greater than (>) less 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 (including one of the co-authors in research work) 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.
H 0 : No more than 30% of the registered voters in Santa Clara County voted in the primary election. p ≤ 30
H a : More than 30% 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%. State the null and alternative hypotheses.
H 0 : The drug reduces cholesterol by 25%. p = 0.25
H a : The drug does not reduce cholesterol by 25%. p ≠ 0.25
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:
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
We want to test if college students take less than five years to graduate from college, on the average. The null and alternative hypotheses are:
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
In an issue of U.S. News and World Report , an article on school standards stated that about half of all students in France, Germany, and Israel take advanced placement exams and a third pass. The same article stated that 6.6% of U.S. students take advanced placement exams and 4.4% pass. Test if the percentage of U.S. students who take advanced placement exams is more than 6.6%. State the null and alternative hypotheses.
H 0 : p ≤ 0.066
H a : p > 0.066
On a state driver’s test, about 40% pass the test on the first try. We want to test if more than 40% 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
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. The null statement must always contain some form of equality (=, ≤ or ≥) Always write the alternative hypothesis , typically denoted with H a or H 1 , using less than, greater than, or not equals symbols, i.e., (≠, >, or <). If we reject the null hypothesis, then we can assume there is enough evidence to support the alternative hypothesis. Never state that a claim is proven true or false. Keep in mind the underlying fact that hypothesis testing is based on probability laws; therefore, we can talk only in terms of non-absolute certainties.
H 0 and H a are contradictory.
The alternative hypothesis.
Adam Hayes, Ph.D., CFA, is a financial writer with 15+ years Wall Street experience as a derivatives trader. Besides his extensive derivative trading expertise, Adam is an expert in economics and behavioral finance. Adam received his master's in economics from The New School for Social Research and his Ph.D. from the University of Wisconsin-Madison in sociology. He is a CFA charterholder as well as holding FINRA Series 7, 55 & 63 licenses. He currently researches and teaches economic sociology and the social studies of finance at the Hebrew University in Jerusalem.
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.
Alex Dos Diaz / Investopedia
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 (H 1 ).
For the examples below, the alternative hypothesis would be:
In other words, the alternative hypothesis is a direct contradiction of the null hypothesis.
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 not 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 not 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 not 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:
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.
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.
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.
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.
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.
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.
What is the null hypothesis, how to state the null hypothesis, null hypothesis overview.
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).
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.
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 .
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
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!
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Gonick, L. (1993). The Cartoon Guide to Statistics . HarperPerennial. Kotz, S.; et al., eds. (2006), Encyclopedia of Statistical Sciences , Wiley.
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Methodology
Published on May 6, 2022 by Shona McCombes . Revised on November 20, 2023.
A hypothesis is a statement that can be tested by scientific research. If you want to test a relationship between two or more variables, you need to write hypotheses before you start your experiment or data collection .
Daily apple consumption leads to fewer doctor’s visits.
What is a hypothesis, developing a hypothesis (with example), hypothesis examples, other interesting articles, frequently asked questions about writing hypotheses.
A hypothesis states your predictions about what your research will find. It is a tentative answer to your research question that has not yet been tested. For some research projects, you might have to write several hypotheses that address different aspects of your research question.
A hypothesis is not just a guess – it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).
Hypotheses propose a relationship between two or more types of variables .
If there are any control variables , extraneous variables , or confounding variables , be sure to jot those down as you go to minimize the chances that research bias will affect your results.
In this example, the independent variable is exposure to the sun – the assumed cause . The dependent variable is the level of happiness – the assumed effect .
Step 1. ask a question.
Writing a hypothesis begins with a research question that you want to answer. The question should be focused, specific, and researchable within the constraints of your project.
Your initial answer to the question should be based on what is already known about the topic. Look for theories and previous studies to help you form educated assumptions about what your research will find.
At this stage, you might construct a conceptual framework to ensure that you’re embarking on a relevant topic . This can also help you identify which variables you will study and what you think the relationships are between them. Sometimes, you’ll have to operationalize more complex constructs.
Now you should have some idea of what you expect to find. Write your initial answer to the question in a clear, concise sentence.
You need to make sure your hypothesis is specific and testable. There are various ways of phrasing a hypothesis, but all the terms you use should have clear definitions, and the hypothesis should contain:
To identify the variables, you can write a simple prediction in if…then form. The first part of the sentence states the independent variable and the second part states the dependent variable.
In academic research, hypotheses are more commonly phrased in terms of correlations or effects, where you directly state the predicted relationship between variables.
If you are comparing two groups, the hypothesis can state what difference you expect to find between them.
If your research involves statistical hypothesis testing , you will also have to write a null hypothesis . The null hypothesis is the default position that there is no association between the variables. The null hypothesis is written as H 0 , while the alternative hypothesis is H 1 or H a .
Research question | Hypothesis | Null hypothesis |
---|---|---|
What are the health benefits of eating an apple a day? | Increasing apple consumption in over-60s will result in decreasing frequency of doctor’s visits. | Increasing apple consumption in over-60s will have no effect on frequency of doctor’s visits. |
Which airlines have the most delays? | Low-cost airlines are more likely to have delays than premium airlines. | Low-cost and premium airlines are equally likely to have delays. |
Can flexible work arrangements improve job satisfaction? | Employees who have flexible working hours will report greater job satisfaction than employees who work fixed hours. | There is no relationship between working hour flexibility and job satisfaction. |
How effective is high school sex education at reducing teen pregnancies? | Teenagers who received sex education lessons throughout high school will have lower rates of unplanned pregnancy teenagers who did not receive any sex education. | High school sex education has no effect on teen pregnancy rates. |
What effect does daily use of social media have on the attention span of under-16s? | There is a negative between time spent on social media and attention span in under-16s. | There is no relationship between social media use and attention span in under-16s. |
If you want to know more about the research process , methodology , research bias , or statistics , make sure to check out some of our other articles with explanations and examples.
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A hypothesis is not just a guess — it should be based on existing theories and knowledge. It also has to be testable, which means you can support or refute it through scientific research methods (such as experiments, observations and statistical analysis of data).
Null and alternative hypotheses are used in statistical hypothesis testing . The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.
Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics. It is used by scientists to test specific predictions, called hypotheses , by calculating how likely it is that a pattern or relationship between variables could have arisen by chance.
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McCombes, S. (2023, November 20). How to Write a Strong Hypothesis | Steps & Examples. Scribbr. Retrieved August 30, 2024, from https://www.scribbr.com/methodology/hypothesis/
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Last Updated: January 17, 2024 Fact Checked
This article was co-authored by Joseph Quinones and by wikiHow staff writer, Jennifer Mueller, JD . Joseph Quinones is a Physics Teacher working at South Bronx Community Charter High School. Joseph specializes in astronomy and astrophysics and is interested in science education and science outreach, currently practicing ways to make physics accessible to more students with the goal of bringing more students of color into the STEM fields. He has experience working on Astrophysics research projects at the Museum of Natural History (AMNH). Joseph recieved his Bachelor's degree in Physics from Lehman College and his Masters in Physics Education from City College of New York (CCNY). He is also a member of a network called New York City Men Teach. There are 7 references cited in this article, which can be found at the bottom of the page. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 29,248 times.
Are you working on a research project and struggling with how to write a null hypothesis? Well, you've come to the right place! Start by recognizing that the basic definition of "null" is "none" or "zero"—that's your biggest clue as to what a null hypothesis should say. Keep reading to learn everything you need to know about the null hypothesis, including how it relates to your research question and your alternative hypothesis as well as how to use it in different types of studies.
Thanks for reading our article! If you’d like to learn more about physics, check out our in-depth interview with Joseph Quinones .
Dec 3, 2022
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Chapter 13: Inferential Statistics
Learning Objectives
As we have seen, psychological research typically involves measuring one or more variables for a sample and computing descriptive statistics for that sample. In general, however, the researcher’s goal is not to draw conclusions about that sample but to draw conclusions about the population that the sample was selected from. Thus researchers must use sample statistics to draw conclusions about the corresponding values in the population. These corresponding values in the population are called parameters . Imagine, for example, that a researcher measures the number of depressive symptoms exhibited by each of 50 clinically depressed adults and computes the mean number of symptoms. The researcher probably wants to use this sample statistic (the mean number of symptoms for the sample) to draw conclusions about the corresponding population parameter (the mean number of symptoms for clinically depressed adults).
Unfortunately, sample statistics are not perfect estimates of their corresponding population parameters. This is because there is a certain amount of random variability in any statistic from sample to sample. The mean number of depressive symptoms might be 8.73 in one sample of clinically depressed adults, 6.45 in a second sample, and 9.44 in a third—even though these samples are selected randomly from the same population. Similarly, the correlation (Pearson’s r ) between two variables might be +.24 in one sample, −.04 in a second sample, and +.15 in a third—again, even though these samples are selected randomly from the same population. This random variability in a statistic from sample to sample is called sampling error . (Note that the term error here refers to random variability and does not imply that anyone has made a mistake. No one “commits a sampling error.”)
One implication of this is that when there is a statistical relationship in a sample, it is not always clear that there is a statistical relationship in the population. A small difference between two group means in a sample might indicate that there is a small difference between the two group means in the population. But it could also be that there is no difference between the means in the population and that the difference in the sample is just a matter of sampling error. Similarly, a Pearson’s r value of −.29 in a sample might mean that there is a negative relationship in the population. But it could also be that there is no relationship in the population and that the relationship in the sample is just a matter of sampling error.
In fact, any statistical relationship in a sample can be interpreted in two ways:
The purpose of null hypothesis testing is simply to help researchers decide between these two interpretations.
Null hypothesis testing is a formal approach to deciding between two interpretations of a statistical relationship in a sample. One interpretation is called the null hypothesis (often symbolized H 0 and read as “H-naught”). This is the idea that there is no relationship in the population and that the relationship in the sample reflects only sampling error. Informally, the null hypothesis is that the sample relationship “occurred by chance.” The other interpretation is called the alternative hypothesis (often symbolized as H 1 ). This is the idea that there is a relationship in the population and that the relationship in the sample reflects this relationship in the population.
Again, every statistical relationship in a sample can be interpreted in either of these two ways: It might have occurred by chance, or it might reflect a relationship in the population. So researchers need a way to decide between them. Although there are many specific null hypothesis testing techniques, they are all based on the same general logic. The steps are as follows:
Following this logic, we can begin to understand why Mehl and his colleagues concluded that there is no difference in talkativeness between women and men in the population. In essence, they asked the following question: “If there were no difference in the population, how likely is it that we would find a small difference of d = 0.06 in our sample?” Their answer to this question was that this sample relationship would be fairly likely if the null hypothesis were true. Therefore, they retained the null hypothesis—concluding that there is no evidence of a sex difference in the population. We can also see why Kanner and his colleagues concluded that there is a correlation between hassles and symptoms in the population. They asked, “If the null hypothesis were true, how likely is it that we would find a strong correlation of +.60 in our sample?” Their answer to this question was that this sample relationship would be fairly unlikely if the null hypothesis were true. Therefore, they rejected the null hypothesis in favour of the alternative hypothesis—concluding that there is a positive correlation between these variables in the population.
A crucial step in null hypothesis testing is finding the likelihood of the sample result if the null hypothesis were true. This probability is called the p value . A low p value means that the sample result would be unlikely if the null hypothesis were true and leads to the rejection of the null hypothesis. A high p value means that the sample result would be likely if the null hypothesis were true and leads to the retention of the null hypothesis. But how low must the p value be before the sample result is considered unlikely enough to reject the null hypothesis? In null hypothesis testing, this criterion is called α (alpha) and is almost always set to .05. If there is less than a 5% chance of a result as extreme as the sample result if the null hypothesis were true, then the null hypothesis is rejected. When this happens, the result is said to be statistically significant . If there is greater than a 5% chance of a result as extreme as the sample result when the null hypothesis is true, then the null hypothesis is retained. This does not necessarily mean that the researcher accepts the null hypothesis as true—only that there is not currently enough evidence to conclude that it is true. Researchers often use the expression “fail to reject the null hypothesis” rather than “retain the null hypothesis,” but they never use the expression “accept the null hypothesis.”
The Misunderstood p Value
The p value is one of the most misunderstood quantities in psychological research (Cohen, 1994) [1] . Even professional researchers misinterpret it, and it is not unusual for such misinterpretations to appear in statistics textbooks!
The most common misinterpretation is that the p value is the probability that the null hypothesis is true—that the sample result occurred by chance. For example, a misguided researcher might say that because the p value is .02, there is only a 2% chance that the result is due to chance and a 98% chance that it reflects a real relationship in the population. But this is incorrect . The p value is really the probability of a result at least as extreme as the sample result if the null hypothesis were true. So a p value of .02 means that if the null hypothesis were true, a sample result this extreme would occur only 2% of the time.
You can avoid this misunderstanding by remembering that the p value is not the probability that any particular hypothesis is true or false. Instead, it is the probability of obtaining the sample result if the null hypothesis were true.
Recall that null hypothesis testing involves answering the question, “If the null hypothesis were true, what is the probability of a sample result as extreme as this one?” In other words, “What is the p value?” It can be helpful to see that the answer to this question depends on just two considerations: the strength of the relationship and the size of the sample. Specifically, the stronger the sample relationship and the larger the sample, the less likely the result would be if the null hypothesis were true. That is, the lower the p value. This should make sense. Imagine a study in which a sample of 500 women is compared with a sample of 500 men in terms of some psychological characteristic, and Cohen’s d is a strong 0.50. If there were really no sex difference in the population, then a result this strong based on such a large sample should seem highly unlikely. Now imagine a similar study in which a sample of three women is compared with a sample of three men, and Cohen’s d is a weak 0.10. If there were no sex difference in the population, then a relationship this weak based on such a small sample should seem likely. And this is precisely why the null hypothesis would be rejected in the first example and retained in the second.
Of course, sometimes the result can be weak and the sample large, or the result can be strong and the sample small. In these cases, the two considerations trade off against each other so that a weak result can be statistically significant if the sample is large enough and a strong relationship can be statistically significant even if the sample is small. Table 13.1 shows roughly how relationship strength and sample size combine to determine whether a sample result is statistically significant. The columns of the table represent the three levels of relationship strength: weak, medium, and strong. The rows represent four sample sizes that can be considered small, medium, large, and extra large in the context of psychological research. Thus each cell in the table represents a combination of relationship strength and sample size. If a cell contains the word Yes , then this combination would be statistically significant for both Cohen’s d and Pearson’s r . If it contains the word No , then it would not be statistically significant for either. There is one cell where the decision for d and r would be different and another where it might be different depending on some additional considerations, which are discussed in Section 13.2 “Some Basic Null Hypothesis Tests”
Sample Size | Weak relationship | Medium-strength relationship | Strong relationship |
---|---|---|---|
Small ( = 20) | No | No | = Maybe = Yes |
Medium ( = 50) | No | Yes | Yes |
Large ( = 100) | = Yes = No | Yes | Yes |
Extra large ( = 500) | Yes | Yes | Yes |
Although Table 13.1 provides only a rough guideline, it shows very clearly that weak relationships based on medium or small samples are never statistically significant and that strong relationships based on medium or larger samples are always statistically significant. If you keep this lesson in mind, you will often know whether a result is statistically significant based on the descriptive statistics alone. It is extremely useful to be able to develop this kind of intuitive judgment. One reason is that it allows you to develop expectations about how your formal null hypothesis tests are going to come out, which in turn allows you to detect problems in your analyses. For example, if your sample relationship is strong and your sample is medium, then you would expect to reject the null hypothesis. If for some reason your formal null hypothesis test indicates otherwise, then you need to double-check your computations and interpretations. A second reason is that the ability to make this kind of intuitive judgment is an indication that you understand the basic logic of this approach in addition to being able to do the computations.
Table 13.1 illustrates another extremely important point. A statistically significant result is not necessarily a strong one. Even a very weak result can be statistically significant if it is based on a large enough sample. This is closely related to Janet Shibley Hyde’s argument about sex differences (Hyde, 2007) [2] . The differences between women and men in mathematical problem solving and leadership ability are statistically significant. But the word significant can cause people to interpret these differences as strong and important—perhaps even important enough to influence the college courses they take or even who they vote for. As we have seen, however, these statistically significant differences are actually quite weak—perhaps even “trivial.”
This is why it is important to distinguish between the statistical significance of a result and the practical significance of that result. Practical significance refers to the importance or usefulness of the result in some real-world context. Many sex differences are statistically significant—and may even be interesting for purely scientific reasons—but they are not practically significant. In clinical practice, this same concept is often referred to as “clinical significance.” For example, a study on a new treatment for social phobia might show that it produces a statistically significant positive effect. Yet this effect still might not be strong enough to justify the time, effort, and other costs of putting it into practice—especially if easier and cheaper treatments that work almost as well already exist. Although statistically significant, this result would be said to lack practical or clinical significance.
Key Takeaways
“Null Hypothesis” long description: A comic depicting a man and a woman talking in the foreground. In the background is a child working at a desk. The man says to the woman, “I can’t believe schools are still teaching kids about the null hypothesis. I remember reading a big study that conclusively disproved it years ago.” [Return to “Null Hypothesis”]
“Conditional Risk” long description: A comic depicting two hikers beside a tree during a thunderstorm. A bolt of lightning goes “crack” in the dark sky as thunder booms. One of the hikers says, “Whoa! We should get inside!” The other hiker says, “It’s okay! Lightning only kills about 45 Americans a year, so the chances of dying are only one in 7,000,000. Let’s go on!” The comic’s caption says, “The annual death rate among people who know that statistic is one in six.” [Return to “Conditional Risk”]
Values in a population that correspond to variables measured in a study.
The random variability in a statistic from sample to sample.
A formal approach to deciding between two interpretations of a statistical relationship in a sample.
The idea that there is no relationship in the population and that the relationship in the sample reflects only sampling error.
The idea that there is a relationship in the population and that the relationship in the sample reflects this relationship in the population.
When the relationship found in the sample would be extremely unlikely, the idea that the relationship occurred “by chance” is rejected.
When the relationship found in the sample is likely to have occurred by chance, the null hypothesis is not rejected.
The probability that, if the null hypothesis were true, the result found in the sample would occur.
How low the p value must be before the sample result is considered unlikely in null hypothesis testing.
When there is less than a 5% chance of a result as extreme as the sample result occurring and the null hypothesis is rejected.
Research Methods in Psychology - 2nd Canadian Edition Copyright © 2015 by Paul C. Price, Rajiv Jhangiani, & I-Chant A. Chiang is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License , except where otherwise noted.
Hypothesis testing, the null and alternative hypothesis.
In order to undertake hypothesis testing you need to express your research hypothesis as a null and alternative hypothesis. The null hypothesis and alternative hypothesis are statements regarding the differences or effects that occur in the population. You will use your sample to test which statement (i.e., the null hypothesis or alternative hypothesis) is most likely (although technically, you test the evidence against the null hypothesis). So, with respect to our teaching example, the null and alternative hypothesis will reflect statements about all statistics students on graduate management courses.
The null hypothesis is essentially the "devil's advocate" position. That is, it assumes that whatever you are trying to prove did not happen ( hint: it usually states that something equals zero). For example, the two different teaching methods did not result in different exam performances (i.e., zero difference). Another example might be that there is no relationship between anxiety and athletic performance (i.e., the slope is zero). The alternative hypothesis states the opposite and is usually the hypothesis you are trying to prove (e.g., the two different teaching methods did result in different exam performances). Initially, you can state these hypotheses in more general terms (e.g., using terms like "effect", "relationship", etc.), as shown below for the teaching methods example:
Null Hypotheses (H ): | Undertaking seminar classes has no effect on students' performance. |
Alternative Hypothesis (H ): | Undertaking seminar class has a positive effect on students' performance. |
Depending on how you want to "summarize" the exam performances will determine how you might want to write a more specific null and alternative hypothesis. For example, you could compare the mean exam performance of each group (i.e., the "seminar" group and the "lectures-only" group). This is what we will demonstrate here, but other options include comparing the distributions , medians , amongst other things. As such, we can state:
Null Hypotheses (H ): | The mean exam mark for the "seminar" and "lecture-only" teaching methods is the same in the population. |
Alternative Hypothesis (H ): | The mean exam mark for the "seminar" and "lecture-only" teaching methods is not the same in the population. |
Now that you have identified the null and alternative hypotheses, you need to find evidence and develop a strategy for declaring your "support" for either the null or alternative hypothesis. We can do this using some statistical theory and some arbitrary cut-off points. Both these issues are dealt with next.
The level of statistical significance is often expressed as the so-called p -value . Depending on the statistical test you have chosen, you will calculate a probability (i.e., the p -value) of observing your sample results (or more extreme) given that the null hypothesis is true . Another way of phrasing this is to consider the probability that a difference in a mean score (or other statistic) could have arisen based on the assumption that there really is no difference. Let us consider this statement with respect to our example where we are interested in the difference in mean exam performance between two different teaching methods. If there really is no difference between the two teaching methods in the population (i.e., given that the null hypothesis is true), how likely would it be to see a difference in the mean exam performance between the two teaching methods as large as (or larger than) that which has been observed in your sample?
So, you might get a p -value such as 0.03 (i.e., p = .03). This means that there is a 3% chance of finding a difference as large as (or larger than) the one in your study given that the null hypothesis is true. However, you want to know whether this is "statistically significant". Typically, if there was a 5% or less chance (5 times in 100 or less) that the difference in the mean exam performance between the two teaching methods (or whatever statistic you are using) is as different as observed given the null hypothesis is true, you would reject the null hypothesis and accept the alternative hypothesis. Alternately, if the chance was greater than 5% (5 times in 100 or more), you would fail to reject the null hypothesis and would not accept the alternative hypothesis. As such, in this example where p = .03, we would reject the null hypothesis and accept the alternative hypothesis. We reject it because at a significance level of 0.03 (i.e., less than a 5% chance), the result we obtained could happen too frequently for us to be confident that it was the two teaching methods that had an effect on exam performance.
Whilst there is relatively little justification why a significance level of 0.05 is used rather than 0.01 or 0.10, for example, it is widely used in academic research. However, if you want to be particularly confident in your results, you can set a more stringent level of 0.01 (a 1% chance or less; 1 in 100 chance or less).
When considering whether we reject the null hypothesis and accept the alternative hypothesis, we need to consider the direction of the alternative hypothesis statement. For example, the alternative hypothesis that was stated earlier is:
Alternative Hypothesis (H ): | Undertaking seminar classes has a positive effect on students' performance. |
The alternative hypothesis tells us two things. First, what predictions did we make about the effect of the independent variable(s) on the dependent variable(s)? Second, what was the predicted direction of this effect? Let's use our example to highlight these two points.
Sarah predicted that her teaching method (independent variable: teaching method), whereby she not only required her students to attend lectures, but also seminars, would have a positive effect (that is, increased) students' performance (dependent variable: exam marks). If an alternative hypothesis has a direction (and this is how you want to test it), the hypothesis is one-tailed. That is, it predicts direction of the effect. If the alternative hypothesis has stated that the effect was expected to be negative, this is also a one-tailed hypothesis.
Alternatively, a two-tailed prediction means that we do not make a choice over the direction that the effect of the experiment takes. Rather, it simply implies that the effect could be negative or positive. If Sarah had made a two-tailed prediction, the alternative hypothesis might have been:
Alternative Hypothesis (H ): | Undertaking seminar classes has an effect on students' performance. |
In other words, we simply take out the word "positive", which implies the direction of our effect. In our example, making a two-tailed prediction may seem strange. After all, it would be logical to expect that "extra" tuition (going to seminar classes as well as lectures) would either have a positive effect on students' performance or no effect at all, but certainly not a negative effect. However, this is just our opinion (and hope) and certainly does not mean that we will get the effect we expect. Generally speaking, making a one-tail prediction (i.e., and testing for it this way) is frowned upon as it usually reflects the hope of a researcher rather than any certainty that it will happen. Notable exceptions to this rule are when there is only one possible way in which a change could occur. This can happen, for example, when biological activity/presence in measured. That is, a protein might be "dormant" and the stimulus you are using can only possibly "wake it up" (i.e., it cannot possibly reduce the activity of a "dormant" protein). In addition, for some statistical tests, one-tailed tests are not possible.
Let's return finally to the question of whether we reject or fail to reject the null hypothesis.
If our statistical analysis shows that the significance level is below the cut-off value we have set (e.g., either 0.05 or 0.01), we reject the null hypothesis and accept the alternative hypothesis. Alternatively, if the significance level is above the cut-off value, we fail to reject the null hypothesis and cannot accept the alternative hypothesis. You should note that you cannot accept the null hypothesis, but only find evidence against it.
Statistics By Jim
Making statistics intuitive
By Jim Frost 69 Comments
Failing to reject the null hypothesis is an odd way to state that the results of your hypothesis test are not statistically significant. Why the peculiar phrasing? “Fail to reject” sounds like one of those double negatives that writing classes taught you to avoid. What does it mean exactly? There’s an excellent reason for the odd wording!
In this post, learn what it means when you fail to reject the null hypothesis and why that’s the correct wording. While accepting the null hypothesis sounds more straightforward, it is not statistically correct!
Before proceeding, let’s recap some necessary information. In all statistical hypothesis tests, you have the following two hypotheses:
We assume that the null hypothesis is correct until we have enough evidence to suggest otherwise.
After you perform a hypothesis test, there are only two possible outcomes.
Related posts : Hypothesis Testing Overview and The Null Hypothesis
To understand why we don’t accept the null, consider the fact that you can’t prove a negative. A lack of evidence only means that you haven’t proven that something exists. It does not prove that something doesn’t exist. It might exist, but your study missed it. That’s a huge difference and it is the reason for the convoluted wording. Let’s look at several analogies.
Lack of proof doesn’t represent proof that something doesn’t exist!
Perhaps the prosecutor conducted a shoddy investigation and missed clues? Or, the defendant successfully covered his tracks? Consequently, the verdict in these cases is “not guilty.” That judgment doesn’t say the defendant is proven innocent, just that there wasn’t enough evidence to move the jury from the default assumption of innocence.
The hypothesis test assesses the evidence in your sample. If your test fails to detect an effect, it’s not proof that the effect doesn’t exist. It just means your sample contained an insufficient amount of evidence to conclude that it exists. Like the species that were presumed extinct, or the prosecutor who missed clues, the effect might exist in the overall population but not in your particular sample. Consequently, the test results fail to reject the null hypothesis, which is analogous to a “not guilty” verdict in a trial. There just wasn’t enough evidence to move the hypothesis test from the default position that the null is true.
The critical point across these analogies is that a lack of evidence does not prove something does not exist—just that you didn’t find it in your specific investigation. Hence, you never accept the null hypothesis.
Related post : The Significance Level as an Evidentiary Standard
Accepting the null hypothesis would indicate that you’ve proven an effect doesn’t exist. As you’ve seen, that’s not the case at all. You can’t prove a negative! Instead, the strength of your evidence falls short of being able to reject the null. Consequently, we fail to reject it.
Failing to reject the null indicates that our sample did not provide sufficient evidence to conclude that the effect exists. However, at the same time, that lack of evidence doesn’t prove that the effect does not exist. Capturing all that information leads to the convoluted wording!
What are the possible implications of failing to reject the null hypothesis? Let’s work through them.
First, it is possible that the effect truly doesn’t exist in the population, which is why your hypothesis test didn’t detect it in the sample. Makes sense, right? While that is one possibility, it doesn’t end there.
Another possibility is that the effect exists in the population, but the test didn’t detect it for a variety of reasons. These reasons include the following:
Notice how studies that collect a small amount of data or low-quality data are likely to miss an effect that exists? These studies had inadequate statistical power to detect the effect. We certainly don’t want to take results from low-quality studies as proof that something doesn’t exist!
However, failing to detect an effect does not necessarily mean a study is low-quality. Random chance in the sampling process can work against even the best research projects!
If you’re learning about hypothesis testing and like the approach I use in my blog, check out my eBook!
May 8, 2024 at 9:08 am
Thank you very much for explaining the topic. It brings clarity and makes statistics very simple and interesting. Its helping me in the field of Medical Research.
February 26, 2024 at 7:54 pm
Hi Jim, My question is that can I reverse Null hyposthesis and start with Null: µ1 ≠ µ2 ? Then, if I can reject Null, I will end up with µ1=µ2 for mean comparison and this what I am looking for. But isn’t this cheating?
February 26, 2024 at 11:41 pm
That can be done but it requires you to revamp the entire test. Keep in mind that the reason you normally start out with the null equating to no relationship is because the researchers typically want to prove that a relationship or effect exists. This format forces the researchers to collect a substantial amount of high quality data to have a chance at demonstrating that an effect exists. If they collect a small sample and/or poor quality (e.g., noisy or imprecise), then the results default back to the null stating that no effect exists. So, they have to collect good data and work hard to get findings that suggest the effect exists.
There are tests that flip it around as you suggest where the null states that a relationship does exist. For example, researchers perform an equivalency test when they want to show that there is no difference. That the groups are equal. The test is designed such that it requires a good sample size and high quality data to have a chance at proving equivalency. If they have a small sample size and/or poor quality data, the results default back to the groups being unequal, which is not what they want to show.
So, choose the null hypothesis and corresponding analysis based on what you hope to find. Choose the null hypothesis that forces you to work hard to reject it and get the results that you want. It forces you to collect better evidence to make your case and the results default back to what you don’t want if you do a poor job.
I hope that makes sense!
October 13, 2023 at 5:10 am
Really appreciate how you have been able to explain something difficult in very simple terms. Also covering why you can’t accept a null hypothesis – something which I think is frequently missed. Thank you, Jim.
February 22, 2022 at 11:18 am
Hi Jim, I really appreciate your blog, making difficult things sound simple is a great gift.
I have a doubt about the p-value. You said there are two options when it comes to hypothesis tests results . Reject or failing to reject the null, depending on the p-value and your significant level.
But… a P-value of 0,001 means a stronger evidence than a P-value of 0,01? ( both with a significant level of 5%. Or It doesn`t matter, and just every p-Value under your significant level means the same burden of evidence against the null?
I hope I made my point clear. Thanks a lot for your time.
February 23, 2022 at 9:06 pm
There are different schools of thought about this question. The traditional approach is clear cut. Your results are statistically significance when your p-value is less than or equal to your significance level. When the p-value is greater than the significance level, your results are not significant.
However, as you point out, lower p-values indicate stronger evidence against the null hypothesis. I write about this aspect of p-values in several articles, interpreting p-values (near the end) and p-values and reproducibility .
Personally, I consider both aspects. P-values near 0.05 provide weak evidence. Consequently, I’d be willing to say that p-values less than or equal to 0.05 are statistically significant, but when they’re near 0.05, I’d consider it as a preliminary result that requires more research. However, if the p-value is less 0.01, or even better 0.001, then that’s much stronger evidence and I’ll give those results more weight in my evaluation.
If you read those two articles, I think you’ll see what I mean.
January 1, 2022 at 6:00 pm
HI, I have a quick question that you may be able to help me with. I am using SPSS and carrying out a Mann W U Test it says to retain the null hypothesis. The hypothesis is that males are faster than women at completing a task. So is that saying that they are or are not
January 1, 2022 at 8:17 pm
In that case, your sample data provides insufficient evidence to conclude that males are faster. The results do not prove that males and females are the same speed. You just don’t have enough evidence to say males are faster. In this post, I cover the reasons why you can’t prove the null is true.
November 23, 2021 at 5:36 pm
What if I have to prove in my hypothesis that there shouldn’t be any affect of treatment on patients? Can I say that if my null hypothesis is accepted i have got my results (no effect)? I am confused what to do in this situation. As for null hypothesis we always have to write it with some type of equality. What if I want my result to be what i have stated in null hypothesis i.e. no effect? How to write statements in this case? I am using non parametric test, Mann whitney u test
November 27, 2021 at 4:56 pm
You need to perform an equivalence test, which is a special type of procedure when you want to prove that the results are equal. The problem with a regular hypothesis test is that when you fail to reject the null, you’re not proving that they the outcomes are equal. You can fail to reject the null thanks to a small sample size, noisy data, or a small effect size even when the outcomes are truly different at the population level. An equivalence test sets things up so you need strong evidence to really show that two outcomes are equal.
Unfortunately, I don’t have any content for equivalence testing at this point, but you can read an article about it at Wikipedia: Equivalence Test .
August 13, 2021 at 9:41 pm
Great explanation and great analogies! Thanks.
August 11, 2021 at 2:02 am
I got problems with analysis. I did wound healing experiments with drugs treatment (total 9 groups). When I do the 2-way ANOVA in excel, I got the significant results in sample (Drug Treatment) and columns (Day, Timeline) . But I did not get the significantly results in interactions. Can I still reject the null hypothesis and continue the post-hoc test?
Thank you very much.
June 13, 2021 at 4:51 am
Hi Jim, There are so many books covering maths/programming related to statistics/DS, but may be hardly any book to develop an intuitive understanding. Thanks to you for filling up that gap. After statistics, hypothesis-testing, regression, will it be possible for you to write such books on more topics in DS such as trees, deep-learning etc.
I recently started with reading your book on hypothesis testing (just finished the first chapter). I have a question w.r.t the fuel cost example (from first chapter), where a random sample of 25 families (with sample mean 330.6) is taken. To do the hypothesis testing here, we are taking a sampling distribution with a mean of 260. Then based on the p-value and significance level, we find whether to reject or accept the null hypothesis. The entire decision (to accept or reject the null hypothesis) is based on the sampling distribution about which i have the following questions : a) we are assuming that the sampling distribution is normally distributed. what if it has some other distribution, how can we find that ? b) We have assumed that the sampling distribution is normally distributed and then further assumed that its mean is 260 (as required for the hypothesis testing). But we need the standard deviation as well to define the normal distribution, can you please let me know how do we find the standard deviation for the sampling distribution ? Thanks.
April 24, 2021 at 2:25 pm
Maybe its the idea of “Innocent until proven guilty”? Your Null assume the person is not guilty, and your alternative assumes the person is guilty, only when you have enough evidence (finding statistical significance P0.05 you have failed to reject null hypothesis, null stands,implying the person is not guilty. Or, the person remain innocent.. Correct me if you think it’s wrong but this is the way I interpreted.
April 25, 2021 at 5:10 pm
I used the courtroom/trial analogy within this post. Read that for more details. I’d agree with your general take on the issue except when you have enough evidence you actually reject the null, which in the trial means the defendant is found guilty.
April 17, 2021 at 6:10 am
Can regression analysis be done using 5 companies variables for predicting working capital management and profitability positive/negative relationship?
Also, does null hypothesis rejecting means whatsoever is stated in null hypothesis that is false proved through regression analysis?
I have very less knowledge about regression analysis. Please help me, Sir. As I have my project report due on next week. Thanks in advance!
April 18, 2021 at 10:48 pm
Hi Ahmed, yes, regression analysis can be used for the scenario you describe as long as you have the required data.
For more about the null hypothesis in relation to regression analysis, read my post about regression coefficients and their p-values . I describe the null hypothesis in it.
January 26, 2021 at 7:32 pm
With regards to the legal example above. While your explanation makes sense when simplified to this statistical level, from a legal perspective it is not correct. The presumption of innocence means one does not need to be proven innocent. They are innocent. The onus of proof lies with proving they are guilty. So if you can’t prove someones guilt then in fact you must accept the null hypothesis that they are innocent. It’s not a statistical test so a little bit misleading using it an example, although I see why you would.
If it were a statistical test, then we would probably be rather paranoid that everyone is a murderer but they just haven’t been proven to be one yet.
Great article though, a nice simple and thoughtout explanation.
January 26, 2021 at 9:11 pm
It seems like you misread my post. The hypothesis testing/legal analogy is very strong both in making the case and in the result.
In hypothesis testing, the data have to show beyond a reasonable doubt that the alternative hypothesis is true. In a court case, the prosecutor has to present sufficient evidence to show beyond a reasonable doubt that the defendant is guilty.
In terms of the test/case results. When the evidence (data) is insufficient, you fail to reject the null hypothesis but you do not conclude that the data proves the null is true. In a legal case that has insufficient evidence, the jury finds the defendant to be “not guilty” but they do not say that s/he is proven innocent. To your point specifically, it is not accurate to say that “not guilty” is the same as “proven innocent.”
It’s a very strong parallel.
January 9, 2021 at 11:45 am
Just a question, in my research on hypotheses for an assignment, I am finding it difficult to find an exact definition for a hypothesis itself. I know the defintion, but I’m looking for a citable explanation, any ideas?
January 10, 2021 at 1:37 am
To be clear, do you need to come up with a statistical hypothesis? That’s one where you’ll use a particular statistical hypothesis test. If so, I’ll need to know more about what you’re studying, your variables, and the type of hypothesis test you plan to use.
There are also scientific hypotheses that you’ll state in your proposals, study papers, etc. Those are different from statistical hypotheses (although related). However, those are very study area specific and I don’t cover those types on this blog because this is a statistical blog. But, if it’s a statistical hypothesis for a hypothesis test, then let me know the information I mention above and I can help you out!
November 7, 2020 at 8:33 am
Hi, good read, I’m kind of a novice here, so I’m trying to write a research paper, and I’m trying to make a hypothesis. however looking at the literature, there are contradicting results.
researcher A found that there is relationship between X and Y
however, researcher B found that there is no relationship between X and Y
therefore, what is the null hypothesis between X and y? do we choose what we assumed to be correct for our study? or is is somehow related to the alternative hypothesis? I’m confused.
thank you very much for the help.
November 8, 2020 at 12:07 am
Hypotheses for a statistical test are different than a researcher’s hypothesis. When you’re constructing the statistical hypothesis, you don’t need to consider what other researchers have found. Instead, you construct them so that the test only produces statistically significant results (rejecting the null) when your data provides strong evidence. I talk about that process in this post.
Typically, researchers are hoping to establish that an effect or relationship exists. Consequently, the null and alternative hypotheses are typically the following:
Null: The effect or relationship doesn’t not exist. Alternative: The effect or relationship does exist.
However, if you’re hoping to prove that there is no effect or no relationship, you then need to flip those hypotheses and use a special test, such as an equivalences test.
So, there’s no need to consider what researchers have found but instead what you’re looking for. In most cases, you are looking for an effect/relationship, so you’d go with the hypotheses as I show them above.
I hope that helps!
October 22, 2020 at 6:13 pm
Great, deep detailed answer. Appreciated!
September 16, 2020 at 12:03 pm
Thank you for explaining it too clearly. I have the following situation with a Box Bohnken design of three levels and three factors for multiple responses. F-value for second order model is not significant (failing to reject null hypothesis, p-value > 0.05) but, lack of fit of the model is not significant. What can you suggest me about statistical analysis?
September 17, 2020 at 2:42 am
Are your first order effects significant?
You want the lack of fit to be nonsignificant. If it’s significant, that means the model doesn’t fit the data well. So, you’re good there! 🙂
September 14, 2020 at 5:18 pm
thank you for all the explicit explanation on the subject.
However, i still got a question about “accepting the null hypothesis”. from textbook, the p-value is the probability that a statistic would take a value that is as extreme as or more extreme than that actually observed.
so, that’s why when p<0.01 we reject the null hypothesis, because it's too rare (p0.05, i can understand that for most cases we cannot accept the null, for example, if p=0.5, it means that the probability to get a statistic from the distribution is 0.5, which is totally random.
But how about when the p is very close to 1, like p=0.95, or p=0.99999999, can’t we say that the probability that the statistic is not from this distribution is less than 0.05, | or in another way, the probability that the statistic is from the distribution is almost 1. can’t we accept the null in such circumstance?
September 11, 2020 at 12:14 pm
Wow! This is beautifully explained. “Lack of proof doesn’t represent proof that something doesn’t exist!”. This kinda, hit me with such force. Can I then, use the same analogy for many other things in life? LOL! 🙂
H0 = God does not exist; H1 = God does exist; WE fail to reject H0 as there is no evidence.
Thank you sir, this has answered many of my questions, statistically speaking! No pun intended with the above.
September 11, 2020 at 4:58 pm
Hi, LOL, I’m glad it had such meaning for you! I’ll leave the determination about the existence of god up to each person, but in general, yes, I think statistical thinking can be helpful when applied to real life. It is important to realize that lack of proof truly is not proof that something doesn’t exist. But, I also consider other statistical concepts, such as confounders and sampling methodology, to be useful keeping in mind when I’m considering everyday life stuff–even when I’m not statistically analyzing it. Those concepts are generally helpful when trying to figure out what is going on in your life! Are there other alternative explanations? Is what you’re perceiving likely to be biased by something that’s affecting the “data” you can observe? Am I drawing a conclusion based on a large or small sample? How strong is the evidence?
A lot of those concepts are great considerations even when you’re just informally assessing and draw conclusions about things happening in your daily life.
August 13, 2020 at 12:04 am
Dear Jim, thanks for clarifying. absolutely, now it makes sense. the topic is murky but it is good to have your guidance, and be clear. I have not come across an instructor as clear in explaining as you do. Appreciate your direction. Thanks a lot, Geetanjali
August 15, 2020 at 3:48 pm
Hi Geetanjali,
I’m glad my website is helpful! That makes my day hearing that. Thanks so much for writing!
August 12, 2020 at 9:37 am
Hi Jim. I am doing data analyis for my masters thesis and my hypothesis testings were insignificant. And I am ok with that. But there is something bothering me. It is the low reliabilities of the 4-Items sub-scales (.55, .68, .75), though the overall alpha is good (.85). I just wonder if it is affecting my hypothesis testings.
August 11, 2020 at 9:23 pm
Thank you sir for replying, yes sir we it’s a RCT study.. where we did within and between the groups analysis and found p>0.05 in between the groups using Mann Whitney U test. So in such cases if the results comes like this we need to Mention that we failed reject the null hypothesis? Is that correct? Whether it tells that the study is inefficient as we couldn’t accept the alternative hypothesis. Thanks is advance.
August 11, 2020 at 9:43 pm
Hi Saumya, ah, this becomes clearer. When ask statistical questions, please be sure to include all relevant information because the details are extremely important. I didn’t know it was an RCT with a treatment and control group. Yes, given that your p-value is greater than your significance level, you fail to reject the null hypothesis. The results are not significant. The experiment provides insufficient evidence to conclude that the outcome in the treatment group is different than the control group.
By the way, you never accept the alternative hypothesis (or the null). The two options are to either reject the null or fail to reject the null. In your case, you fail to reject the null hypothesis.
I hope this helps!
August 11, 2020 at 9:41 am
Sir, p value is0.05, by which we interpret that both the groups are equally effective. In this case I had to reject the alternative hypothesis/ failed to reject null hypothessis.
August 11, 2020 at 12:37 am
sir, within the group analysis the p value for both the groups is significant (p0.05, by which we interpret that though both the treatments are effective, there in no difference between the efficacy of one over the other.. in other words.. no intervention is superior and both are equally effective.
August 11, 2020 at 2:45 pm
Thanks for the additional details. If I understand correctly, there were separate analyses before that determined each treatment had a statistically significance effect. However, when you compare the two treatments, there difference between them is not statistically significant.
If that’s the case, the interpretation is fairly straightforward. You have evidence that suggests that both treatments are effective. However, you don’t have evidence to conclude that one is better than the other.
August 10, 2020 at 9:26 am
Hi thank you for a wonderful explanation. I have a doubt: My Null hypothesis says: no significant difference between the effect fo A and B treatment Alternative hypothesis: there will be significant difference between the effect of A and B treatment. and my results show that i fail to reject null hypothesis.. Both the treatments were effective, but not significant difference.. how do I interpret this?
August 10, 2020 at 1:32 pm
First, I need to ask you a question. If your p-value is not significant, and so you fail to reject the null, why do you say that the treatment is effective? I can answer you question better after knowing the reason you say that. Thanks!
August 9, 2020 at 9:40 am
Dear Jim, thanks for making stats much more understandable and answering all question so painstakingly. I understand the following on p value and null. If our sample yields a p value of .01, it means that that there is a 1% probability that our kind of sample exists in the population. that is a rare event. So why shouldn’t we accept the HO as the probability of our event was v rare. Pls can you correct me. Thanks, G
August 10, 2020 at 1:53 pm
That’s a great question! They key thing to remember is that p-values are a conditional probability. P-value calculations assume that the null hypothesis is true. So, a p-value of 0.01 indicates that there is a 1% probability of observing your sample results, or more extreme, *IF* the null hypothesis is true.
The kicker is that we don’t whether the null is true or not. But, using this process does limit the likelihood of a false positive to your significance level (alpha). But, we don’t know whether the null is true and you had an unusual sample or whether the null is false. Usually, with a p-value of 0.01, we’d reject the null and conclude it is false.
I hope that answered your question. This topic can be murky and I wasn’t quite clear which part you needed clarification.
August 4, 2020 at 11:16 pm
Thank you for the wonderful explanation. However, I was just curious to know that what if in a particular test, we get a p-value less than the level of significance, leading to evidence against null hypothesis. Is there any possibility that our interpretation of population effect might be wrong due to randomness of samples? Also, how do we conclude whether the evidence is enough for our alternate hypothesis?
August 4, 2020 at 11:55 pm
Hi Abhilash,
Yes, unfortunately, when you’re working with samples, there’s always the possibility that random chance will cause your sample to not represent the population. For information about these errors, read my post about the types of errors in hypothesis testing .
In hypothesis testing, you determine whether your evidence is strong enough to reject the null. You don’t accept the alternative hypothesis. I cover that in my post about interpreting p-values .
August 1, 2020 at 3:50 pm
Hi, I am trying to interpret this phenomenon after my research. The null hypothesis states that “The use of combined drugs A and B does not lower blood pressure when compared to if drug A or B is used singularly”
The alternate hypothesis states: The use of combined drugs A and B lower blood pressure compared to if drug A or B is used singularly.
At the end of the study, majority of the people did not actually combine drugs A and B, rather indicated they either used drug A or drug B but not a combination. I am finding it very difficult to explain this outcome more so that it is a descriptive research. Please how do I go about this? Thanks a lot
June 22, 2020 at 10:01 am
What confuses me is how we set/determine the null hypothesis? For example stating that two sets of data are either no different or have no relationship will give completely different outcomes, so which is correct? Is the null that they are different or the same?
June 22, 2020 at 2:16 pm
Typically, the null states there is no effect/no relationship. That’s true for 99% of hypothesis tests. However, there are some equivalence tests where you are trying to prove that the groups are equal. In that case, the null hypothesis states that groups are not equal.
The null hypothesis is typically what you *don’t* want to find. You have to work hard, design a good experiment, collect good data, and end up with sufficient evidence to favor the alternative hypothesis. Usually in an experiment you want to find an effect. So, usually the null states there is no effect and you have get good evidence to reject that notion.
However, there are a few tests where you actually want to prove something is equal, so you need the null to state that they’re not equal in those cases and then do all the hard work and gather good data to suggest that they are equal. Basically, set up the hypothesis so it takes a good experiment and solid evidence to be able to reject the null and favor the hypothesis that you’re hoping is true.
June 5, 2020 at 11:54 am
Thank you for the explanation. I have one question that. If Null hypothesis is failed to reject than is possible to interpret the analysis further?
June 5, 2020 at 7:36 pm
Hi Mottakin,
Typically, if your result is that you fail to reject the null hypothesis there’s not much further interpretation. You don’t want to be in a situation where you’re endlessly trying new things on a quest for obtaining significant results. That’s data mining.
May 25, 2020 at 7:55 am
I hope all is well. I am enjoying your blog. I am not a statistician, however, I use statistical formulae to provide insight on the direction in which data is going. I have used both the regression analysis and a T-Test. I know that both use a null hypothesis and an alternative hypothesis. Could you please clarity the difference between a regression analysis and a T-Test? Are there conditions where one is a better option than the other?
May 26, 2020 at 9:18 pm
t-Tests compare the means of one or two groups. Regression analysis typically describes the relationships between a set of independent variables and the dependent variables. Interestingly, you can actually use regression analysis to perform a t-test. However, that would be overkill. If you just want to compare the means of one or two groups, use a t-test. Read my post about performing t-tests in Excel to see what they can do. If you have a more complex model than just comparing one or two means, regression might be the way to go. Read my post about when to use regression analysis .
May 12, 2020 at 5:45 pm
This article is really enlightening but there is still some darkness looming around. I see that low p-values mean strong evidence against null hypothesis and finding such a sample is highly unlikely when null hypothesis is true. So , is it OK to say that when p-value is 0.01 , it was very unlikely to have found such a sample but we still found it and hence finding such a sample has not occurred just by chance which leads towards rejection of null hypothesis.
May 12, 2020 at 11:16 pm
That’s mostly correct. I wouldn’t say, “has not occurred by chance.” So, when you get a very low p-value it does mean that you are unlikely to obtain that sample if the null is true. However, once you obtain that result, you don’t know for sure which of the two occurred:
You really don’t know for sure. However, by the decision making results you set about the strength of evidence required to reject the null, you conclude that the effect exists. Just always be aware that it could be a false positive.
That’s all a long way of saying that your sample was unlikely to occur by chance if the null is true.
April 29, 2020 at 11:59 am
Why do we consult the statistical tables to find out the critical values of our test statistics?
April 30, 2020 at 5:05 pm
Statistical tables started back in the “olden days” when computers didn’t exist. You’d calculate the test statistic value for your sample. Then, you’d look in the appropriate table and using the degrees of freedom for your design and find the critical values for the test statistic. If the value of your test statistics exceeded the critical value, your results were statistically significant.
With powerful and readily available computers, researchers could analyze their data and calculate the p-values and compare them directly to the significance level.
I hope that answers your question!
April 15, 2020 at 10:12 am
If we are not able to reject the null hypothesis. What could be the solution?
April 16, 2020 at 11:13 pm
Hi Shazzad,
The first thing to recognize is that failing to reject the null hypothesis might not be an error. If the null hypothesis is false, then the correct outcome is failing to reject the null.
However, if the null hypothesis is false and you fail to reject, it is a type II error, or a false negative. Read my post about types of errors in hypothesis tests for more information.
This type of error can occur for a variety of reasons, including the following:
There are various other possibilities, but those are several common problems.
April 14, 2020 at 12:19 pm
Thank you so much for this article! I am taking my first Statistics class in college and I have one question about this.
I understand that the default position is that the null is correct, and you explained that (just like a court case), the sample evidence must EXCEED the “evidentiary standard” (which is the significance level) to conclude that an effect/relationship exists. And, if an effect/relationship exists, that means that it’s the alternative hypothesis that “wins” (not sure if that’s the correct way of wording it, but I’m trying to make this as simple as possible in my head!).
But what I don’t understand is that if the P-value is GREATER than the significance value, we fail to reject the null….because shouldn’t a higher P-value, mean that our sample evidence EXCEEDS the evidentiary standard (aka the significance level), and therefore an effect/relationship exists? In my mind it would make more sense to reject the null, because our P-value is higher and therefore we have enough evidence to reject the null.
I hope I worded this in a way that makes sense. Thank you in advance!
April 14, 2020 at 10:42 pm
That’s a great question. The key thing to remember is that higher p-values correspond to weaker evidence against the null hypothesis. A high p-value indicates that your sample is likely (high probability = high p-value) if the null hypothesis is true. Conversely, low p-values represent stronger evidence against the null. You were unlikely (low probability = low p-value) to have collect a sample with the measured characteristics if the null is true.
So, there is negative correlation between p-values and strength of evidence against the null hypothesis. Low p-values indicate stronger evidence. Higher p-value represent weaker evidence.
In a nutshell, you reject the null hypothesis with a low p-value because it indicates your sample data are unusual if the null is true. When it’s unusual enough, you reject the null.
March 5, 2020 at 11:10 am
There is something I am confused about. If our significance level is .05 and our resulting p-value is .02 (thus the strength of our evidence is strong enough to reject the null hypothesis), do we state that we reject the null hypothesis with 95% confidence or 98% confidence?
My guess is our confidence level is 95% since or alpha was .05. But if the strength of our evidence is 98%, why wouldn’t we use that as our stated confidence in our results?
March 5, 2020 at 4:19 pm
Hi Michael,
You’d state that you can reject the null at a significance level of 5% or conversely at the 95% confidence level. A key reason is to avoid cherry picking your results. In other words, you don’t want to choose the significance level based on your results.
Consequently, set the significance level/confidence level before performing your analysis. Then, use those preset levels to determine statistical significance. I always recommend including the exact p-value when you report on statistical significance. Exact p-values do provide information about the strength of evidence against the null.
March 5, 2020 at 9:58 am
Thank you for sharing this knowledge , it is very appropriate in explaining some observations in the study of forest biodiversity.
March 4, 2020 at 2:01 am
Thank you so much. This provides for my research
March 3, 2020 at 7:28 pm
If one couples this with what they call estimated monetary value of risk in risk management, one can take better decisions.
March 3, 2020 at 3:12 pm
Thank you for providing this clear insight.
March 3, 2020 at 3:29 am
Nice article Jim. The risk of such failure obviously reduces when a lower significance level is specified.One benefits most by reading this article in conjunction with your other article “Understanding Significance Levels in Statistics”.
March 3, 2020 at 2:43 am
That’s fine. My question is why doesn’t the numerical value of type 1 error coincide with the significance level in the backdrop that the type 1 error and the significance level are both the same ? I hope you got my question.
March 3, 2020 at 3:30 am
Hi, they are equal. As I indicated, the significance level equals the type I error rate.
March 3, 2020 at 1:27 am
Kindly elighten me on one confusion. We set out our significance level before setting our hypothesis. When we calculate the type 1 error, which happens to be a significance level, the numerical value doesn’t equals (either undermining value comes out or an exceeding value comescout ) our significance level that was preassigned. Why is this so ?
March 3, 2020 at 2:24 am
Hi Ratnadeep,
You’re correct. The significance level (alpha) is the same as the type I error rate. However, you compare the p-value to the significance level. It’s the p-value that can be greater than or less than the significance level.
The significance level is the evidentiary standard. How strong does the evidence in your sample need to be before you can reject the null? The p-value indicates the strength of the evidence that is present in your sample. By comparing the p-value to the significance level, you’re comparing the actual strength of the sample evidence to the evidentiary standard to determine whether your sample evidence is strong enough to conclude that the effect exists in the population.
I write about this in my post about the understanding significance levels . I think that will help answer your questions!
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.
Table of contents:
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 .
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 .
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.
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.
Also, read:
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
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.
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).
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.
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. |
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.
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.
Hypothesis testing is defined as a form of inferential statistics, which allows making conclusions from the entire population based on the sample representative.
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.
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.
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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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 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.
When your sample contains sufficient evidence, you can reject the null and conclude that the effect is statistically significant. Statisticians often denote the null hypothesis as H 0 or H A.. 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.
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.
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 ...
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.
The null hypothesis and the alternative hypothesis are types of conjectures used in statistical tests to make statistical inferences, which are formal methods of reaching conclusions and separating scientific claims from statistical noise.. The statement being tested in a test of statistical significance is called the null hypothesis. The test of significance is designed to assess the strength ...
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.
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.
Null Hypothesis Examples. "Hyperactivity is unrelated to eating sugar " is an example of a null hypothesis. If the hypothesis is tested and found to be false, using statistics, then a connection between hyperactivity and sugar ingestion may be indicated. A significance test is the most common statistical test used to establish confidence in a ...
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: It is a statement about the population that either is believed to be true or is used to put forth an argument unless it can be shown to be incorrect beyond a reasonable doubt.
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 ...
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.
The alternate hypothesis is usually your initial hypothesis that predicts a relationship between variables. The null hypothesis is a prediction of no relationship between the variables you are interested in. Hypothesis testing example. You want to test whether there is a relationship between gender and height. Based on your knowledge of human ...
A hypothesis test is a formal statistical test we use to reject or fail to reject a statistical hypothesis. We always use the following steps to perform a hypothesis test: Step 1: State the null and alternative hypotheses. The null hypothesis, denoted as H0, is the hypothesis that the sample data occurs purely from chance.
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H 0 (Null Hypothesis): Population parameter =, ≤, ≥ some value. H A (Alternative Hypothesis): Population parameter <, >, ≠ some value. Note that the null hypothesis always contains the equal sign. We interpret the hypotheses as follows: Null hypothesis: The sample data provides no evidence to support some claim being made by an individual.
6. Write a null hypothesis. If your research involves statistical hypothesis testing, you will also have to write a null hypothesis. The null hypothesis is the default position that there is no association between the variables. The null hypothesis is written as H 0, while the alternative hypothesis is H 1 or H a.
16.3.5 Step 5: Determine the probability of the data under the null hypothesis. This is the step where NHST starts to violate our intuition - rather than determining the likelihood that the null hypothesis is true given the data, we instead determine the likelihood of the data under the null hypothesis - because we started out by assuming that the null hypothesis is true!
Write a statistical null hypothesis as a mathematical equation, such as. μ 1 = μ 2 {\displaystyle \mu _ {1}=\mu _ {2}} if you're comparing group means. Adjust the format of your null hypothesis to match the statistical method you used to test it, such as using "mean" if you're comparing the mean between 2 groups.
A crucial step in null hypothesis testing is finding the likelihood of the sample result if the null hypothesis were true. This probability is called the p value. A low p value means that the sample result would be unlikely if the null hypothesis were true and leads to the rejection of the null hypothesis. A high p value means that the sample ...
Rejecting or failing to reject the null hypothesis. Let's return finally to the question of whether we reject or fail to reject the null hypothesis. If our statistical analysis shows that the significance level is below the cut-off value we have set (e.g., either 0.05 or 0.01), we reject the null hypothesis and accept the alternative hypothesis.
When your p-value is less than or equal to your significance level, you reject the null hypothesis. The data favors the alternative hypothesis. Congratulations! Your results are statistically significant. When your p-value is greater than your significance level, you fail to reject the null hypothesis. Your results are not significant.
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.