first possibility is that there is truly no difference between the treatments but the study finds that they are different. This is called a Type-1 error or false-positive error or alpha error. This means falsely rejecting the null hypothesis.

The second possibility is that there is a difference between the treatments and the study does not pick up this difference. This is called a Type 2 error or false-negative error or beta error. This means falsely accepting the null hypothesis.

The power of the study is the ability to detect a difference between groups and is the converse of the beta error; i.e., power = 1-beta error. Alpha and beta errors are finalized when the protocol is written and form the basis for sample size calculation for the study. In an ideal world, we would not like any error in the results of our study; however, we would need to do the study in the entire population (infinite sample size) to be able to get a 0% alpha and beta error. These two errors enable us to do studies with realistic sample sizes, with the compromise that there is a small possibility that the results may not always reflect the truth. The basis for this will be discussed in a subsequent paper in this series dealing with sample size calculation.

Conventionally, type 1 or alpha error is set at 5%. This means, that at the end of the study, if there is a difference between groups, we want to be 95% certain that this is a true difference and allow only a 5% probability that this difference has occurred by chance (false positive). Type 2 or beta error is usually set between 10% and 20%; therefore, the power of the study is 90% or 80%. This means that if there is a difference between groups, we want to be 80% (or 90%) certain that the study will detect that difference. For example, in the ABLE study, sample size was calculated with a type 1 error of 5% (two-sided) and power of 90% (type 2 error of 10%) (1).

Table 1 gives a summary of the two types of statistical errors with an example

Statistical errors

 (a) Types of statistical errors : Null hypothesis is True False Null hypothesis is actually True Correct results! Falsely rejecting null hypothesis - Type I error False Falsely accepting null hypothesis - Type II error Correct results! (b) Possible statistical errors in the ABLE trial There is difference in mortality between groups receiving fresh RBCs and standard-issue RBCs There difference in mortality between groups receiving fresh RBCs and standard-issue RBCs Truth There is difference in mortality between groups receiving fresh RBCs and standard-issue RBCs Correct results! Falsely rejecting null hypothesis - Type I error There difference in mortality between groups receiving fresh RBCs and standard-issue RBCs Falsely accepting null hypothesis - Type II error Correct results!

In the next article in this series, we will look at the meaning and interpretation of ‘ p ’ value and confidence intervals for hypothesis testing.

Source of support: Nil

Conflict of interest: None

## Null Hypothesis Examples

ThoughtCo / Hilary Allison

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In statistical analysis, the null hypothesis assumes there is no meaningful relationship between two variables. Testing the null hypothesis can tell you whether your results are due to the effect of manipulating ​a dependent variable or due to chance. It's often used in conjunction with an alternative hypothesis, which assumes there is, in fact, a relationship between two variables.

The null hypothesis is among the easiest hypothesis to test using statistical analysis, making it perhaps the most valuable hypothesis for the scientific method. By evaluating a null hypothesis in addition to another hypothesis, researchers can support their conclusions with a higher level of confidence. Below are examples of how you might formulate a null hypothesis to fit certain questions.

## What Is the Null Hypothesis?

The null hypothesis states there is no relationship between the measured phenomenon (the dependent variable ) and the independent variable , which is the variable an experimenter typically controls or changes. You do not​ need to believe that the null hypothesis is true to test it. On the contrary, you will likely suspect there is a relationship between a set of variables. One way to prove that this is the case is to reject the null hypothesis. Rejecting a hypothesis does not mean an experiment was "bad" or that it didn't produce results. In fact, it is often one of the first steps toward further inquiry.

To distinguish it from other hypotheses , the null hypothesis is written as ​ H 0  (which is read as “H-nought,” "H-null," or "H-zero"). A significance test is used to determine the likelihood that the results supporting the null hypothesis are not due to chance. A confidence level of 95% or 99% is common. Keep in mind, even if the confidence level is high, there is still a small chance the null hypothesis is not true, perhaps because the experimenter did not account for a critical factor or because of chance. This is one reason why it's important to repeat experiments.

## Examples of the Null Hypothesis

To write a null hypothesis, first start by asking a question. Rephrase that question in a form that assumes no relationship between the variables. In other words, assume a treatment has no effect. Write your hypothesis in a way that reflects this.

 Are teens better at math than adults? Age has no effect on mathematical ability. Does taking aspirin every day reduce the chance of having a heart attack? Taking aspirin daily does not affect heart attack risk. Do teens use cell phones to access the internet more than adults? Age has no effect on how cell phones are used for internet access. Do cats care about the color of their food? Cats express no food preference based on color. Does chewing willow bark relieve pain? There is no difference in pain relief after chewing willow bark versus taking a placebo.

## Other Types of Hypotheses

In addition to the null hypothesis, the alternative hypothesis is also a staple in traditional significance tests . It's essentially the opposite of the null hypothesis because it assumes the claim in question is true. For the first item in the table above, for example, an alternative hypothesis might be "Age does have an effect on mathematical ability."

## Key Takeaways

• In hypothesis testing, the null hypothesis assumes no relationship between two variables, providing a baseline for statistical analysis.
• Rejecting the null hypothesis suggests there is evidence of a relationship between variables.
• By formulating a null hypothesis, researchers can systematically test assumptions and draw more reliable conclusions from their experiments.
• Difference Between Independent and Dependent Variables
• Examples of Independent and Dependent Variables
• The Difference Between Control Group and Experimental Group
• What Is a Hypothesis? (Science)
• What 'Fail to Reject' Means in a Hypothesis Test
• Definition of a Hypothesis
• Null Hypothesis Definition and Examples
• Scientific Method Vocabulary Terms
• Null Hypothesis and Alternative Hypothesis
• Hypothesis Test for the Difference of Two Population Proportions
• How to Conduct a Hypothesis Test
• What Is a P-Value?
• What Are the Elements of a Good Hypothesis?
• Hypothesis Test Example
• What Is the Difference Between Alpha and P-Values?
• Understanding Path Analysis

## What is The Null Hypothesis & When Do You Reject The Null Hypothesis

Julia Simkus

Editor at Simply Psychology

BA (Hons) Psychology, Princeton University

Julia Simkus is a graduate of Princeton University with a Bachelor of Arts in Psychology. She is currently studying for a Master's Degree in Counseling for Mental Health and Wellness in September 2023. Julia's research has been published in peer reviewed journals.

Saul Mcleod, PhD

Editor-in-Chief for Simply Psychology

BSc (Hons) Psychology, MRes, PhD, University of Manchester

Saul Mcleod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

Olivia Guy-Evans, MSc

Associate Editor for Simply Psychology

BSc (Hons) Psychology, MSc Psychology of Education

Olivia Guy-Evans is a writer and associate editor for Simply Psychology. She has previously worked in healthcare and educational sectors.

A null hypothesis is a statistical concept suggesting no significant difference or relationship between measured variables. It’s the default assumption unless empirical evidence proves otherwise.

The null hypothesis states no relationship exists between the two variables being studied (i.e., one variable does not affect the other).

The null hypothesis is the statement that a researcher or an investigator wants to disprove.

Testing the null hypothesis can tell you whether your results are due to the effects of manipulating ​ the dependent variable or due to random chance.

## How to Write a Null Hypothesis

Null hypotheses (H0) start as research questions that the investigator rephrases as statements indicating no effect or relationship between the independent and dependent variables.

It is a default position that your research aims to challenge or confirm.

## For example, if studying the impact of exercise on weight loss, your null hypothesis might be:

There is no significant difference in weight loss between individuals who exercise daily and those who do not.

## Examples of Null Hypotheses

Research QuestionNull Hypothesis
Do teenagers use cell phones more than adults?Teenagers and adults use cell phones the same amount.
Do tomato plants exhibit a higher rate of growth when planted in compost rather than in soil?Tomato plants show no difference in growth rates when planted in compost rather than soil.
Does daily meditation decrease the incidence of depression?Daily meditation does not decrease the incidence of depression.
Does daily exercise increase test performance?There is no relationship between daily exercise time and test performance.
Does the new vaccine prevent infections?The vaccine does not affect the infection rate.
Does flossing your teeth affect the number of cavities?Flossing your teeth has no effect on the number of cavities.

## When Do We Reject The Null Hypothesis?

We reject the null hypothesis when the data provide strong enough evidence to conclude that it is likely incorrect. This often occurs when the p-value (probability of observing the data given the null hypothesis is true) is below a predetermined significance level.

If the collected data does not meet the expectation of the null hypothesis, a researcher can conclude that the data lacks sufficient evidence to back up the null hypothesis, and thus the null hypothesis is rejected.

Rejecting the null hypothesis means that a relationship does exist between a set of variables and the effect is statistically significant ( p > 0.05).

If the data collected from the random sample is not statistically significance , then the null hypothesis will be accepted, and the researchers can conclude that there is no relationship between the variables.

You need to perform a statistical test on your data in order to evaluate how consistent it is with the null hypothesis. A p-value is one statistical measurement used to validate a hypothesis against observed data.

Calculating the p-value is a critical part of null-hypothesis significance testing because it quantifies how strongly the sample data contradicts the null hypothesis.

The level of statistical significance is often expressed as a  p  -value between 0 and 1. The smaller the p-value, the stronger the evidence that you should reject the null hypothesis.

Usually, a researcher uses a confidence level of 95% or 99% (p-value of 0.05 or 0.01) as general guidelines to decide if you should reject or keep the null.

When your p-value is less than or equal to your significance level, you reject the null hypothesis.

In other words, smaller p-values are taken as stronger evidence against the null hypothesis. Conversely, when the p-value is greater than your significance level, you fail to reject the null hypothesis.

In this case, the sample data provides insufficient data to conclude that the effect exists in the population.

Because you can never know with complete certainty whether there is an effect in the population, your inferences about a population will sometimes be incorrect.

When you incorrectly reject the null hypothesis, it’s called a type I error. When you incorrectly fail to reject it, it’s called a type II error.

## Why Do We Never Accept The Null Hypothesis?

The reason we do not say “accept the null” is because we are always assuming the null hypothesis is true and then conducting a study to see if there is evidence against it. And, even if we don’t find evidence against it, a null hypothesis is not accepted.

A lack of evidence only means that you haven’t proven that something exists. It does not prove that something doesn’t exist.

It is risky to conclude that the null hypothesis is true merely because we did not find evidence to reject it. It is always possible that researchers elsewhere have disproved the null hypothesis, so we cannot accept it as true, but instead, we state that we failed to reject the null.

One can either reject the null hypothesis, or fail to reject it, but can never accept it.

## Why Do We Use The Null Hypothesis?

We can never prove with 100% certainty that a hypothesis is true; We can only collect evidence that supports a theory. However, testing a hypothesis can set the stage for rejecting or accepting this hypothesis within a certain confidence level.

The null hypothesis is useful because it can tell us whether the results of our study are due to random chance or the manipulation of a variable (with a certain level of confidence).

A null hypothesis is rejected if the measured data is significantly unlikely to have occurred and a null hypothesis is accepted if the observed outcome is consistent with the position held by the null hypothesis.

Rejecting the null hypothesis sets the stage for further experimentation to see if a relationship between two variables exists.

Hypothesis testing is a critical part of the scientific method as it helps decide whether the results of a research study support a particular theory about a given population. Hypothesis testing is a systematic way of backing up researchers’ predictions with statistical analysis.

It helps provide sufficient statistical evidence that either favors or rejects a certain hypothesis about the population parameter.

## Purpose of a Null Hypothesis

• The primary purpose of the null hypothesis is to disprove an assumption.
• Whether rejected or accepted, the null hypothesis can help further progress a theory in many scientific cases.
• A null hypothesis can be used to ascertain how consistent the outcomes of multiple studies are.

## Do you always need both a Null Hypothesis and an Alternative Hypothesis?

The null (H0) and alternative (Ha or H1) hypotheses are two competing claims that describe the effect of the independent variable on the dependent variable. They are mutually exclusive, which means that only one of the two hypotheses can be true.

While the null hypothesis states that there is no effect in the population, an alternative hypothesis states that there is statistical significance between two variables.

The goal of hypothesis testing is to make inferences about a population based on a sample. In order to undertake hypothesis testing, you must express your research hypothesis as a null and alternative hypothesis. Both hypotheses are required to cover every possible outcome of the study.

## What is the difference between a null hypothesis and an alternative hypothesis?

The alternative hypothesis is the complement to the null hypothesis. The null hypothesis states that there is no effect or no relationship between variables, while the alternative hypothesis claims that there is an effect or relationship in the population.

It is the claim that you expect or hope will be true. The null hypothesis and the alternative hypothesis are always mutually exclusive, meaning that only one can be true at a time.

## What are some problems with the null hypothesis?

One major problem with the null hypothesis is that researchers typically will assume that accepting the null is a failure of the experiment. However, accepting or rejecting any hypothesis is a positive result. Even if the null is not refuted, the researchers will still learn something new.

## Why can a null hypothesis not be accepted?

We can either reject or fail to reject a null hypothesis, but never accept it. If your test fails to detect an effect, this is not proof that the effect doesn’t exist. It just means that your sample did not have enough evidence to conclude that it exists.

We can’t accept a null hypothesis because a lack of evidence does not prove something that does not exist. Instead, we fail to reject it.

Failing to reject the null indicates that the sample did not provide sufficient enough evidence to conclude that an effect exists.

If the p-value is greater than the significance level, then you fail to reject the null hypothesis.

## Is a null hypothesis directional or non-directional?

A hypothesis test can either contain an alternative directional hypothesis or a non-directional alternative hypothesis. A directional hypothesis is one that contains the less than (“<“) or greater than (“>”) sign.

A nondirectional hypothesis contains the not equal sign (“≠”).  However, a null hypothesis is neither directional nor non-directional.

A null hypothesis is a prediction that there will be no change, relationship, or difference between two variables.

The directional hypothesis or nondirectional hypothesis would then be considered alternative hypotheses to the null hypothesis.

Gill, J. (1999). The insignificance of null hypothesis significance testing.  Political research quarterly ,  52 (3), 647-674.

Krueger, J. (2001). Null hypothesis significance testing: On the survival of a flawed method.  American Psychologist ,  56 (1), 16.

Masson, M. E. (2011). A tutorial on a practical Bayesian alternative to null-hypothesis significance testing.  Behavior research methods ,  43 , 679-690.

Nickerson, R. S. (2000). Null hypothesis significance testing: a review of an old and continuing controversy.  Psychological methods ,  5 (2), 241.

Rozeboom, W. W. (1960). The fallacy of the null-hypothesis significance test.  Psychological bulletin ,  57 (5), 416.

• Math Article

## Null Hypothesis

In mathematics, Statistics deals with the study of research and surveys on the numerical data. For taking surveys, we have to define the hypothesis. Generally, there are two types of hypothesis. One is a null hypothesis, and another is an alternative hypothesis .

In probability and statistics, the null hypothesis is a comprehensive statement or default status that there is zero happening or nothing happening. For example, there is no connection among groups or no association between two measured events. It is generally assumed here that the hypothesis is true until any other proof has been brought into the light to deny the hypothesis. Let us learn more here with definition, symbol, principle, types and example, in this article.

• Comparison with Alternative Hypothesis

## Null Hypothesis Definition

The null hypothesis is a kind of hypothesis which explains the population parameter whose purpose is to test the validity of the given experimental data. This hypothesis is either rejected or not rejected based on the viability of the given population or sample . In other words, the null hypothesis is a hypothesis in which the sample observations results from the chance. It is said to be a statement in which the surveyors wants to examine the data. It is denoted by H 0 .

## Null Hypothesis Symbol

In statistics, the null hypothesis is usually denoted by letter H with subscript ‘0’ (zero), such that H 0 . It is pronounced as H-null or H-zero or H-nought. At the same time, the alternative hypothesis expresses the observations determined by the non-random cause. It is represented by H 1 or H a .

## Null Hypothesis Principle

The principle followed for null hypothesis testing is, collecting the data and determining the chances of a given set of data during the study on some random sample, assuming that the null hypothesis is true. In case if the given data does not face the expected null hypothesis, then the outcome will be quite weaker, and they conclude by saying that the given set of data does not provide strong evidence against the null hypothesis because of insufficient evidence. Finally, the researchers tend to reject that.

## Null Hypothesis Formula

Here, the hypothesis test formulas are given below for reference.

The formula for the null hypothesis is:

H 0 :  p = p 0

The formula for the alternative hypothesis is:

H a = p >p 0 , < p 0 ≠ p 0

The formula for the test static is:

Remember that,  p 0  is the null hypothesis and p – hat is the sample proportion.

## Types of Null Hypothesis

There are different types of hypothesis. They are:

Simple Hypothesis

It completely specifies the population distribution. In this method, the sampling distribution is the function of the sample size.

Composite Hypothesis

The composite hypothesis is one that does not completely specify the population distribution.

Exact Hypothesis

Exact hypothesis defines the exact value of the parameter. For example μ= 50

Inexact Hypothesis

This type of hypothesis does not define the exact value of the parameter. But it denotes a specific range or interval. For example 45< μ <60

## Null Hypothesis Rejection

Sometimes the null hypothesis is rejected too. If this hypothesis is rejected means, that research could be invalid. Many researchers will neglect this hypothesis as it is merely opposite to the alternate hypothesis. It is a better practice to create a hypothesis and test it. The goal of researchers is not to reject the hypothesis. But it is evident that a perfect statistical model is always associated with the failure to reject the null hypothesis.

## How do you Find the Null Hypothesis?

The null hypothesis says there is no correlation between the measured event (the dependent variable) and the independent variable. We don’t have to believe that the null hypothesis is true to test it. On the contrast, you will possibly assume that there is a connection between a set of variables ( dependent and independent).

## When is Null Hypothesis Rejected?

The null hypothesis is rejected using the P-value approach. If the P-value is less than or equal to the α, there should be a rejection of the null hypothesis in favour of the alternate hypothesis. In case, if P-value is greater than α, the null hypothesis is not rejected.

## Null Hypothesis and Alternative Hypothesis

Now, let us discuss the difference between the null hypothesis and the alternative hypothesis.

 1 The null hypothesis is a statement. There exists no relation between two variables Alternative hypothesis a statement, there exists some relationship between two measured phenomenon 2 Denoted by H Denoted by H 3 The observations of this hypothesis are the result of chance The observations of this hypothesis are the result of real effect 4 The mathematical formulation of the null hypothesis is an equal sign The mathematical formulation alternative hypothesis is an inequality sign such as greater than, less than, etc.

## Null Hypothesis Examples

Here, some of the examples of the null hypothesis are given below. Go through the below ones to understand the concept of the null hypothesis in a better way.

If a medicine reduces the risk of cardiac stroke, then the null hypothesis should be “the medicine does not reduce the chance of cardiac stroke”. This testing can be performed by the administration of a drug to a certain group of people in a controlled way. If the survey shows that there is a significant change in the people, then the hypothesis is rejected.

Few more examples are:

1). Are there is 100% chance of getting affected by dengue?

Ans: There could be chances of getting affected by dengue but not 100%.

2). Do teenagers are using mobile phones more than grown-ups to access the internet?

Ans: Age has no limit on using mobile phones to access the internet.

3). Does having apple daily will not cause fever?

Ans: Having apple daily does not assure of not having fever, but increases the immunity to fight against such diseases.

4). Do the children more good in doing mathematical calculations than grown-ups?

Ans: Age has no effect on Mathematical skills.

In many common applications, the choice of the null hypothesis is not automated, but the testing and calculations may be automated. Also, the choice of the null hypothesis is completely based on previous experiences and inconsistent advice. The choice can be more complicated and based on the variety of applications and the diversity of the objectives.

The main limitation for the choice of the null hypothesis is that the hypothesis suggested by the data is based on the reasoning which proves nothing. It means that if some hypothesis provides a summary of the data set, then there would be no value in the testing of the hypothesis on the particular set of data.

## Frequently Asked Questions on Null Hypothesis

What is meant by the null hypothesis.

In Statistics, a null hypothesis is a type of hypothesis which explains the population parameter whose purpose is to test the validity of the given experimental data.

## What are the benefits of hypothesis testing?

Hypothesis testing is defined as a form of inferential statistics, which allows making conclusions from the entire population based on the sample representative.

## When a null hypothesis is accepted and rejected?

The null hypothesis is either accepted or rejected in terms of the given data. If P-value is less than α, then the null hypothesis is rejected in favor of the alternative hypothesis, and if the P-value is greater than α, then the null hypothesis is accepted in favor of the alternative hypothesis.

## Why is the null hypothesis important?

The importance of the null hypothesis is that it provides an approximate description of the phenomena of the given data. It allows the investigators to directly test the relational statement in a research study.

## How to accept or reject the null hypothesis in the chi-square test?

If the result of the chi-square test is bigger than the critical value in the table, then the data does not fit the model, which represents the rejection of the null hypothesis.

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## Exploring the Null Hypothesis: Definition and Purpose

Updated: July 5, 2023 by Ken Feldman

Hypothesis testing is a branch of statistics in which, using data from a sample, an inference is made about a population parameter or a population probability distribution .

First, a hypothesis statement and assumption is made about the population parameter or probability distribution. This initial statement is called the Null Hypothesis and is denoted by H o. An alternative or alternate hypothesis (denoted Ha ), is then stated which will be the opposite of the Null Hypothesis.

The hypothesis testing process and analysis involves using sample data to determine whether or not you can be statistically confident that you can reject or fail to reject the H o. If the H o is rejected, the statistical conclusion is that the alternative or alternate hypothesis Ha is true.

## Overview: What is the Null Hypothesis (Ho)?

Hypothesis testing applies to all forms of statistical inquiry. For example, it can be used to determine whether there are differences between population parameters or an understanding about slopes of regression lines or equality of probability distributions.

In all cases, the first thing you do is state the Null and Alternate Hypotheses. The word Null in the context of hypothesis testing means “nothing” or “zero.”

As an example, if we wanted to test whether there was a difference in two population means based on the calculations from two samples, we would state the Null Hypothesis in the form of:

Ho: mu1 = mu2 or mu1- mu2 = 0

In other words, there is no difference, or the difference is zero. Note that the notation is in the form of a population parameter, not a sample statistic.

Since you are using sample data to make your inferences about the population, it’s possible you’ll make an error. In the case of the Null Hypothesis, we can make one of two errors.

•   Type 1 , or alpha error: An alpha error is when you mistakenly reject the Null and believe that something significant happened. In other words, you believe that the means of the two populations are different when they aren’t.
• Type 2, or beta error: A beta error is when you fail to reject the null when you should have.  In this case, you missed something significant and failed to take action.

A classic example is when you get the results back from your doctor after taking a blood test. If the doctor says you have an infection when you really don’t, that is an alpha error. That is thinking that there is something significant going on when there isn’t. We also call that a false positive. The doctor rejected the null that “there was zero infection” and missed the call.

On the other hand, if the doctor told you that everything was OK when you really did have an infection, then he made a beta, or type 2, error. He failed to reject the Null Hypothesis when he should have. That is called a false negative.

The decision to reject or not to reject the Null Hypothesis is based on three numbers.

• Alpha, which you get to choose. Alpha is the risk you are willing to assume of falsely rejecting the Null. The typical values for alpha are 1%, 5%, or 10%. Depending on the importance of the conclusion, you only want to falsely claim a difference when there is none, 1%, 5%, or 10% of the time.
• Beta, which is typically 20%. This means you’re willing to be wrong 20% of the time in failing to reject the null when you should have.
• P-value, which is calculated from the data. The p-value is the actual risk you have in being wrong if you reject the null. You would like that to be low.

Your decision as to what to do about the null is made by comparing the alpha value (your assumed risk) with the p-value (actual risk). If the actual risk is lower than your assumed risk, you can feel comfortable in rejecting the null and claiming something has happened. But, if the actual risk is higher than your assumed risk you will be taking a bigger risk than you want by rejecting the null.

## RELATED: NULL VS. ALTERNATIVE HYPOTHESIS

3 benefits of the null hypothesis .

The stating and testing of the null hypothesis is the foundation of hypothesis testing. By doing so, you set the parameters for your statistical inference.

## 1. Statistical assurance of determining differences between population parameters

Just looking at the mathematical difference between the means of two samples and making a decision is woefully inadequate. By statistically testing the null hypothesis, you will have more confidence in any inferences you want to make about populations based on your samples.

## 2. Statistically based estimation of the probability of a population distribution

Many statistical tests require assumptions of specific distributions. Many of these tests assume that the population follows the normal distribution . If it doesn’t, the test may be invalid.

## 3. Assess the strength of your conclusions as to what to do with the null hypothesis

Hypothesis testing calculations will provide some relative strength to your decisions as to whether you reject or fail to reject the null hypothesis.

## Why is the Null Hypothesis important to understand?

The interpretation of the statistics relative to the null hypothesis is what’s important.

## 1. Properly write the null hypothesis to properly capture what you are seeking to prove

The null is always written in the same format. That is, the lack of difference or some other condition. The alternative hypothesis can be written in three formats depending on what you want to prove.

## 2. Frame your statement and select an appropriate alpha risk

You don’t want to place too big of a hurdle or burden on your decision-making relative to action on the null hypothesis by selecting an alpha value that is too high or too low.

## 3. There are decision errors when deciding on how to respond to the Null Hypothesis

Since your decision relative to rejecting or not rejecting the null is based on statistical calculations, it is important to understand how that decision works.

## An industry example of using the Null Hypothesis

The new director of marketing just completed the rollout of a new marketing campaign targeting the Hispanic market. Early indications showed that the campaign was successful in increasing sales in the Hispanic market.

He came to that conclusion by comparing a sample of sales prior to the campaign and current sales after implementation of the campaign. He was anxious to proudly tell his boss how successful the campaign was. But, he decided to first check with his Lean Six Sigma Black Belt to see whether she agreed with his conclusion.

The Black Belt first asked the director his tolerance for risk of being wrong by telling the boss the campaign was successful when in fact, it wasn’t. That was the alpha value. The Director picked 5% since he was new and didn’t want to make a false claim so early in his career. He also picked 20% as his beta value.

When the Black Belt was done analyzing the data, she found out that the p-value was 15%.  That meant if the director told the VP the campaign worked, there was a 15% chance he would be wrong and that the campaign probably needed some revising. Since he was only willing to be wrong 5% of the time, the decision was to not reject the null since his 5% assumed risk was less than the 15% actual risk.

## 3 best practices when thinking about the Null Hypothesis

Using hypothesis testing to help make better data-driven decisions requires that you properly address the Null Hypothesis.

## 1. Always use the proper nomenclature when stating the Null Hypothesis

The null will always be in the form of decisions regarding the population, not the sample.

## 2. The Null Hypothesis will always be written as the absence of some parameter or process characteristic

The writing of the Alternate Hypothesis can vary, so be sure you understand exactly what condition you are testing against.

## 3. Pick a reasonable alpha risk so you’re not always failing to reject the Null Hypothesis

Being too cautious will lead you to make beta errors, and you’ll never learn anything about your population data.

What form should the null hypothesis be written in.

The Null Hypothesis should always be in the form of no difference or zero and always refer to the state of the population, not the sample.

## What is an alpha error?

An alpha error, or Type 1 error, is rejecting the Null Hypothesis and claiming a significant event has occurred when, in fact, that is not true and the Null should not have been rejected.

## How do I use the alpha error and p-value to decide on what decision I should make about the Null Hypothesis?

The most common way of answering this is, “If the p-value is low (less than the alpha), the Null should be rejected. If the p-value is high (greater than the alpha) then the Null should not be rejected.”

## Becoming familiar with the Null Hypothesis (Ho)

The proper writing of the Null Hypothesis is the basis for applying hypothesis testing to help you make better data-driven decisions. The format of the Null will always be in the form of zero, or the non-existence of some condition. It will always refer to a population parameter and not the sample you use to do your hypothesis testing calculations.

Be aware of the two types of errors you can make when deciding on what to do with the Null. Select reasonable risks values for your alpha and beta risks. By comparing your alpha risk with the calculated risk computed from the data, you will have sufficient information to make a wise decision as to whether you should reject the Null Hypothesis or not.

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## What Is a Null Hypothesis?

The alternative hypothesis.

• Null Hypothesis and Investments

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A null hypothesis is a type of statistical hypothesis that proposes that no statistical significance exists in a set of given observations. Hypothesis testing is used to assess the credibility of a hypothesis by using sample data. Sometimes referred to simply as the “null,” it is represented as H 0 .

The null hypothesis, also known as “the conjecture,” is used in quantitative analysis to test theories about markets, investing strategies, and economies to decide if an idea is true or false.

## Key Takeaways

• A null hypothesis is a type of conjecture in statistics that proposes that there is no difference between certain characteristics of a population or data-generating process.
• The alternative hypothesis proposes that there is a difference.
• Hypothesis testing provides a method to reject a null hypothesis within a certain confidence level.
• If you can reject the null hypothesis, it provides support for the alternative hypothesis.
• Null hypothesis testing is the basis of the principle of falsification in science.

Alex Dos Diaz / Investopedia

## Understanding a Null Hypothesis

A gambler may be interested in whether a game of chance is fair. If it is, then the expected earnings per play come to zero for both players. If it is not, then the expected earnings are positive for one player and negative for the other.

To test whether the game is fair, the gambler collects earnings data from many repetitions of the game, calculates the average earnings from these data, then tests the null hypothesis that the expected earnings are not different from zero.

If the average earnings from the sample data are sufficiently far from zero, then the gambler will reject the null hypothesis and conclude the alternative hypothesis—namely, that the expected earnings per play are different from zero. If the average earnings from the sample data are near zero, then the gambler will not reject the null hypothesis, concluding instead that the difference between the average from the data and zero is explainable by chance alone.

A null hypothesis can only be rejected, not proven.

The null hypothesis assumes that any kind of difference between the chosen characteristics that you see in a set of data is due to chance. For example, if the expected earnings for the gambling game are truly equal to zero, then any difference between the average earnings in the data and zero is due to chance.

Analysts look to reject   the null hypothesis because doing so is a strong conclusion. This requires evidence in the form of an observed difference that is too large to be explained solely by chance. Failing to reject the null hypothesis—that the results are explainable by chance alone—is a weak conclusion because it allows that while factors other than chance may be at work, they may not be strong enough for the statistical test to detect them.

An important point to note is that we are testing the null hypothesis because there is an element of doubt about its validity. Whatever information that is against the stated null hypothesis is captured in the alternative (alternate) hypothesis (H1).

For the examples below, the alternative hypothesis would be:

• Students score an average that is not equal to seven.
• The mean annual return of a mutual fund is not equal to 8% per year.

In other words, the alternative hypothesis is a direct contradiction of the null hypothesis.

## Null Hypothesis Examples

Here is a simple example: A school principal claims that students in her school score an average of seven out of 10 in exams. The null hypothesis is that the population mean is 7.0. To test this null hypothesis, we record marks of, say, 30 students ( sample ) from the entire student population of the school (say, 300) and calculate the mean of that sample.

We can then compare the (calculated) sample mean to the (hypothesized) population mean of 7.0 and attempt to reject the null hypothesis. (The null hypothesis here—that the population mean is 7.0—cannot be proved using the sample data. It can only be rejected.)

Take another example: The annual return of a particular  mutual fund  is claimed to be 8%. Assume that the mutual fund has been in existence for 20 years. The null hypothesis is that the mean return is 8% for the mutual fund. We take a random sample of annual returns of the mutual fund for, say, five years (sample) and calculate the sample mean. We then compare the (calculated) sample mean to the (claimed) population mean (8%) to test the null hypothesis.

For the above examples, null hypotheses are:

• Example A: Students in the school score an average of seven out of 10 in exams.
• Example B: The mean annual return of the mutual fund is 8% per year.

For the purposes of determining whether to reject the null hypothesis (abbreviated H0), said hypothesis is assumed, for the sake of argument, to be true. Then the likely range of possible values of the calculated statistic (e.g., the average score on 30 students’ tests) is determined under this presumption (e.g., the range of plausible averages might range from 6.2 to 7.8 if the population mean is 7.0).

If the sample average is outside of this range, the null hypothesis is rejected. Otherwise, the difference is said to be “explainable by chance alone,” being within the range that is determined by chance alone.

## How Null Hypothesis Testing Is Used in Investments

As an example related to financial markets, assume Alice sees that her investment strategy produces higher average returns than simply buying and holding a stock . The null hypothesis states that there is no difference between the two average returns, and Alice is inclined to believe this until she can conclude contradictory results.

Refuting the null hypothesis would require showing statistical significance, which can be found by a variety of tests. The alternative hypothesis would state that the investment strategy has a higher average return than a traditional buy-and-hold strategy.

One tool that can determine the statistical significance of the results is the p-value. A p-value represents the probability that a difference as large or larger than the observed difference between the two average returns could occur solely by chance.

A p-value that is less than or equal to 0.05 often indicates whether there is evidence against the null hypothesis. If Alice conducts one of these tests, such as a test using the normal model, resulting in a significant difference between her returns and the buy-and-hold returns (the p-value is less than or equal to 0.05), she can then reject the null hypothesis and conclude the alternative hypothesis.

## How Is the Null Hypothesis Identified?

The analyst or researcher establishes a null hypothesis based on the research question or problem they are trying to answer. Depending on the question, the null may be identified differently. For example, if the question is simply whether an effect exists (e.g., does X influence Y?), the null hypothesis could be H 0 : X = 0. If the question is instead, is X the same as Y, the H 0 would be X = Y. If it is that the effect of X on Y is positive, H 0 would be X > 0. If the resulting analysis shows an effect that is statistically significantly different from zero, the null can be rejected.

## How Is Null Hypothesis Used in Finance?

In finance , a null hypothesis is used in quantitative analysis. It tests the premise of an investing strategy, the markets, or an economy to determine if it is true or false.

For instance, an analyst may want to see if two stocks, ABC and XYZ, are closely correlated. The null hypothesis would be ABC ≠ XYZ.

## How Are Statistical Hypotheses Tested?

Statistical hypotheses are tested by a four-step process . The first is for the analyst to state the two hypotheses so that only one can be right. The second is to formulate an analysis plan, which outlines how the data will be evaluated. The third is to carry out the plan and physically analyze the sample data. The fourth and final step is to analyze the results and either reject the null hypothesis or claim that the observed differences are explainable by chance alone.

## What Is an Alternative Hypothesis?

An alternative hypothesis is a direct contradiction of a null hypothesis. This means that if one of the two hypotheses is true, the other is false.

A null hypothesis states there is no difference between groups or relationship between variables. It is a type of statistical hypothesis and proposes that no statistical significance exists in a set of given observations. "Null" means nothing.

The null hypothesis is used in quantitative analysis to test theories about economies, investing strategies, and markets to decide if an idea is true or false. Hypothesis testing assesses the credibility of a hypothesis by using sample data. It is represented as H 0 and is sometimes simply known as “the null.”

Sage Publishing. “ Chapter 8: Introduction to Hypothesis Testing .” Page 4.

Sage Publishing. “ Chapter 8: Introduction to Hypothesis Testing .” Pages 4 to 7.

Sage Publishing. “ Chapter 8: Introduction to Hypothesis Testing ,” Page 7.

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## Null Hypothesis

Null hypothesis is used to make decisions based on data and by using statistical tests. Null hypothesis is represented using H o and it states that there is no difference between the characteristics of two samples. Null hypothesis is generally a statement of no difference. The rejection of null hypothesis is equivalent to the acceptance of the alternate hypothesis.

Let us learn more about null hypotheses, tests for null hypotheses, the difference between null hypothesis and alternate hypothesis, with the help of examples, FAQs.

 1 2 3 4

## What Is Null Hypothesis?

Null hypothesis states that there is no significant difference between the observed characteristics across two sample sets. Null hypothesis states the observed population parameters or variables is the same across the samples. The null hypothesis states that there is no relationship between the sample parameters, the independent variable, and the dependent variable. The term null hypothesis is used in instances to mean that there is no differences in the two means, or that the difference is not so significant.

If the experimental outcome is the same as the theoretical outcome then the null hypothesis holds good. But if there are any differences in the observed parameters across the samples then the null hypothesis is rejected, and we consider an alternate hypothesis. The rejection of the null hypothesis does not mean that there were flaws in the basic experimentation, but it sets the stage for further research. Generally, the strength of the evidence is tested against the null hypothesis.

Null hypothesis and alternate hypothesis are the two approaches used across statistics. The alternate hypothesis states that there is a significant difference between the parameters across the samples. The alternate hypothesis is the inverse of null hypothesis. An important reason to reject the null hypothesis and consider the alternate hypothesis is due to experimental or sampling errors.

## Tests For Null Hypothesis

The two important approaches of statistical interference of null hypothesis are significance testing and hypothesis testing. The null hypothesis is a theoretical hypothesis and is based on insufficient evidence, which requires further testing to prove if it is true or false.

## Significance Testing

The aim of significance testing is to provide evidence to reject the null hypothesis. If the difference is strong enough then reject the null hypothesis and accept the alternate hypothesis. The testing is designed to test the strength of the evidence against the hypothesis. The four important steps of significance testing are as follows.

• First state the null and alternate hypotheses.
• Calculate the test statistics.
• Find the p-value.
• Test the p-value with the α and decide if the null hypothesis should be rejected or accepted.

If the p-value is lesser than the significance level α, then the null hypothesis is rejected. And if the p-value is greater than the significance level α, then the null hypothesis is accepted.

• Hypothesis Testing

Hypothesis testing takes the parameters from the sample and makes a derivation about the population. A hypothesis is an educated guess about a sample, which can be tested either through an experiment or an observation. Initially, a tentative assumption is made about the sample in the form of a null hypothesis.

There are four steps to perform hypothesis testing. They are:

• Identify the null hypothesis.
• Define the null hypothesis statement.
• Choose the test to be performed.
• Accept the null hypothesis or the alternate hypothesis.

There are often errors in the process of testing the hypothesis. The two important errors observed in hypothesis testing is as follows.

• Type - I error is rejecting the null hypothesis when the null hypothesis is actually true.
• Type - II error is accepting the null hypothesis when the null hypothesis is actually false.

## Difference Between Null Hypothesis And Alternate Hypothesis

The difference between null hypothesis and alternate hypothesis can be understood through the following points.

• The opposite of the null hypothesis is the alternate hypothesis and it is the claim which is being proved by research to be true.
• The null hypothesis states that the two samples of the population are the same, and the alternate hypothesis states that there is a significant difference between the two samples of the population.
• The null hypothesis is designated as H o and the alternate hypothesis is designated as H a .
• For the null hypothesis, the same means are assumed to be equal, and we have H 0 : µ 1 = µ 2. And for the alternate hypothesis, the sample means are unequal, and we have H a : µ 1 ≠ µ 2.
• The observed population parameters and variables are the same across the samples, for a null hypothesis, but in an alternate hypothesis, there is a significant difference between the observed parameters and variables across the samples.

☛ Related Topics

The following topics help in a better understanding of the null hypothesis.

• Probability and Statistics
• Basic Statistics Formula
• Sample Space

## Examples on Null Hypothesis

Example 1: A medical experiment and trial is conducted to check if a particular drug can serve as the vaccine for Covid-19, and can prevent from occurrence of Corona. Write the null hypothesis and the alternate hypothesis for this situation.

The given situation refers to a possible new drug and its effectiveness of being a vaccine for Covid-19 or not. The null hypothesis (H o ) and alternate hypothesis (H a ) for this medical experiment is as follows.

• H 0 : The use of the new drug is not helpful for the prevention of Covid-19.
• H a : The use of the new drug serves as a vaccine and helps for the prevention of Covid-19.

Example 2: The teacher has prepared a set of important questions and informs the student that preparing these questions helps in scoring more than 60% marks in the board exams. Write the null hypothesis and the alternate hypothesis for this situation.

The given situation refers to the teacher who has claimed that her important questions helps to score more than 60% marks in the board exams. The null hypothesis(H o ) and alternate hypothesis(H a ) for this situation is as follows.

• H o : The important questions given by the teacher does not really help the students to get a score of more than 60% in the board exams.
• H a : The important questions given by the teacher is helpful for the students to score more than 60% marks in the board exams.

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## Practice Questions on Null Hypothesis

Faqs on null hypothesis, what is null hypothesis in maths.

Null hypothesis is used in statistics and it states if there is any significant difference between the two samples. The acceptance of null hypothesis mean that there is no significant difference between the two samples. And the rejection of null hypothesis means that the two samples are different, and we need to accept the alternate hypothesis. The null hypothesis statement is represented as H 0 and the alternate hypothesis is represented as H a .

## How Do You Test Null Hypothesis?

The null hypothesis is broadly tested using two methods. The null hypothesis can be tested using significance testing and hypothesis testing.Broadly the test for null hypothesis is performed across four stages. First the null hypothesis is identified, secondly the null hypothesis is defined. Next a suitable test is used to test the hypothesis, and finally either the null hypothesis or the alternate hypothesis is accepted.

## How To Accept or Reject Null Hypothesis?

The null hypothesis is accepted or rejected based on the result of the hypothesis testing. The p value is found and the significance level is defined. If the p-value is lesser than the significance level α, then the null hypothesis is rejected. And if the p-value is greater than the significance level α, then the null hypothesis is accepted.

## What Is the Difference Between Null Hypothesis And Alternate Hypothesis?

The null hypothesis states that there is no significant difference between the two samples, and the alternate hypothesis states that there is a significant difference between the two samples. The null hypothesis is referred using H o and the alternate hypothesis is referred using H a . As per null hypothesis the observed variables and parameters are the same across the samples, but as per alternate hypothesis there is a significant difference between the observed variables and parameters across the samples.

## What Is Null Hypothesis Example?

A few quick examples of null hypothesis are as follows.

• The salary of a person is independent of his profession, is an example of null hypothesis. And the salary is dependent on the profession of a person, is an alternate hypothesis.
• The performance of the students in Maths from two different classes is a null hypothesis. And the performance of the students from each of the classes is different, is an example of alternate hypothesis.
• The nutrient content of mango and a mango milk shake is equal and it can be taken as a null hypothesis. The test to prove the different nutrient content of the two is referred to as alternate hypothesis.

## What is Null Hypothesis? What Is Its Importance in Research?

Scientists begin their research with a hypothesis that a relationship of some kind exists between variables. The null hypothesis is the opposite stating that no such relationship exists. Null hypothesis may seem unexciting, but it is a very important aspect of research. In this article, we discuss what null hypothesis is, how to make use of it, and why you should use it to improve your statistical analyses.

## What is the Null Hypothesis?

The null hypothesis can be tested using statistical analysis  and is often written as H 0 (read as “H-naught”). Once you determine how likely the sample relationship would be if the H 0   were true, you can run your analysis. Researchers use a significance test to determine the likelihood that the results supporting the H 0 are not due to chance.

The null hypothesis is not the same as an alternative hypothesis. An alternative hypothesis states, that there is a relationship between two variables, while H 0 posits the opposite. Let us consider the following example.

A researcher wants to discover the relationship between exercise frequency and appetite. She asks:

Q: Does increased exercise frequency lead to increased appetite? Alternative hypothesis: Increased exercise frequency leads to increased appetite. H 0 assumes that there is no relationship between the two variables: Increased exercise frequency does not lead to increased appetite.

Let us look at another example of how to state the null hypothesis:

Q: Does insufficient sleep lead to an increased risk of heart attack among men over age 50? H 0 : The amount of sleep men over age 50 get does not increase their risk of heart attack.

## Why is Null Hypothesis Important?

Many scientists often neglect null hypothesis in their testing. As shown in the above examples, H 0 is often assumed to be the opposite of the hypothesis being tested. However, it is good practice to include H 0 and ensure it is carefully worded. To understand why, let us return to our previous example. In this case,

Alternative hypothesis: Getting too little sleep leads to an increased risk of heart attack among men over age 50.

H 0 : The amount of sleep men over age 50 get has no effect on their risk of heart attack.

Note that this H 0 is different than the one in our first example. What if we were to conduct this experiment and find that neither H 0 nor the alternative hypothesis was supported? The experiment would be considered invalid . Take our original H 0 in this case, “the amount of sleep men over age 50 get, does not increase their risk of heart attack”. If this H 0 is found to be untrue, and so is the alternative, we can still consider a third hypothesis. Perhaps getting insufficient sleep actually decreases the risk of a heart attack among men over age 50. Because we have tested H 0 , we have more information that we would not have if we had neglected it.

## Do I Really Need to Test It?

The biggest problem with the null hypothesis is that many scientists see accepting it as a failure of the experiment. They consider that they have not proven anything of value. However, as we have learned from the replication crisis , negative results are just as important as positive ones. While they may seem less appealing to publishers, they can tell the scientific community important information about correlations that do or do not exist. In this way, they can drive science forward and prevent the wastage of resources.

Do you test for the null hypothesis? Why or why not? Let us know your thoughts in the comments below.

The following null hypotheses were formulated for this study: Ho1. There are no significant differences in the factors that influence urban gardening when respondents are grouped according to age, sex, household size, social status and average combined monthly income.

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Null hypothesis

Null hypothesis n., plural: null hypotheses [nʌl haɪˈpɒθɪsɪs] Definition: a hypothesis that is valid or presumed true until invalidated by a statistical test

## Null Hypothesis Definition

Null hypothesis is defined as “the commonly accepted fact (such as the sky is blue) and researcher aim to reject or nullify this fact”.

More formally, we can define a null hypothesis as “a statistical theory suggesting that no statistical relationship exists between given observed variables” .

In biology , the null hypothesis is used to nullify or reject a common belief. The researcher carries out the research which is aimed at rejecting the commonly accepted belief.

## What Is a Null Hypothesis?

A hypothesis is defined as a theory or an assumption that is based on inadequate evidence. It needs and requires more experiments and testing for confirmation. There are two possibilities that by doing more experiments and testing, a hypothesis can be false or true. It means it can either prove wrong or true (Blackwelder, 1982).

For example, Susie assumes that mineral water helps in the better growth and nourishment of plants over distilled water. To prove this hypothesis, she performs this experiment for almost a month. She watered some plants with mineral water and some with distilled water.

In a hypothesis when there are no statistically significant relationships among the two variables, the hypothesis is said to be a null hypothesis. The investigator is trying to disprove such a hypothesis. In the above example of plants, the null hypothesis is:

There are no statistical relationships among the forms of water that are given to plants for growth and nourishment.

Usually, an investigator tries to prove the null hypothesis wrong and tries to explain a relation and association between the two variables.

An opposite and reverse of the null hypothesis are known as the alternate hypothesis . In the example of plants the alternate hypothesis is:

There are statistical relationships among the forms of water that are given to plants for growth and nourishment.

The example below shows the difference between null vs alternative hypotheses:

Alternate Hypothesis: The world is round Null Hypothesis: The world is not round.

Copernicus and many other scientists try to prove the null hypothesis wrong and false. By their experiments and testing, they make people believe that alternate hypotheses are correct and true. If they do not prove the null hypothesis experimentally wrong then people will not believe them and never consider the alternative hypothesis true and correct.

The alternative and null hypothesis for Susie’s assumption is:

• Null Hypothesis: If one plant is watered with distilled water and the other with mineral water, then there is no difference in the growth and nourishment of these two plants.
• Alternative Hypothesis:  If one plant is watered with distilled water and the other with mineral water, then the plant with mineral water shows better growth and nourishment.

The null hypothesis suggests that there is no significant or statistical relationship. The relation can either be in a single set of variables or among two sets of variables.

Most people consider the null hypothesis true and correct. Scientists work and perform different experiments and do a variety of research so that they can prove the null hypothesis wrong or nullify it. For this purpose, they design an alternate hypothesis that they think is correct or true. The null hypothesis symbol is H 0 (it is read as H null or H zero ).

Why is it named the “Null”?

The name null is given to this hypothesis to clarify and explain that the scientists are working to prove it false i.e. to nullify the hypothesis. Sometimes it confuses the readers; they might misunderstand it and think that statement has nothing. It is blank but, actually, it is not. It is more appropriate and suitable to call it a nullifiable hypothesis instead of the null hypothesis.

Why do we need to assess it? Why not just verify an alternate one?

In science, the scientific method is used. It involves a series of different steps. Scientists perform these steps so that a hypothesis can be proved false or true. Scientists do this to confirm that there will be any limitation or inadequacy in the new hypothesis. Experiments are done by considering both alternative and null hypotheses, which makes the research safe. It gives a negative as well as a bad impact on research if a null hypothesis is not included or a part of the study. It seems like you are not taking your research seriously and not concerned about it and just want to impose your results as correct and true if the null hypothesis is not a part of the study.

## Development of the Null

In statistics, firstly it is necessary to design alternate and null hypotheses from the given problem. Splitting the problem into small steps makes the pathway towards the solution easier and less challenging. how to write a null hypothesis?

Writing a null hypothesis consists of two steps:

• Firstly, initiate by asking a question.
• Secondly, restate the question in such a way that it seems there are no relationships among the variables.

In other words, assume in such a way that the treatment does not have any effect.

Questions Null Hypothesis
Are adults doing better at mathematics than teenagers? Mathematical ability does not depend on age.
Does the risk of a heart attack reduce by daily intake of aspirin? A heart attack is not affected by the daily dose of aspirin.
Are teenagers using cell phones to access the internet more than elders? Age does not affect the usage of cell phones for internet access.
Are cats concerned about their food color? Cats do not prefer food based on color.
Does pain relieve by chewing willow bark? Pain is not relieved by chewing willow bark.

The usual recovery duration after knee surgery is considered almost 8 weeks.

A researcher thinks that the recovery period may get elongated if patients go to a physiotherapist for rehabilitation twice per week, instead of thrice per week, i.e. recovery duration reduces if the patient goes three times for rehabilitation instead of two times.

Step 1: Look for the problem in the hypothesis. The hypothesis either be a word or can be a statement. In the above example the hypothesis is:

“The expected recovery period in knee rehabilitation is more than 8 weeks”

Step 2: Make a mathematical statement from the hypothesis. Averages can also be represented as μ, thus the null hypothesis formula will be.

In the above equation, the hypothesis is equivalent to H1, the average is denoted by μ and > that the average is greater than eight.

Step 3: Explain what will come up if the hypothesis does not come right i.e., the rehabilitation period may not proceed more than 08 weeks.

There are two options: either the recovery will be less than or equal to 8 weeks.

H 0 : μ ≤ 8

In the above equation, the null hypothesis is equivalent to H 0 , the average is denoted by μ and ≤ represents that the average is less than or equal to eight.

What will happen if the scientist does not have any knowledge about the outcome?

Problem: An investigator investigates the post-operative impact and influence of radical exercise on patients who have operative procedures of the knee. The chances are either the exercise will improve the recovery or will make it worse. The usual time for recovery is 8 weeks.

Step 1: Make a null hypothesis i.e. the exercise does not show any effect and the recovery time remains almost 8 weeks.

H 0 : μ = 8

In the above equation, the null hypothesis is equivalent to H 0 , the average is denoted by μ, and the equal sign (=) shows that the average is equal to eight.

Step 2: Make the alternate hypothesis which is the reverse of the null hypothesis. Particularly what will happen if treatment (exercise) makes an impact?

In the above equation, the alternate hypothesis is equivalent to H1, the average is denoted by μ and not equal sign (≠) represents that the average is not equal to eight.

## Significance Tests

To get a reasonable and probable clarification of statistics (data), a significance test is performed. The null hypothesis does not have data. It is a piece of information or statement which contains numerical figures about the population. The data can be in different forms like in means or proportions. It can either be the difference of proportions and means or any odd ratio.

The following table will explain the symbols:

 P-value Probability of success Size of sample Null Hypothesis Alternate Hypothesis

P-value is the chief statistical final result of the significance test of the null hypothesis.

• P-value = Pr(data or data more extreme | H 0 true)
• | = “given”
• Pr = probability
• H 0 = the null hypothesis

The first stage of Null Hypothesis Significance Testing (NHST) is to form an alternate and null hypothesis. By this, the research question can be briefly explained.

Null Hypothesis = no effect of treatment, no difference, no association Alternative Hypothesis = effective treatment, difference, association

When to reject the null hypothesis?

Researchers will reject the null hypothesis if it is proven wrong after experimentation. Researchers accept null hypothesis to be true and correct until it is proven wrong or false. On the other hand, the researchers try to strengthen the alternate hypothesis. The binomial test is performed on a sample and after that, a series of tests were performed (Frick, 1995).

Step 1: Evaluate and read the research question carefully and consciously and make a null hypothesis. Verify the sample that supports the binomial proportion. If there is no difference then find out the value of the binomial parameter.

Show the null hypothesis as:

H 0 :p= the value of p if H 0 is true

To find out how much it varies from the proposed data and the value of the null hypothesis, calculate the sample proportion.

Step 2: In test statistics, find the binomial test that comes under the null hypothesis. The test must be based on precise and thorough probabilities. Also make a list of pmf that apply, when the null hypothesis proves true and correct.

When H 0 is true, X~b(n, p)

N = size of the sample

P = assume value if H 0 proves true.

Step 3: Find out the value of P. P-value is the probability of data that is under observation.

Rise or increase in the P value = Pr(X ≥ x)

X = observed number of successes

P value = Pr(X ≤ x).

Step 4: Demonstrate the findings or outcomes in a descriptive detailed way.

• Sample proportion
• The direction of difference (either increases or decreases)

## Perceived Problems With the Null Hypothesis

Variable or model selection and less information in some cases are the chief important issues that affect the testing of the null hypothesis. Statistical tests of the null hypothesis are reasonably not strong. There is randomization about significance. (Gill, 1999) The main issue with the testing of the null hypothesis is that they all are wrong or false on a ground basis.

There is another problem with the a-level . This is an ignored but also a well-known problem. The value of a-level is without a theoretical basis and thus there is randomization in conventional values, most commonly 0.q, 0.5, or 0.01. If a fixed value of a is used, it will result in the formation of two categories (significant and non-significant) The issue of a randomized rejection or non-rejection is also present when there is a practical matter which is the strong point of the evidence related to a scientific matter.

The P-value has the foremost importance in the testing of null hypothesis but as an inferential tool and for interpretation, it has a problem. The P-value is the probability of getting a test statistic at least as extreme as the observed one.

The main point about the definition is: Observed results are not based on a-value

Moreover, the evidence against the null hypothesis was overstated due to unobserved results. A-value has importance more than just being a statement. It is a precise statement about the evidence from the observed results or data. Similarly, researchers found that P-values are objectionable. They do not prefer null hypotheses in testing. It is also clear that the P-value is strictly dependent on the null hypothesis. It is computer-based statistics. In some precise experiments, the null hypothesis statistics and actual sampling distribution are closely related but this does not become possible in observational studies.

Some researchers pointed out that the P-value is depending on the sample size. If the true and exact difference is small, a null hypothesis even of a large sample may get rejected. This shows the difference between biological importance and statistical significance. (Killeen, 2005)

Another issue is the fix a-level, i.e., 0.1. On the basis, if a-level a null hypothesis of a large sample may get accepted or rejected. If the size of simple is infinity and the null hypothesis is proved true there are still chances of Type I error. That is the reason this approach or method is not considered consistent and reliable. There is also another problem that the exact information about the precision and size of the estimated effect cannot be known. The only solution is to state the size of the effect and its precision.

## Null Hypothesis Examples

Here are some examples:

## Example 1: Hypotheses with One Sample of One Categorical Variable

Among all the population of humans, almost 10% of people prefer to do their task with their left hand i.e. left-handed. Let suppose, a researcher in the Penn States says that the population of students at the College of Arts and Architecture is mostly left-handed as compared to the general population of humans in general public society. In this case, there is only a sample and there is a comparison among the known population values to the population proportion of sample value.

• Research Question: Do artists more expected to be left-handed as compared to the common population persons in society?
• Response Variable: Sorting the student into two categories. One category has left-handed persons and the other category have right-handed persons.
• Form Null Hypothesis: Arts and Architecture college students are no more predicted to be lefty as compared to the common population persons in society (Lefty students of Arts and Architecture college population is 10% or p= 0.10)

## Example 2: Hypotheses with One Sample of One Measurement Variable

A generic brand of antihistamine Diphenhydramine making medicine in the form of a capsule, having a 50mg dose. The maker of the medicines is concerned that the machine has come out of calibration and is not making more capsules with the suitable and appropriate dose.

• Research Question: Does the statistical data recommended about the mean and average dosage of the population differ from 50mg?
• Response Variable: Chemical assay used to find the appropriate dosage of the active ingredient.
• Null Hypothesis: Usually, the 50mg dosage of capsules of this trade name (population average and means dosage =50 mg).

## Example 3: Hypotheses with Two Samples of One Categorical Variable

Several people choose vegetarian meals on a daily basis. Typically, the researcher thought that females like vegetarian meals more than males.

• Research Question: Does the data recommend that females (women) prefer vegetarian meals more than males (men) regularly?
• Response Variable: Cataloguing the persons into vegetarian and non-vegetarian categories. Grouping Variable: Gender
• Null Hypothesis: Gender is not linked to those who like vegetarian meals. (Population percent of women who eat vegetarian meals regularly = population percent of men who eat vegetarian meals regularly or p women = p men).

## Example 4: Hypotheses with Two Samples of One Measurement Variable

Nowadays obesity and being overweight is one of the major and dangerous health issues. Research is performed to confirm that a low carbohydrates diet leads to faster weight loss than a low-fat diet.

• Research Question: Does the given data recommend that usually, a low-carbohydrate diet helps in losing weight faster as compared to a low-fat diet?
• Response Variable: Weight loss (pounds)
• Explanatory Variable: Form of diet either low carbohydrate or low fat
• Null Hypothesis: There is no significant difference when comparing the mean loss of weight of people using a low carbohydrate diet to people using a diet having low fat. (population means loss of weight on a low carbohydrate diet = population means loss of weight on a diet containing low fat).

## Example 5: Hypotheses about the relationship between Two Categorical Variables

A case-control study was performed. The study contains nonsmokers, stroke patients, and controls. The subjects are of the same occupation and age and the question was asked if someone at their home or close surrounding smokes?

• Research Question: Did second-hand smoke enhance the chances of stroke?
• Variables: There are 02 diverse categories of variables. (Controls and stroke patients) (whether the smoker lives in the same house). The chances of having a stroke will be increased if a person is living with a smoker.
• Null Hypothesis: There is no significant relationship between a passive smoker and stroke or brain attack. (odds ratio between stroke and the passive smoker is equal to 1).

## Example 6: Hypotheses about the relationship between Two Measurement Variables

A financial expert observes that there is somehow a positive and effective relationship between the variation in stock rate price and the quantity of stock bought by non-management employees

• Response variable- Regular alteration in price
• Explanatory Variable- Stock bought by non-management employees
• Null Hypothesis: The association and relationship between the regular stock price alteration ($) and the daily stock-buying by non-management employees ($) = 0.

## Example 7: Hypotheses about comparing the relationship between Two Measurement Variables in Two Samples

• Research Question: Is the relation between the bill paid in a restaurant and the tip given to the waiter, is linear? Is this relation different for dining and family restaurants?
• Explanatory Variable- total bill amount
• Response Variable- the amount of tip
• Null Hypothesis: The relationship and association between the total bill quantity at a family or dining restaurant and the tip, is the same.

Try to answer the quiz below to check what you have learned so far about the null hypothesis.

• Blackwelder, W. C. (1982). “Proving the null hypothesis” in clinical trials. Controlled Clinical Trials , 3(4), 345–353.
• Frick, R. W. (1995). Accepting the null hypothesis. Memory & Cognition, 23(1), 132–138.
• Gill, J. (1999). The insignificance of null hypothesis significance testing. Political Research Quarterly , 52(3), 647–674.
• Killeen, P. R. (2005). An alternative to null-hypothesis significance tests. Psychological Science, 16(5), 345–353.

©BiologyOnline.com. Content provided and moderated by Biology Online Editors.

Last updated on June 16th, 2022

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## Null Hypothesis

A hypothesis that states that there is no relationship between two population parameters

## What is the Null Hypothesis?

The null hypothesis states that there is no relationship between two population parameters, i.e., an independent variable and a dependent variable . If the hypothesis shows a relationship between the two parameters, the outcome could be due to an experimental or sampling error. However, if the null hypothesis returns false, there is a relationship in the measured phenomenon.

The null hypothesis is useful because it can be tested to conclude whether or not there is a relationship between two measured phenomena. It can inform the user whether the results obtained are due to chance or manipulating a phenomenon. Testing a hypothesis sets the stage for rejecting or accepting a hypothesis within a certain confidence level.

Two main approaches to statistical inference in a null hypothesis can be used– significance testing by Ronald Fisher and hypothesis testing by Jerzy Neyman and Egon Pearson. Fisher’s significance testing approach states that a null hypothesis is rejected if the measured data is significantly unlikely to have occurred (the null hypothesis is false). Therefore, the null hypothesis is rejected and replaced with an alternative hypothesis.

If the observed outcome is consistent with the position held by the null hypothesis, the hypothesis is accepted. On the other hand, the hypothesis testing by Neyman and Pearson is compared to an alternative hypothesis to make a conclusion about the observed data. The two hypotheses are differentiated based on observed data.

• A null hypothesis refers to a hypothesis that states that there is no relationship between two population parameters.
• Researchers reject or disprove the null hypothesis to set the stage for further experimentation or research that explains the position of interest.
• The inverse of a null hypothesis is an alternative hypothesis, which states that there is statistical significance between two variables.

## How the Null Hypothesis Works

A null hypothesis is a theory based on insufficient evidence that requires further testing to prove whether the observed data is true or false. For example, a null hypothesis statement can be “the rate of plant growth is not affected by sunlight.” It can be tested by measuring the growth of plants in the presence of sunlight and comparing this with the growth of plants in the absence of sunlight.

Rejecting the null hypothesis sets the stage for further experimentation to see a relationship between the two variables exists. Rejecting a null hypothesis does not necessarily mean that the experiment did not produce the required results, but it sets the stage for further experimentation.

To differentiate the null hypothesis from other forms of hypothesis, a null hypothesis is written as H 0 , while the alternate hypothesis is written as H A or H 1 . A significance test is used to establish confidence in a null hypothesis and determine whether the observed data is not due to chance or manipulation of data.

Researchers test the hypothesis by examining a random sample of the plants being grown with or without sunlight. If the outcome demonstrates a statistically significant change in the observed change, the null hypothesis is rejected.

## Null Hypothesis Example

The annual return of ABC Limited bonds is assumed to be 7.5%. To test if the scenario is true or false, we take the null hypothesis to be “the mean annual return for ABC limited bond is not 7.5%.” To test the hypothesis, we first accept the null hypothesis.

Any information that is against the stated null hypothesis is taken to be the alternative hypothesis for the purpose of testing the hypotheses. In such a case, the alternative hypothesis is “the mean annual return of ABC Limited is 7.5%.”

We take samples of the annual returns of the bond for the last five years to calculate the sample mean for the previous five years. The result is then compared to the assumed annual return average of 7.5% to test the null hypothesis.

The average annual returns for the five-year period are 7.5%; the null hypothesis is rejected. Consequently, the alternative hypothesis is accepted.

## What is an Alternative Hypothesis?

An alternative hypothesis is the inverse of a null hypothesis. An alternative hypothesis and a null hypothesis are mutually exclusive, which means that only one of the two hypotheses can be true.

A statistical significance exists between the two variables. If samples used to test the null hypothesis return false, it means that the alternate hypothesis is true, and there is statistical significance between the two variables.

## Purpose of Hypothesis Testing

Hypothesis testing is a statistical process of testing an assumption regarding a phenomenon or population parameter. It is a critical part of the scientific method, which is a systematic approach to assessing theories through observations and determining the probability that a stated statement is true or false.

A good theory can make accurate predictions. For an analyst who makes predictions, hypothesis testing is a rigorous way of backing up his prediction with statistical analysis. It also helps determine sufficient statistical evidence that favors a certain hypothesis about the population parameter.

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## Null Hypothesis

Null Hypothesis , often denoted as H 0, is a foundational concept in statistical hypothesis testing. It represents an assumption that no significant difference, effect, or relationship exists between variables within a population. It serves as a baseline assumption, positing no observed change or effect occurring. The null is t he truth or falsity of an idea in analysis.

In this article, we will discuss the null hypothesis in detail, along with some solved examples and questions on the null hypothesis.

Table of Content

## What is Null Hypothesis?

Null hypothesis symbol, formula of null hypothesis, types of null hypothesis, null hypothesis examples, principle of null hypothesis, how do you find null hypothesis, null hypothesis in statistics, null hypothesis and alternative hypothesis, null hypothesis and alternative hypothesis examples, null hypothesis – practice problems.

Null Hypothesis in statistical analysis suggests the absence of statistical significance within a specific set of observed data. Hypothesis testing, using sample data, evaluates the validity of this hypothesis. Commonly denoted as H 0 or simply “null,” it plays an important role in quantitative analysis, examining theories related to markets, investment strategies, or economies to determine their validity.

## Null Hypothesis Meaning

Null Hypothesis represents a default position, often suggesting no effect or difference, against which researchers compare their experimental results. The Null Hypothesis, often denoted as H 0 asserts a default assumption in statistical analysis. It posits no significant difference or effect, serving as a baseline for comparison in hypothesis testing.

The null Hypothesis is represented as H 0 , the Null Hypothesis symbolizes the absence of a measurable effect or difference in the variables under examination.

Certainly, a simple example would be asserting that the mean score of a group is equal to a specified value like stating that the average IQ of a population is 100.

The Null Hypothesis is typically formulated as a statement of equality or absence of a specific parameter in the population being studied. It provides a clear and testable prediction for comparison with the alternative hypothesis. The formulation of the Null Hypothesis typically follows a concise structure, stating the equality or absence of a specific parameter in the population.

## Mean Comparison (Two-sample t-test)

H 0 : μ 1 = μ 2

This asserts that there is no significant difference between the means of two populations or groups.

## Proportion Comparison

H 0 : p 1 − p 2 = 0

This suggests no significant difference in proportions between two populations or conditions.

## Equality in Variance (F-test in ANOVA)

H 0 : σ 1 = σ 2

This states that there’s no significant difference in variances between groups or populations.

## Independence (Chi-square Test of Independence):

H 0 : Variables are independent

This asserts that there’s no association or relationship between categorical variables.

Null Hypotheses vary including simple and composite forms, each tailored to the complexity of the research question. Understanding these types is pivotal for effective hypothesis testing.

## Equality Null Hypothesis (Simple Null Hypothesis)

The Equality Null Hypothesis, also known as the Simple Null Hypothesis, is a fundamental concept in statistical hypothesis testing that assumes no difference, effect or relationship between groups, conditions or populations being compared.

## Non-Inferiority Null Hypothesis

In some studies, the focus might be on demonstrating that a new treatment or method is not significantly worse than the standard or existing one.

## Superiority Null Hypothesis

The concept of a superiority null hypothesis comes into play when a study aims to demonstrate that a new treatment, method, or intervention is significantly better than an existing or standard one.

## Independence Null Hypothesis

In certain statistical tests, such as chi-square tests for independence, the null hypothesis assumes no association or independence between categorical variables.

## Homogeneity Null Hypothesis

In tests like ANOVA (Analysis of Variance), the null hypothesis suggests that there’s no difference in population means across different groups.

• Medicine: Null Hypothesis: “No significant difference exists in blood pressure levels between patients given the experimental drug versus those given a placebo.”
• Education: Null Hypothesis: “There’s no significant variation in test scores between students using a new teaching method and those using traditional teaching.”
• Economics: Null Hypothesis: “There’s no significant change in consumer spending pre- and post-implementation of a new taxation policy.”
• Environmental Science: Null Hypothesis: “There’s no substantial difference in pollution levels before and after a water treatment plant’s establishment.”

The principle of the null hypothesis is a fundamental concept in statistical hypothesis testing. It involves making an assumption about the population parameter or the absence of an effect or relationship between variables.

In essence, the null hypothesis (H 0 ) proposes that there is no significant difference, effect, or relationship between variables. It serves as a starting point or a default assumption that there is no real change, no effect or no difference between groups or conditions.

The null hypothesis is usually formulated to be tested against an alternative hypothesis (H 1 or H [Tex]\alpha [/Tex] ) which suggests that there is an effect, difference or relationship present in the population.

## Null Hypothesis Rejection

Rejecting the Null Hypothesis occurs when statistical evidence suggests a significant departure from the assumed baseline. It implies that there is enough evidence to support the alternative hypothesis, indicating a meaningful effect or difference. Null Hypothesis rejection occurs when statistical evidence suggests a deviation from the assumed baseline, prompting a reconsideration of the initial hypothesis.

Identifying the Null Hypothesis involves defining the status quotient, asserting no effect and formulating a statement suitable for statistical analysis.

## When is Null Hypothesis Rejected?

The Null Hypothesis is rejected when statistical tests indicate a significant departure from the expected outcome, leading to the consideration of alternative hypotheses. It occurs when statistical evidence suggests a deviation from the assumed baseline, prompting a reconsideration of the initial hypothesis.

In statistical hypothesis testing, researchers begin by stating the null hypothesis, often based on theoretical considerations or previous research. The null hypothesis is then tested against an alternative hypothesis (Ha), which represents the researcher’s claim or the hypothesis they seek to support.

The process of hypothesis testing involves collecting sample data and using statistical methods to assess the likelihood of observing the data if the null hypothesis were true. This assessment is typically done by calculating a test statistic, which measures the difference between the observed data and what would be expected under the null hypothesis.

In the realm of hypothesis testing, the null hypothesis (H 0 ) and alternative hypothesis (H₁ or Ha) play critical roles. The null hypothesis generally assumes no difference, effect, or relationship between variables, suggesting that any observed change or effect is due to random chance. Its counterpart, the alternative hypothesis, asserts the presence of a significant difference, effect, or relationship between variables, challenging the null hypothesis. These hypotheses are formulated based on the research question and guide statistical analyses.

## Difference Between Null Hypothesis and Alternative Hypothesis

The null hypothesis (H 0 ) serves as the baseline assumption in statistical testing, suggesting no significant effect, relationship, or difference within the data. It often proposes that any observed change or correlation is merely due to chance or random variation. Conversely, the alternative hypothesis (H 1 or Ha) contradicts the null hypothesis, positing the existence of a genuine effect, relationship or difference in the data. It represents the researcher’s intended focus, seeking to provide evidence against the null hypothesis and support for a specific outcome or theory. These hypotheses form the crux of hypothesis testing, guiding the assessment of data to draw conclusions about the population being studied.

Criteria

Null Hypothesis

Alternative Hypothesis

Definition

Assumes no effect or difference

Asserts a specific effect or difference

Symbol

H

H (or Ha)

Formulation

States equality or absence of parameter

States a specific value or relationship

Testing Outcome

Rejected if evidence of a significant effect

Accepted if evidence supports the hypothesis

Let’s envision a scenario where a researcher aims to examine the impact of a new medication on reducing blood pressure among patients. In this context:

Null Hypothesis (H 0 ): “The new medication does not produce a significant effect in reducing blood pressure levels among patients.”

Alternative Hypothesis (H 1 or Ha): “The new medication yields a significant effect in reducing blood pressure levels among patients.”

The null hypothesis implies that any observed alterations in blood pressure subsequent to the medication’s administration are a result of random fluctuations rather than a consequence of the medication itself. Conversely, the alternative hypothesis contends that the medication does indeed generate a meaningful alteration in blood pressure levels, distinct from what might naturally occur or by random chance.

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Example 1: A researcher claims that the average time students spend on homework is 2 hours per night.

Null Hypothesis (H 0 ): The average time students spend on homework is equal to 2 hours per night. Data: A random sample of 30 students has an average homework time of 1.8 hours with a standard deviation of 0.5 hours. Test Statistic and Decision: Using a t-test, if the calculated t-statistic falls within the acceptance region, we fail to reject the null hypothesis. If it falls in the rejection region, we reject the null hypothesis. Conclusion: Based on the statistical analysis, we fail to reject the null hypothesis, suggesting that there is not enough evidence to dispute the claim of the average homework time being 2 hours per night.

Example 2: A company asserts that the error rate in its production process is less than 1%.

Null Hypothesis (H 0 ): The error rate in the production process is 1% or higher. Data: A sample of 500 products shows an error rate of 0.8%. Test Statistic and Decision: Using a z-test, if the calculated z-statistic falls within the acceptance region, we fail to reject the null hypothesis. If it falls in the rejection region, we reject the null hypothesis. Conclusion: The statistical analysis supports rejecting the null hypothesis, indicating that there is enough evidence to dispute the company’s claim of an error rate of 1% or higher.

Q1. A researcher claims that the average time spent by students on homework is less than 2 hours per day. Formulate the null hypothesis for this claim?

Q2. A manufacturing company states that their new machine produces widgets with a defect rate of less than 5%. Write the null hypothesis to test this claim?

Q3. An educational institute believes that their online course completion rate is at least 60%. Develop the null hypothesis to validate this assertion?

Q4. A restaurant claims that the waiting time for customers during peak hours is not more than 15 minutes. Formulate the null hypothesis for this claim?

Q5. A study suggests that the mean weight loss after following a specific diet plan for a month is more than 8 pounds. Construct the null hypothesis to evaluate this statement?

## Summary – Null Hypothesis and Alternative Hypothesis

The null hypothesis (H 0 ) and alternative hypothesis (H a ) are fundamental concepts in statistical hypothesis testing. The null hypothesis represents the default assumption, stating that there is no significant effect, difference, or relationship between variables. It serves as the baseline against which the alternative hypothesis is tested. In contrast, the alternative hypothesis represents the researcher’s hypothesis or the claim to be tested, suggesting that there is a significant effect, difference, or relationship between variables. The relationship between the null and alternative hypotheses is such that they are complementary, and statistical tests are conducted to determine whether the evidence from the data is strong enough to reject the null hypothesis in favor of the alternative hypothesis. This decision is based on the strength of the evidence and the chosen level of significance. Ultimately, the choice between the null and alternative hypotheses depends on the specific research question and the direction of the effect being investigated.

## FAQs on Null Hypothesis

What does null hypothesis stands for.

The null hypothesis, denoted as H 0 ​, is a fundamental concept in statistics used for hypothesis testing. It represents the statement that there is no effect or no difference, and it is the hypothesis that the researcher typically aims to provide evidence against.

## How to Form a Null Hypothesis?

A null hypothesis is formed based on the assumption that there is no significant difference or effect between the groups being compared or no association between variables being tested. It often involves stating that there is no relationship, no change, or no effect in the population being studied.

## When Do we reject the Null Hypothesis?

In statistical hypothesis testing, if the p-value (the probability of obtaining the observed results) is lower than the chosen significance level (commonly 0.05), we reject the null hypothesis. This suggests that the data provides enough evidence to refute the assumption made in the null hypothesis.

## What is a Null Hypothesis in Research?

In research, the null hypothesis represents the default assumption or position that there is no significant difference or effect. Researchers often try to test this hypothesis by collecting data and performing statistical analyses to see if the observed results contradict the assumption.

## What Are Alternative and Null Hypotheses?

The null hypothesis (H0) is the default assumption that there is no significant difference or effect. The alternative hypothesis (H1 or Ha) is the opposite, suggesting there is a significant difference, effect or relationship.

## What Does it Mean to Reject the Null Hypothesis?

Rejecting the null hypothesis implies that there is enough evidence in the data to support the alternative hypothesis. In simpler terms, it suggests that there might be a significant difference, effect or relationship between the groups or variables being studied.

## How to Find Null Hypothesis?

Formulating a null hypothesis often involves considering the research question and assuming that no difference or effect exists. It should be a statement that can be tested through data collection and statistical analysis, typically stating no relationship or no change between variables or groups.

## How is Null Hypothesis denoted?

The null hypothesis is commonly symbolized as H 0 in statistical notation.

## What is the Purpose of the Null hypothesis in Statistical Analysis?

The null hypothesis serves as a starting point for hypothesis testing, enabling researchers to assess if there’s enough evidence to reject it in favor of an alternative hypothesis.

## What happens if we Reject the Null hypothesis?

Rejecting the null hypothesis implies that there is sufficient evidence to support an alternative hypothesis, suggesting a significant effect or relationship between variables.

## What are Test for Null Hypothesis?

Various statistical tests, such as t-tests or chi-square tests, are employed to evaluate the validity of the Null Hypothesis in different scenarios.

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• Type I & Type II Errors | Differences, Examples, Visualizations

## Type I & Type II Errors | Differences, Examples, Visualizations

Published on January 18, 2021 by Pritha Bhandari . Revised on June 22, 2023.

In statistics , a Type I error is a false positive conclusion, while a Type II error is a false negative conclusion.

Making a statistical decision always involves uncertainties, so the risks of making these errors are unavoidable in hypothesis testing .

The probability of making a Type I error is the significance level , or alpha (α), while the probability of making a Type II error is beta (β). These risks can be minimized through careful planning in your study design.

• Type I error (false positive) : the test result says you have coronavirus, but you actually don’t.
• Type II error (false negative) : the test result says you don’t have coronavirus, but you actually do.

Error in statistical decision-making, type i error, type ii error, trade-off between type i and type ii errors, is a type i or type ii error worse, other interesting articles, frequently asked questions about type i and ii errors.

Using hypothesis testing, you can make decisions about whether your data support or refute your research predictions with null and alternative hypotheses .

Hypothesis testing starts with the assumption of no difference between groups or no relationship between variables in the population—this is the null hypothesis . It’s always paired with an alternative hypothesis , which is your research prediction of an actual difference between groups or a true relationship between variables .

In this case:

• The null hypothesis (H 0 ) is that the new drug has no effect on symptoms of the disease.
• The alternative hypothesis (H 1 ) is that the drug is effective for alleviating symptoms of the disease.

Then , you decide whether the null hypothesis can be rejected based on your data and the results of a statistical test . Since these decisions are based on probabilities, there is always a risk of making the wrong conclusion.

• If your results show statistical significance , that means they are very unlikely to occur if the null hypothesis is true. In this case, you would reject your null hypothesis. But sometimes, this may actually be a Type I error.
• If your findings do not show statistical significance, they have a high chance of occurring if the null hypothesis is true. Therefore, you fail to reject your null hypothesis. But sometimes, this may be a Type II error.

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A Type I error means rejecting the null hypothesis when it’s actually true. It means concluding that results are statistically significant when, in reality, they came about purely by chance or because of unrelated factors.

The risk of committing this error is the significance level (alpha or α) you choose. That’s a value that you set at the beginning of your study to assess the statistical probability of obtaining your results ( p value).

The significance level is usually set at 0.05 or 5%. This means that your results only have a 5% chance of occurring, or less, if the null hypothesis is actually true.

If the p value of your test is lower than the significance level, it means your results are statistically significant and consistent with the alternative hypothesis. If your p value is higher than the significance level, then your results are considered statistically non-significant.

To reduce the Type I error probability, you can simply set a lower significance level.

## Type I error rate

The null hypothesis distribution curve below shows the probabilities of obtaining all possible results if the study were repeated with new samples and the null hypothesis were true in the population .

At the tail end, the shaded area represents alpha. It’s also called a critical region in statistics.

If your results fall in the critical region of this curve, they are considered statistically significant and the null hypothesis is rejected. However, this is a false positive conclusion, because the null hypothesis is actually true in this case!

A Type II error means not rejecting the null hypothesis when it’s actually false. This is not quite the same as “accepting” the null hypothesis, because hypothesis testing can only tell you whether to reject the null hypothesis.

Instead, a Type II error means failing to conclude there was an effect when there actually was. In reality, your study may not have had enough statistical power to detect an effect of a certain size.

Power is the extent to which a test can correctly detect a real effect when there is one. A power level of 80% or higher is usually considered acceptable.

The risk of a Type II error is inversely related to the statistical power of a study. The higher the statistical power, the lower the probability of making a Type II error.

Statistical power is determined by:

• Size of the effect : Larger effects are more easily detected.
• Measurement error : Systematic and random errors in recorded data reduce power.
• Sample size : Larger samples reduce sampling error and increase power.
• Significance level : Increasing the significance level increases power.

To (indirectly) reduce the risk of a Type II error, you can increase the sample size or the significance level.

## Type II error rate

The alternative hypothesis distribution curve below shows the probabilities of obtaining all possible results if the study were repeated with new samples and the alternative hypothesis were true in the population .

The Type II error rate is beta (β), represented by the shaded area on the left side. The remaining area under the curve represents statistical power, which is 1 – β.

Increasing the statistical power of your test directly decreases the risk of making a Type II error.

The Type I and Type II error rates influence each other. That’s because the significance level (the Type I error rate) affects statistical power, which is inversely related to the Type II error rate.

This means there’s an important tradeoff between Type I and Type II errors:

• Setting a lower significance level decreases a Type I error risk, but increases a Type II error risk.
• Increasing the power of a test decreases a Type II error risk, but increases a Type I error risk.

This trade-off is visualized in the graph below. It shows two curves:

• The null hypothesis distribution shows all possible results you’d obtain if the null hypothesis is true. The correct conclusion for any point on this distribution means not rejecting the null hypothesis.
• The alternative hypothesis distribution shows all possible results you’d obtain if the alternative hypothesis is true. The correct conclusion for any point on this distribution means rejecting the null hypothesis.

Type I and Type II errors occur where these two distributions overlap. The blue shaded area represents alpha, the Type I error rate, and the green shaded area represents beta, the Type II error rate.

By setting the Type I error rate, you indirectly influence the size of the Type II error rate as well.

It’s important to strike a balance between the risks of making Type I and Type II errors. Reducing the alpha always comes at the cost of increasing beta, and vice versa .

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For statisticians, a Type I error is usually worse. In practical terms, however, either type of error could be worse depending on your research context.

A Type I error means mistakenly going against the main statistical assumption of a null hypothesis. This may lead to new policies, practices or treatments that are inadequate or a waste of resources.

In contrast, a Type II error means failing to reject a null hypothesis. It may only result in missed opportunities to innovate, but these can also have important practical consequences.

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

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Research bias

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• Regression to the mean

In statistics, a Type I error means rejecting the null hypothesis when it’s actually true, while a Type II error means failing to reject the null hypothesis when it’s actually false.

The risk of making a Type I error is the significance level (or alpha) that you choose. That’s a value that you set at the beginning of your study to assess the statistical probability of obtaining your results ( p value ).

To reduce the Type I error probability, you can set a lower significance level.

The risk of making a Type II error is inversely related to the statistical power of a test. Power is the extent to which a test can correctly detect a real effect when there is one.

To (indirectly) reduce the risk of a Type II error, you can increase the sample size or the significance level to increase statistical power.

Statistical significance is a term used by researchers to state that it is unlikely their observations could have occurred under the null hypothesis of a statistical test . Significance is usually denoted by a p -value , or probability value.

Statistical significance is arbitrary – it depends on the threshold, or alpha value, chosen by the researcher. The most common threshold is p < 0.05, which means that the data is likely to occur less than 5% of the time under the null hypothesis .

When the p -value falls below the chosen alpha value, then we say the result of the test is statistically significant.

In statistics, power refers to the likelihood of a hypothesis test detecting a true effect if there is one. A statistically powerful test is more likely to reject a false negative (a Type II error).

If you don’t ensure enough power in your study, you may not be able to detect a statistically significant result even when it has practical significance. Your study might not have the ability to answer your research question.

## Cite this Scribbr article

If you want to cite this source, you can copy and paste the citation or click the “Cite this Scribbr article” button to automatically add the citation to our free Citation Generator.

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## Pritha Bhandari

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## Research Hypothesis

Ai generator.

Diving into academic research requires a compass, and a thesis statement provides that direction. These clear, concise statements guide your exploration, giving purpose to your research. In the realm of research, thesis statements are pivotal: they set the tone, focus, and context. Whether you’re seeking compelling examples, eager to understand the crafting process, or hunting for tips to refine your thesis, this guide illuminates the intricacies of constructing influential research thesis statements.

## What is a Research Hypothesis Statement? – Definition

A research paper thesis statement is a concise summary of the main point or claim of a paper or essay. In academic settings, it functions as the guiding premise behind any research, setting the tone, focus, and context for the study. It’s a specific assertion, usually encompassing one or two sentences, that presents your perspective on the research topic, based on the evidence you have or will gather. A strong research thesis statement is debatable, meaning there’s a clear argument, and it provides direction for the research, ensuring that the content remains relevant and focused.

## What is an example of a Hypothesis statement in research?

Let’s consider a topic on the effects of climate change on coastal cities. An example thesis statement might be:

“Rising sea levels due to climate change are threatening the infrastructure and economy of coastal cities, necessitating urgent adaptive and preventive measures.”

This good thesis statement indicates the topic (rising sea levels and their effects on coastal cities), the claim (they are threatening infrastructure and economy), and hints at a call to action (the need for adaptive and preventive measures). It provides a clear direction for the research that follows.

## 100 Research Hypothesis Statement Examples

Crafting a potent research thesis statement is akin to laying the foundation stone for a building. It gives your research a clear direction and ensures that your efforts are channelized effectively. The versatility of research topics demands an equally diverse set of strong thesis statements . Let’s delve into a myriad of examples spanning various fields to inspire and guide your research endeavors.

1. Climate Change : “Global warming’s acceleration is predominantly driven by human activities, demanding immediate global mitigation strategies.”

2. Cybersecurity : “Increasing cyber-attacks on financial institutions underscore the need for stronger global cyber regulations.”

3. Mental Health : “The rise in teen depression can be directly correlated with increased screen time and social media usage.”

4. Veganism : “Adopting a vegan lifestyle can significantly reduce individual carbon footprints, contributing to environmental conservation.”

5. E-commerce : “The boom in e-commerce has reshaped traditional retail, pushing brick-and-mortar stores to innovate or perish.”

6. Renewable Energy : “Solar energy, with its decreasing costs, stands as the most viable solution for future global energy demands.”

7. Artificial Intelligence : “AI in medicine promises revolutionary changes but also introduces ethical and privacy concerns.”

8. Childhood Obesity : “The prevalence of childhood obesity in urban areas is closely linked to the decline in physical activity and increased processed food consumption.”

9. Telecommuting : “Remote work enhances employee productivity but also poses challenges for team cohesion and company culture.”

10. Gender Wage Gap : “The gender wage gap persists due to deep-rooted societal norms and not just education or job type disparities.”

11. Space Exploration : “Investing in space exploration is not just about interstellar journeys but also about advancing Earth-bound technologies.”

12. GMO Foods : “While GMO foods promise higher yields, their long-term health implications remain largely understudied.”

13. Urban Planning : “Sustainable urban planning is crucial to combat the escalating pollution and dwindling green spaces in metropolitan regions.”

14. Digital Privacy : “With increasing digital surveillance, individuals are sacrificing privacy for the sake of convenience.”

15. Genomic Editing : “CRISPR technology holds immense promise in treating genetic disorders but raises unsettling ethical dilemmas.”

16. Financial Literacy : “Promoting financial literacy from a young age is essential to combat increasing personal debt levels.”

17. Biodiversity : “Rapid deforestation is not just about lost trees, but the irreversible damage to global biodiversity.”

18. Augmented Reality : “Augmented reality in education can offer immersive learning experiences, bridging the gap between theory and application.”

19. Electric Vehicles : “The rise of electric vehicles is pivotal in the fight against air pollution but challenges the existing infrastructure.”

20. Fast Fashion : “The fast fashion industry, while economically lucrative, is one of the major contributors to environmental degradation.”

21. Internet Censorship : “Internet censorship, under the guise of national security, often stifles free speech and suppresses dissent.”

22. Holistic Education : “Incorporating emotional intelligence training in school curriculums fosters holistic student development.”

23. Antibiotic Resistance : “The indiscriminate use of antibiotics in healthcare and agriculture is hastening the advent of antibiotic-resistant superbugs.”

24. Virtual Reality : “Virtual reality in therapy offers innovative solutions to treat phobias and post-traumatic disorders.”

25. Sustainable Agriculture : “Permaculture practices offer a sustainable alternative to industrial agriculture, promoting biodiversity.”

26. Digital Currency : “Cryptocurrencies, while revolutionizing financial transactions, pose significant challenges for regulatory frameworks.”

27. Ocean Pollution : “Microplastic pollution in oceans affects not just marine life but also enters the human food chain.”

28. Telemedicine : “Telemedicine, propelled by the pandemic, has democratized access to healthcare but requires stringent data security measures.”

29. Drone Technology : “Drones are revolutionizing industries from agriculture to cinematography, yet raise concerns about privacy and security.”

30. Biofuels : “Second-generation biofuels offer a sustainable energy source without competing with food crops.”

31. Quantum Computing : “Quantum computing holds the potential to revolutionize computational speed, but also threatens current encryption methods.”

32. Digital Learning : “Online education democratizes access to knowledge but demands self-discipline and robust digital infrastructure.”

33. Ocean Acidification : “Ocean acidification, an under-discussed consequence of CO2 emissions, threatens marine biodiversity and fisheries.”

34. Human Trafficking : “Modern technologies, while aiding law enforcement, also inadvertently facilitate global human trafficking networks.”

35. 5G Technology : “5G technology promises unprecedented data speeds and connectivity but raises concerns about health and surveillance.”

36. Organic Farming : “Organic farming, beyond being pesticide-free, contributes to soil health and combats soil erosion.”

37. Artificial Photosynthesis : “Artificial photosynthesis could revolutionize renewable energy, mimicking nature to produce fuel from sunlight.”

38. Digital Nomadism : “The rise of digital nomads underscores the evolving definitions of workspaces and work-life balance.”

39. Water Scarcity : “Rainwater harvesting isn’t just an ancient practice but a contemporary solution to global water scarcity.”

40. Machine Learning : “Machine learning in finance can forecast market trends with increased accuracy, but it also amplifies systemic risks.”

41. Urban Green Spaces : “Increasing urban green spaces isn’t just about aesthetics but improving mental health and air quality.”

42. Cultural Preservation : “Digital archiving plays a critical role in cultural preservation in an era of rapid globalization.”

43. Space Tourism : “Space tourism, while exciting, raises pressing questions about environmental impact and space debris.”

44. AgriTech : “Technological interventions in agriculture, from drones to AI, can optimize yields and reduce waste.”

45. Child Online Safety : “Children’s online safety is increasingly threatened by cyberbullying and predatory behaviors, underscoring the need for robust digital education.”

46. Biohacking : “Biohacking offers individual empowerment over one’s biology, but straddles ethical boundaries.”

47. Aquaculture : “Sustainable aquaculture practices can meet global seafood demands without depleting wild fish stocks.”

48. eSports : “The rise of eSports challenges traditional definitions of sports, offering digital athletes lucrative careers.”

49. Green Architecture : “Green architecture goes beyond energy efficiency, embodying sustainability in construction materials and spatial design.”

50. Dark Web : “The dark web, while notorious for illicit activities, also provides a haven for activists in oppressive regimes.”

51. Nanotechnology : “Nanotechnology in medicine promises targeted drug delivery, reducing side effects and improving efficacy.”

52. Animal Rights : “Factory farming, beyond ethical concerns, has significant implications for biodiversity and zoonotic diseases.”

53. Biometric Security : “Biometrics offers enhanced security measures but raises concerns about personal data misuse.”

54. Digital Addiction : “The design of social media platforms, driven by profit motives, exacerbates digital addiction.”

55. Space Colonization : “Colonizing Mars, while technologically challenging, may become a necessity due to Earth’s finite resources.”

56. Green Transport : “Urban public transport solutions, from electric buses to bike-sharing, are pivotal in reducing urban carbon emissions.”

57. Food Waste : “Innovative tech solutions from farm to fork can significantly reduce global food wastage.”

58. 3D Printing : “3D printing revolutionizes manufacturing, enabling bespoke production and reducing transportation emissions.”

59. Bioinformatics : “Bioinformatics bridges biology and computing, accelerating drug discovery and personalized medicine.”

60. Deep Learning : “Deep learning algorithms can transform healthcare diagnostics but necessitate vast data, raising privacy concerns.”

61. Aging Population : “Technological solutions, from telehealth to robotics, can address the challenges posed by an aging global population.”

62. Desalination : “Desalination offers a solution to freshwater scarcity but demands innovative approaches to reduce environmental impacts.”

63. Alternative Meat : “Lab-grown meat might not just satisfy culinary desires but also address environmental and ethical issues.”

64. Geothermal Energy : “Geothermal energy, an often-overlooked renewable source, offers consistent power generation irrespective of weather.”

65. Robotic Surgery : “Robotic surgery enhances precision and reduces invasiveness, but its high costs limit accessibility.”

66. Virtual Collaboration : “While virtual collaboration tools empower global teamwork, they challenge traditional team dynamics and require new communication protocols.”

67. Synthetic Biology : “Synthetic biology holds the promise of custom organisms, but this power also risks unintended ecological consequences.”

68. Augmented Workforce : “Integrating AI into the workforce can enhance productivity, but also necessitates retraining and job realignment strategies.”

69. Quantum Cryptography : “Quantum cryptography could render current encryption obsolete, pushing for a new era of secure communication.”

70. Urban Vertical Farming : “Vertical farming in urban locales can drastically reduce food transportation emissions and ensure fresher produce.”

71. Internet of Things (IoT) : “While IoT devices enhance daily convenience, they exponentially increase potential points of cyber vulnerabilities.”

72. Neurotechnology : “Brain-computer interfaces might redefine human-machine interaction but tread on uncharted ethical terrains.”

73. Digital Twins : “Utilizing digital twins in industry can optimize operational efficiency but requires robust data integrity measures.”

74. Ethical AI : “Ensuring AI ethics isn’t just about preventing biases but also about addressing unintended societal consequences.”

75. Blue Economy : “Sustainable utilization of ocean resources, the blue economy, is paramount for ecological balance and economic progress.”

76. Audio Deepfakes : “The emergence of a deepfakes challenges information reliability, underscoring the need for advanced detection tools.”

77. Microgrid Technology : “Microgrids promise decentralized energy solutions, enhancing resilience against main grid failures.”

78. Autonomous Vehicles : “Self-driving cars have the potential to revolutionize urban mobility, but their integration challenges existing traffic norms.”

79. Tissue Engineering : “Tissue engineering could negate the need for organ donations, but it raises questions about affordability and accessibility.”

80. EdTech in Remote Areas : “Implementing EdTech in remote areas demands more than technology—it requires infrastructure and localized content strategies.”

81. Blockchain in Healthcare : “Blockchain could ensure data transparency in healthcare, yet its adoption faces regulatory and trust barriers.”

82. Floating Cities : “Floating cities might address rising sea levels, but their feasibility hinges on environmental and socio-economic factors.”

83. Digital Heritage Preservation : “Digitizing cultural heritage safeguards it for future generations and enhances global accessibility.”

84. Genetic Data Privacy : “As genetic testing becomes mainstream, the imperative for stringent genetic data privacy protocols intensifies.”

85. Zero-Waste Communities : “Building zero-waste communities isn’t merely environmental but also fosters local economies and community bonds.”

86. Immersive Gaming : “Advancements in immersive gaming can redefine educational methods, making learning more engaging.”

87. Solid-state Batteries : “Solid-state batteries might be the leap needed for electric vehicles to overshadow their combustion-engine counterparts.”

88. Human-AI Collaboration : “Human-AI collaborations in workplaces require reimagined workflows and continuous learning environments.”

89. Underwater Data Centers : “Underwater data centers offer efficient cooling solutions, but their long-term environmental impacts remain to be assessed.”

90. Language Translation AIs : “Real-time AI translators are breaking down language barriers, yet they challenge cultural nuances in communication.”

91. Smart Homes and Security : “While smart homes enhance living convenience, they also introduce new security vulnerabilities.”

92. Digital Museums : “Digital museums democratize art and history access, but can they replicate the tactile essence of physical exhibitions?”

93. Renewable Energy Storage : “Effective storage solutions for renewable energy, like advanced battery technology, are key to a consistent green energy supply.”

94. Drone Deliveries : “Drone deliveries promise rapid logistics but require comprehensive airspace management solutions.”

95. Teleportation Research : “While teleportation remains in the realm of theoretical physics, its research could unravel foundational truths about our universe.”

96. Eco-Tourism : “Eco-tourism, while promoting sustainability, must ensure it doesn’t inadvertently harm local ecosystems.”

97. Virtual Reality in Architecture : “Virtual reality in architectural design enhances client experience, offering immersive building previews.”

98. Lab-on-a-chip Devices : “Lab-on-a-chip devices can revolutionize on-site rapid diagnostics, especially in remote locations.”

99. Quantum Internet : “Quantum internet could redefine data security, promising unhackable communication channels.”

100. Food Biotechnology : “Food biotechnology can address global hunger, but its adoption needs transparent communication about potential risks.”

## Hypothesis Statement Examples for Quantitative Research

• Mobile App Usage : “The frequency of mobile app usage correlates positively with the user’s age, suggesting a generational gap in technology adoption.”
• Physical Activity : “There’s a statistically significant difference in heart rate variability between individuals engaging in aerobic exercises compared to anaerobic ones.”
• Dietary Habits : “A higher intake of omega-3 fatty acids has a direct association with improved cognitive function in adults above 50.”
• Economic Growth : “Foreign direct investment (FDI) has a positive and significant impact on a developing country’s GDP growth.”
• Employee Productivity : “Flexible working hours result in a quantifiable increase in employee productivity and job satisfaction.”
• Medication Efficiency : “Patients taking Drug A showed a 25% more significant reduction in symptoms over three months compared to those on Drug B.”
• Consumer Behavior : “A 10% increase in celebrity endorsement directly results in a 5% rise in product sales.”
• Academic Scores : “Students who participate in extracurricular activities have a measurable improvement in their math and language scores.”
• Air Pollution : “Cities with stringent vehicular emission norms witness a 30% decrease in particulate matter in the atmosphere.”

## Hypothesis Statement Examples for Practical Research

• Water Filtration : “Using activated charcoal in community water filtration systems effectively reduces waterborne diseases by 40%.”
• Ergonomic Furniture : “Introducing ergonomic furniture in office environments decreases employee sick leave due to musculoskeletal issues.”
• Soil Fertility : “Crop rotation with leguminous plants enhances soil fertility, evidenced by a 20% yield increase in subsequent crops.”
• Digital Payment Platforms : “Implementing digital payment platforms in local markets increases transaction transparency and boosts overall sales.”
• Waste Management : “Composting organic municipal waste can effectively reduce landfill contributions by over 60%.”
• Renewable Energy : “Rooftop solar panels in urban households meet 50% of daily energy needs, significantly reducing dependency on grid electricity.”
• Elderly Mobility : “Incorporating daily physiotherapy for the elderly results in a 35% reduction in fall-related injuries.”
• Public Transportation : “Upgrading to electric buses in city transit systems reduces greenhouse gas emissions by 70%.”
• Mental Health : “Workplace wellness programs, including meditation sessions, have tangibly reduced employee stress levels.”
• Agricultural Pests : “Biological pest control methods in farms decrease pesticide use by 50% and increase crop yield.”

## Hypothesis Statement Examples for Survey

• Consumer Preferences : “75% of surveyed customers prefer eco-friendly packaging, citing environmental concerns.”
• Voter’s Opinion : “In a pre-election survey, 65% of voters believe that healthcare reforms are the top priority.”
• Employee Satisfaction : “Based on our annual survey, flexible work hours rank highest in job satisfaction criteria among employees.”
• Tourist Feedback : “90% of tourists visiting the city recommend the establishment of multi-lingual guides in heritage sites.”
• Dietary Choices : “A survey of urban teenagers shows a growing preference for vegan diets due to ethical and health reasons.”
• Public Opinion : “Public transport efficiency and safety are the primary concerns for 80% of city dwellers, as per the latest survey.”
• Student Feedback : “70% of university students feel that online courses should incorporate more interactive sessions.”
• Market Research : “A product survey reveals that 60% of users would willingly pay more for products with extended warranties.”
• Reading Habits : “According to our library survey, digital books are growing in popularity, with a 50% increase in e-book checkouts last year.”
• Healthcare Survey : “Post-treatment surveys indicate that patient aftercare programs significantly enhance patient recovery and satisfaction.”

## Hypothesis Statement Examples for Research Papers

• Climate Change : “Anthropogenic activities, primarily fossil fuel combustion, are the predominant cause of accelerated global warming in the 21st century.”
• Neuroscience : “The neuroplasticity of the adult brain indicates the potential for continuous learning and adaptation throughout life.”
• Sociology : “Social media platforms, while connecting individuals globally, also contribute to increasing feelings of loneliness and isolation.”
• Literature : “Shakespeare’s portrayal of women in his plays reflects the evolving societal views of female empowerment and agency during the Renaissance.”
• Economics : “The 2008 financial crisis was an outcome of a combination of risky investment tools, lax regulatory oversight, and global financial missteps.”
• Biology : “The CRISPR-Cas9 gene editing system, while revolutionary, raises pertinent ethical issues concerning genetic modifications.”
• Psychology : “Childhood trauma can have long-term psychological effects, influencing adult behavior and interpersonal relationships.”
• Political Science : “The rise of populist movements globally can be traced back to increasing economic disparities and feelings of political alienation.”
• Astronomy : “Recent observations of exoplanets suggest that liquid water, and thus the potential for life, may be more common in our galaxy than previously believed.”
• Anthropology : “The migration patterns of ancient human populations, as revealed by DNA studies, challenge traditional theories about early human movement.”

## Hypothesis Statement Examples for Informative Research

• Quantum Physics : “Quantum entanglement, a phenomenon where particles become interconnected and share states, challenges traditional notions of locality in physics.”
• Botany : “Photosynthesis, a process used by plants to convert sunlight into energy, is the foundation of life on Earth, fueling ecosystems and influencing the global climate.”
• Music : “The Baroque period, spanning from 1600 to 1750, brought about significant musical innovations, setting the stage for classical and romantic eras that followed.”
• Architecture : “Gothic architecture, characterized by its pointed arches and ribbed vaults, represented a significant departure from the Romanesque style, emphasizing verticality and light.”
• Zoology : “Migration patterns in monarch butterflies, traveling thousands of miles, remain a fascinating area of study, showcasing nature’s incredible endurance and navigational skills.”
• Geology : “Plate tectonics, the movement of Earth’s lithospheric plates, is responsible for phenomena like earthquakes, volcanic activity, and the creation of mountain ranges.”
• History : “The Renaissance, a cultural movement between the 14th and 17th centuries, marked a period of renewed interest in art, science, and humanism.”
• Medicine : “Vaccination, the practice of administering weakened pathogens to boost immunity, has been instrumental in eradicating and controlling numerous infectious diseases.”
• Philosophy : “Existentialism, a philosophical movement, emphasizes individual freedom, choice, and responsibility in a universe without inherent meaning.”
• Linguistics : “The evolution of languages, influenced by factors like migration, colonization, and trade, provides insight into cultural and social dynamics of human societies.”

## Hypothesis Statement Examples for Research Essay

• Urban Development : “The sustainable development of cities requires a balanced approach that integrates environmental, economic, and social needs.”
• Health and Wellness : “Holistic approaches to health and wellness emphasize the interconnectedness of physical, emotional, and social well-being.”
• Digital Privacy : “In the age of digital interconnectivity, establishing robust privacy frameworks is imperative to protect individual rights and freedoms.”
• Art Movements : “Impressionism, a 19th-century art movement, sought to capture fleeting moments, emphasizing spontaneity and light.”
• Education Systems : “Modern education systems must evolve to emphasize critical thinking, creativity, and emotional intelligence over rote memorization.”
• Gender Studies : “The evolution of gender norms reflects the broader societal shift towards inclusivity and recognition of non-binary identities.”
• Ecosystem Conservation : “Conserving mangrove ecosystems is crucial not just for biodiversity but for coastal protection and local economies.”
• Technology and Society : “The proliferation of AI technologies necessitates a reevaluation of societal norms and values concerning work, ethics, and human relationships.”
• Cultural Evolution : “The global dissemination of pop culture, facilitated by the internet, is reshaping local cultural identities and values.”
• Space Exploration : “Human missions to Mars, while technologically challenging, represent the next frontier in our quest for knowledge and exploration.”

## Hypothesis Statement Examples for History Research

• Ancient Civilizations : “The Indus Valley Civilization’s urban planning and architecture demonstrate advanced engineering and societal organization for its time.”
• Medieval Europe : “The Black Death in medieval Europe, while devastating, led to significant societal, economic, and cultural transformations.”
• Colonial Era : “The impact of colonialism in Africa has lasting socio-political and economic implications that continue to influence contemporary geopolitics.”
• World Wars : “The consequences of World War I directly set the stage for World War II, demonstrating the intricate interplay of global treaties and nationalism.”
• Renaissance Period : “The Renaissance was not just an artistic movement but also marked significant advancements in science, politics, and philosophy.”
• Cold War : “The Cold War era, characterized by the US-USSR rivalry, reshaped global alliances and set the stage for contemporary geopolitical dynamics.”
• Industrial Revolution : “The Industrial Revolution, while a period of economic growth and technological advancement, also led to significant social upheaval and environmental degradation.”
• Ancient East : “The Silk Road was more than just a trade route; it was a conduit for cultural, technological, and philosophical exchange between the East and West.”
• Pre-Columbian America : “Pre-Columbian civilizations like the Maya and Aztec had intricate societal structures, astronomical knowledge, and architectural marvels.”
• Age of Exploration : “The Age of Exploration in the 15th and 16th centuries wasn’t merely about discovering new lands but also about the exchange of ideas, goods, and the spread (and sometimes imposition) of cultural norms.”

In creating thesis statements, always ensure clarity, specificity, and relevance to your research objectives.

## How do you write a Hypothesis statement for a Research project? – Step by Step Guide

A thesis statement is the backbone of your research project, acting as the clear, concise answer to your research question. This pivotal sentence or two guides your study, providing direction and keeping your research focused. Here’s a step-by-step guide to help you craft the perfect thesis statement for your research project:

• Identify Your Research Topic : Before anything else, decide on a topic. It should be something you’re passionate about and is within the scope of your subject or course.
• Narrow Down Your Focus : General topics are usually vast. You need to narrow down your perspective to make your research more specific. For instance, instead of focusing on “climate change effects,” you might narrow it to “effects of climate change on coral reefs.”
• Formulate a Research Question : From your focused topic, come up with a question you’d like to answer. Using the above example, “How does climate change impact coral reefs?”
• Take a Position : A thesis statement is not just a statement of fact but often requires you to take a position. Based on your initial research, decide on a stance. It might be, “Climate change significantly harms coral reefs by causing coral bleaching.”
• Be Concise and Clear : Your thesis should be clear and to the point. Avoid jargon unless it’s essential and make sure the statement can be understood by anyone, even those not specialized in your field.
• Ensure It’s Arguable : A good thesis statement is one that can be debated. If everyone agrees with your statement, then it’s probably just a simple fact and not a suitable thesis.
• Seek Feedback : Before finalizing your thesis statement, share it with colleagues, mentors, or friends to get feedback. They might offer a fresh perspective or insight that you hadn’t considered.
• Refine and Revise : Based on feedback and as your research progresses, be ready to refine and revise your thesis statement. It’s normal for your initial statement to evolve as you delve deeper into your topic.
• Position It Properly : Your thesis statement typically belongs at the end of your introductory paragraph. It sets the tone and provides a roadmap for your readers.
• Stay True to Your Thesis : As you conduct your research and start writing, always refer back to your thesis statement. Ensure that every piece of evidence and argument you present aligns with and supports it.

## Tips for Writing a Research Hypothesis Statement

• Be Specific : A vague thesis statement won’t be of much use. Specify the relationships, aspects, or directions you’ll be exploring in your research.
• Avoid Overused or Clichéd Phrases : Starting with phrases like “In this research, I will…” can make your thesis sound less impactful. Get straight to the point.
• Use Precise Language : Precision is key in research. Make sure your thesis statement reflects this by using terms that convey exactness.
• Maintain Coherence : Ensure that your thesis statement aligns with the contents of your research project. Any deviation can confuse readers.
• Avoid Purely Personal Opinions : While your thesis will reflect a position or perspective, ensure it’s based on evidence, research, and logic rather than purely personal beliefs.
• Consider the “So What?” Test : After writing your thesis statement, ask yourself, “So what?” If the statement doesn’t seem to have much significance, you might want to rethink it.
• Stay Flexible : In the early stages of research, stay open to modifying your thesis statement as you discover more information.
• Ensure It’s One Main Idea : A good thesis statement captures one predominant idea. If you find it has multiple primary ideas, you might be trying to cover too much ground.
• Avoid Ambiguity : Your thesis should leave no room for ambiguity. It should convey a clear, definite meaning.
• Consult Your Advisor : Especially for significant projects like dissertations or theses, always consult your advisor or mentor to ensure your thesis statement is on the right track.

Remember, your thesis statement is a promise to your reader about what you intend to cover in your research project. Make it meaningful, clear, and reflective of the research you’ve conducted.

Text prompt

• Instructive
• Professional

10 Examples of Public speaking

20 Examples of Gas lighting

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1. Examples of the Null Hypothesis

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3. 15 Null Hypothesis Examples (2024)

4. Null hypothesis

5. Null Hypothesis Examples

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1. Understanding the Null Hypothesis

2. Hypothesis Testing: the null and alternative hypotheses

3. Hypothesis|Meaning|Definition|Characteristics|Source|Types|Sociology|Research Methodology|Notes

4. MODULE 4

5. How To Formulate The Hypothesis/What is Hypothesis?

6. Hypothesis: meaning Definition #hypothesis #statistics #statisticsforeconomics #statisticalanalysis

1. Null Hypothesis: Definition, Rejecting & Examples

Learn what a null hypothesis is in statistics and how to write it for different types of effects and tests. Find out when and how to reject the null hypothesis and conclude that an effect or relationship exists in the population.

2. Null hypothesis

The null hypothesis is a default hypothesis that a quantity to be measured is zero (null). Typically, the quantity to be measured is the difference between two situations. For instance, trying to determine if there is a positive proof that an effect has occurred or that samples derive from different batches. [7] [8]

3. Null Hypothesis Definition and Examples

Learn what a null hypothesis is and how to state it in a scientific experiment. See examples of null hypotheses and why they are useful to test.

4. Null & Alternative Hypotheses

The null and alternative hypotheses offer competing answers to your research question. When the research question asks "Does the independent variable affect the dependent variable?": The null hypothesis ( H0) answers "No, there's no effect in the population.". The alternative hypothesis ( Ha) answers "Yes, there is an effect in the ...

5. Null and Alternative Hypotheses

Learn what null and alternative hypotheses are, how to write them, and how to use them in statistical testing. The null hypothesis is the claim that there's no effect in the population, while the alternative hypothesis is the claim that there's an effect in the population.

6. Null Hypothesis Definition and Examples, How to State

Step 1: Figure out the hypothesis from the problem. The hypothesis is usually hidden in a word problem, and is sometimes a statement of what you expect to happen in the experiment. The hypothesis in the above question is "I expect the average recovery period to be greater than 8.2 weeks.". Step 2: Convert the hypothesis to math.

7. 9.1: Null and Alternative Hypotheses

Review. In a hypothesis test, sample data is evaluated in order to arrive at a decision about some type of claim.If certain conditions about the sample are satisfied, then the claim can be evaluated for a population. In a hypothesis test, we: Evaluate the null hypothesis, typically denoted with $$H_{0}$$.The null is not rejected unless the hypothesis test shows otherwise.

8. 9.1 Null and Alternative Hypotheses

The actual test begins by considering two hypotheses.They are called the null hypothesis and the alternative hypothesis.These hypotheses contain opposing viewpoints. H 0, the —null hypothesis: a statement of no difference between sample means or proportions or no difference between a sample mean or proportion and a population mean or proportion. In other words, the difference equals 0.

9. Examples of null and alternative hypotheses

It is the opposite of your research hypothesis. The alternative hypothesis--that is, the research hypothesis--is the idea, phenomenon, observation that you want to prove. If you suspect that girls take longer to get ready for school than boys, then: Alternative: girls time > boys time. Null: girls time <= boys time.

10. Null hypothesis Definition & Meaning

The meaning of NULL HYPOTHESIS is a statistical hypothesis to be tested and accepted or rejected in favor of an alternative; specifically : the hypothesis that an observed difference (as between the means of two samples) is due to chance alone and not due to a systematic cause.

11. Hypothesis Testing

Table of contents. Step 1: State your null and alternate hypothesis. Step 2: Collect data. Step 3: Perform a statistical test. Step 4: Decide whether to reject or fail to reject your null hypothesis. Step 5: Present your findings. Other interesting articles. Frequently asked questions about hypothesis testing.

12. An Introduction to Statistics: Understanding Hypothesis Testing and

HYPOTHESIS TESTING. A clinical trial begins with an assumption or belief, and then proceeds to either prove or disprove this assumption. In statistical terms, this belief or assumption is known as a hypothesis. Counterintuitively, what the researcher believes in (or is trying to prove) is called the "alternate" hypothesis, and the opposite ...

13. How to Formulate a Null Hypothesis (With Examples)

The null hypothesis states there is no relationship between the measured phenomenon (the dependent variable) and the independent variable, which is the variable an experimenter typically controls or changes.You do not need to believe that the null hypothesis is true to test it. On the contrary, you will likely suspect there is a relationship between a set of variables.

14. What Is The Null Hypothesis & When To Reject It

A null hypothesis is a statistical concept suggesting no significant difference or relationship between measured variables. It's the default assumption unless empirical evidence proves otherwise. The null hypothesis states no relationship exists between the two variables being studied (i.e., one variable does not affect the other).

15. Null Hypothesis

Null Hypothesis Definition. The null hypothesis is a kind of hypothesis which explains the population parameter whose purpose is to test the validity of the given experimental data. This hypothesis is either rejected or not rejected based on the viability of the given population or sample. In other words, the null hypothesis is a hypothesis in ...

16. Exploring the Null Hypothesis: Definition and Purpose

The word Null in the context of hypothesis testing means "nothing" or "zero.". As an example, if we wanted to test whether there was a difference in two population means based on the calculations from two samples, we would state the Null Hypothesis in the form of: Ho: mu1 = mu2 or mu1- mu2 = 0. In other words, there is no difference, or ...

17. Null Hypothesis: What Is It, and How Is It Used in Investing?

Null Hypothesis: A null hypothesis is a type of hypothesis used in statistics that proposes that no statistical significance exists in a set of given observations. The null hypothesis attempts to ...

18. Null Hypothesis

Null hypothesis is used to make decisions based on data and by using statistical tests. Null hypothesis is represented using H o and it states that there is no difference between the characteristics of two samples. Null hypothesis is generally a statement of no difference. The rejection of null hypothesis is equivalent to the acceptance of the ...

19. What is Null Hypothesis? What Is Its Importance in Research?

Scientists begin their research with a hypothesis that a relationship of some kind exists between variables. The null hypothesis is the opposite stating that no such relationship exists. Null hypothesis may seem unexciting, but it is a very important aspect of research. In this article, we discuss what null hypothesis is, how to make use of it ...

20. Null hypothesis

Biology definition: A null hypothesis is an assumption or proposition where an observed difference between two samples of a statistical population is purely accidental and not due to systematic causes. It is the hypothesis to be investigated through statistical hypothesis testing so that when refuted indicates that the alternative hypothesis is true. . Thus, a null hypothesis is a hypothesis ...

21. Null Hypothesis

A null hypothesis is a theory based on insufficient evidence that requires further testing to prove whether the observed data is true or false. For example, a null hypothesis statement can be "the rate of plant growth is not affected by sunlight.". It can be tested by measuring the growth of plants in the presence of sunlight and comparing ...

22. Null Hypothesis

Null Hypothesis, often denoted as H0, is a foundational concept in statistical hypothesis testing. It represents an assumption that no significant difference, effect, or relationship exists between variables within a population. It serves as a baseline assumption, positing no observed change or effect occurring.

23. Type I & Type II Errors

The null hypothesis distribution curve below shows the probabilities of obtaining all possible results if the study were repeated with new samples and the null hypothesis were true in the population. ... Definition and Examples The p-value shows the likelihood of your data occurring under the null hypothesis. P-values help determine statistical ...

24. Research Hypothesis

Null Hypothesis ; Hypothesis If Then ; Hypothesis For Kids ; Testing Hypothesis Statement ; Scientific Hypothesis ; Science Hypothesis ; Home; English; ... What is a Research Hypothesis Statement? - Definition. A research paper thesis statement is a concise summary of the main point or claim of a paper or essay. In academic settings, it ...

25. 9.2: Null and Alternative Hypotheses

Review. In a hypothesis test, sample data is evaluated in order to arrive at a decision about some type of claim.If certain conditions about the sample are satisfied, then the claim can be evaluated for a population. In a hypothesis test, we: Evaluate the null hypothesis, typically denoted with $$H_{0}$$.The null is not rejected unless the hypothesis test shows otherwise.