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.
Content preview.
Arcu felis bibendum ut tristique et egestas quis:
5.2 - writing hypotheses.
The first step in conducting a hypothesis test is to write the hypothesis statements that are going to be tested. For each test you will have a null hypothesis (\(H_0\)) and an alternative hypothesis (\(H_a\)).
When writing hypotheses there are three things that we need to know: (1) the parameter that we are testing (2) the direction of the test (non-directional, right-tailed or left-tailed), and (3) the value of the hypothesized parameter.
Hypotheses are always written in terms of population parameters (e.g., \(p\) and \(\mu\)). The tables below display all of the possible hypotheses for the parameters that we have learned thus far. Note that the null hypothesis always includes the equality (i.e., =).
Research Question | Is the population mean different from \( \mu_{0} \)? | Is the population mean greater than \(\mu_{0}\)? | Is the population mean less than \(\mu_{0}\)? |
---|---|---|---|
Null Hypothesis, \(H_{0}\) | \(\mu=\mu_{0} \) | \(\mu=\mu_{0} \) | \(\mu=\mu_{0} \) |
Alternative Hypothesis, \(H_{a}\) | \(\mu\neq \mu_{0} \) | \(\mu> \mu_{0} \) | \(\mu<\mu_{0} \) |
Type of Hypothesis Test | Two-tailed, non-directional | Right-tailed, directional | Left-tailed, directional |
Research Question | Is there a difference in the population? | Is there a mean increase in the population? | Is there a mean decrease in the population? |
---|---|---|---|
Null Hypothesis, \(H_{0}\) | \(\mu_d=0 \) | \(\mu_d =0 \) | \(\mu_d=0 \) |
Alternative Hypothesis, \(H_{a}\) | \(\mu_d \neq 0 \) | \(\mu_d> 0 \) | \(\mu_d<0 \) |
Type of Hypothesis Test | Two-tailed, non-directional | Right-tailed, directional | Left-tailed, directional |
Research Question | Is the population proportion different from \(p_0\)? | Is the population proportion greater than \(p_0\)? | Is the population proportion less than \(p_0\)? |
---|---|---|---|
Null Hypothesis, \(H_{0}\) | \(p=p_0\) | \(p= p_0\) | \(p= p_0\) |
Alternative Hypothesis, \(H_{a}\) | \(p\neq p_0\) | \(p> p_0\) | \(p< p_0\) |
Type of Hypothesis Test | Two-tailed, non-directional | Right-tailed, directional | Left-tailed, directional |
Research Question | Are the population means different? | Is the population mean in group 1 greater than the population mean in group 2? | Is the population mean in group 1 less than the population mean in groups 2? |
---|---|---|---|
Null Hypothesis, \(H_{0}\) | \(\mu_1=\mu_2\) | \(\mu_1 = \mu_2 \) | \(\mu_1 = \mu_2 \) |
Alternative Hypothesis, \(H_{a}\) | \(\mu_1 \ne \mu_2 \) | \(\mu_1 \gt \mu_2 \) | \(\mu_1 \lt \mu_2\) |
Type of Hypothesis Test | Two-tailed, non-directional | Right-tailed, directional | Left-tailed, directional |
Research Question | Are the population proportions different? | Is the population proportion in group 1 greater than the population proportion in groups 2? | Is the population proportion in group 1 less than the population proportion in group 2? |
---|---|---|---|
Null Hypothesis, \(H_{0}\) | \(p_1 = p_2 \) | \(p_1 = p_2 \) | \(p_1 = p_2 \) |
Alternative Hypothesis, \(H_{a}\) | \(p_1 \ne p_2\) | \(p_1 \gt p_2 \) | \(p_1 \lt p_2\) |
Type of Hypothesis Test | Two-tailed, non-directional | Right-tailed, directional | Left-tailed, directional |
Research Question | Is the slope in the population different from 0? | Is the slope in the population positive? | Is the slope in the population negative? |
---|---|---|---|
Null Hypothesis, \(H_{0}\) | \(\beta =0\) | \(\beta= 0\) | \(\beta = 0\) |
Alternative Hypothesis, \(H_{a}\) | \(\beta\neq 0\) | \(\beta> 0\) | \(\beta< 0\) |
Type of Hypothesis Test | Two-tailed, non-directional | Right-tailed, directional | Left-tailed, directional |
Research Question | Is the correlation in the population different from 0? | Is the correlation in the population positive? | Is the correlation in the population negative? |
---|---|---|---|
Null Hypothesis, \(H_{0}\) | \(\rho=0\) | \(\rho= 0\) | \(\rho = 0\) |
Alternative Hypothesis, \(H_{a}\) | \(\rho \neq 0\) | \(\rho > 0\) | \(\rho< 0\) |
Type of Hypothesis Test | Two-tailed, non-directional | Right-tailed, directional | Left-tailed, directional |
by Marco Taboga , PhD
In a statistical test, observed data is used to decide whether or not to reject a restriction on the data-generating probability distribution.
The assumption that the restriction is true is called null hypothesis , while the statement that the restriction is not true is called alternative hypothesis.
A correct specification of the alternative hypothesis is essential to decide between one-tailed and two-tailed tests.
Table of contents
Choice between one-tailed and two-tailed tests, the critical region, the interpretation of the rejection, the interpretation must be coherent with the alternative hypothesis.
More details, keep reading the glossary.
In order to fully understand the concept of alternative hypothesis, we need to remember the essential elements of a statistical inference problem:
we observe a sample drawn from an unknown probability distribution;
in principle, any valid probability distribution could have generated the sample;
however, we usually place some a priori restrictions on the set of possible data-generating distributions;
A couple of simple examples follow.
When we conduct a statistical test, we formulate a null hypothesis as a restriction on the statistical model.
The alternative hypothesis is
The alternative hypothesis is used to decide whether a test should be one-tailed or two-tailed.
The null hypothesis is rejected if the test statistic falls within a critical region that has been chosen by the statistician.
The critical region is a set of values that may comprise:
only the left tail of the distribution or only the right tail (one-tailed test);
both the left and the right tail (two-tailed test).
The choice of the critical region depends on the alternative hypothesis. Let us see why.
The interpretation is different depending on the tail of the distribution in which the test statistic falls.
The choice between a one-tailed or a two-tailed test needs to be done in such a way that the interpretation of a rejection is always coherent with the alternative hypothesis.
When we deal with the power function of a test, the term "alternative hypothesis" has a special meaning.
We conclude with a caveat about the interpretation of the outcome of a test of hypothesis.
The interpretation of a rejection of the null is controversial.
According to some statisticians, rejecting the null is equivalent to accepting the alternative.
However, others deem that rejecting the null does not necessarily imply accepting the alternative. In fact, it is possible to think of situations in which both hypotheses can be rejected. Let us see why.
According to the conceptual framework illustrated by the images above, there are three possibilities:
the null is true;
the alternative is true;
neither the null nor the alternative is true because the true data-generating distribution has been excluded from the statistical model (we say that the model is mis-specified).
If we are in case 3, accepting the alternative after a rejection of the null is an incorrect decision. Moreover, a second test in which the alternative becomes the new null may lead us to another rejection.
You can find more details about the alternative hypothesis in the lecture on Hypothesis testing .
Previous entry: Almost sure
Next entry: Binomial coefficient
Please cite as:
Taboga, Marco (2021). "Alternative hypothesis", Lectures on probability theory and mathematical statistics. Kindle Direct Publishing. Online appendix. https://www.statlect.com/glossary/alternative-hypothesis.
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Published on November 8, 2019 by Rebecca Bevans . Revised on June 22, 2023.
Hypothesis testing is a formal procedure for investigating our ideas about the world using statistics . It is most often used by scientists to test specific predictions, called hypotheses, that arise from theories.
There are 5 main steps in hypothesis testing:
Though the specific details might vary, the procedure you will use when testing a hypothesis will always follow some version of these steps.
Step 1: state your null and alternate hypothesis, step 2: collect data, step 3: perform a statistical test, step 4: decide whether to reject or fail to reject your null hypothesis, step 5: present your findings, other interesting articles, frequently asked questions about hypothesis testing.
After developing your initial research hypothesis (the prediction that you want to investigate), it is important to restate it as a null (H o ) and alternate (H a ) hypothesis so that you can test it mathematically.
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.
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For a statistical test to be valid , it is important to perform sampling and collect data in a way that is designed to test your hypothesis. If your data are not representative, then you cannot make statistical inferences about the population you are interested in.
There are a variety of statistical tests available, but they are all based on the comparison of within-group variance (how spread out the data is within a category) versus between-group variance (how different the categories are from one another).
If the between-group variance is large enough that there is little or no overlap between groups, then your statistical test will reflect that by showing a low p -value . This means it is unlikely that the differences between these groups came about by chance.
Alternatively, if there is high within-group variance and low between-group variance, then your statistical test will reflect that with a high p -value. This means it is likely that any difference you measure between groups is due to chance.
Your choice of statistical test will be based on the type of variables and the level of measurement of your collected data .
Based on the outcome of your statistical test, you will have to decide whether to reject or fail to reject your null hypothesis.
In most cases you will use the p -value generated by your statistical test to guide your decision. And in most cases, your predetermined level of significance for rejecting the null hypothesis will be 0.05 – that is, when there is a less than 5% chance that you would see these results if the null hypothesis were true.
In some cases, researchers choose a more conservative level of significance, such as 0.01 (1%). This minimizes the risk of incorrectly rejecting the null hypothesis ( Type I error ).
The results of hypothesis testing will be presented in the results and discussion sections of your research paper , dissertation or thesis .
In the results section you should give a brief summary of the data and a summary of the results of your statistical test (for example, the estimated difference between group means and associated p -value). In the discussion , you can discuss whether your initial hypothesis was supported by your results or not.
In the formal language of hypothesis testing, we talk about rejecting or failing to reject the null hypothesis. You will probably be asked to do this in your statistics assignments.
However, when presenting research results in academic papers we rarely talk this way. Instead, we go back to our alternate hypothesis (in this case, the hypothesis that men are on average taller than women) and state whether the result of our test did or did not support the alternate hypothesis.
If your null hypothesis was rejected, this result is interpreted as “supported the alternate hypothesis.”
These are superficial differences; you can see that they mean the same thing.
You might notice that we don’t say that we reject or fail to reject the alternate hypothesis . This is because hypothesis testing is not designed to prove or disprove anything. It is only designed to test whether a pattern we measure could have arisen spuriously, or by chance.
If we reject the null hypothesis based on our research (i.e., we find that it is unlikely that the pattern arose by chance), then we can say our test lends support to our hypothesis . But if the pattern does not pass our decision rule, meaning that it could have arisen by chance, then we say the test is inconsistent with our hypothesis .
If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.
Methodology
Research bias
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.
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).
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.
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Bevans, R. (2023, June 22). Hypothesis Testing | A Step-by-Step Guide with Easy Examples. Scribbr. Retrieved July 11, 2024, from https://www.scribbr.com/statistics/hypothesis-testing/
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Once you have developed a clear and focused research question or set of research questions, you’ll be ready to conduct further research, a literature review, on the topic to help you make an educated guess about the answer to your question(s). This educated guess is called a hypothesis.
In research, there are two types of hypotheses: null and alternative. They work as a complementary pair, each stating that the other is wrong.
Null Hypothesis: H 0 : There is no difference in the salary of factory workers based on gender. Alternative Hypothesis : H a : Male factory workers have a higher salary than female factory workers.
Null Hypothesis : H 0 : There is no relationship between height and shoe size. Alternative Hypothesis : H a : There is a positive relationship between height and shoe size.
Null Hypothesis : H 0 : Experience on the job has no impact on the quality of a brick mason’s work. Alternative Hypothesis : H a : The quality of a brick mason’s work is influenced by on-the-job experience.
Alternative hypothesis defines there is a statistically important relationship between two variables. Whereas null hypothesis states there is no statistical relationship between the two variables. In statistics, we usually come across various kinds of hypotheses. A statistical hypothesis is supposed to be a working statement which is assumed to be logical with given data. It should be noticed that a hypothesis is neither considered true nor false.
The alternative hypothesis is a statement used in statistical inference experiment. It is contradictory to the null hypothesis and denoted by H a or H 1 . We can also say that it is simply an alternative to the null. In hypothesis testing, an alternative theory is a statement which a researcher is testing. This statement is true from the researcher’s point of view and ultimately proves to reject the null to replace it with an alternative assumption. In this hypothesis, the difference between two or more variables is predicted by the researchers, such that the pattern of data observed in the test is not due to chance.
To check the water quality of a river for one year, the researchers are doing the observation. As per the null hypothesis, there is no change in water quality in the first half of the year as compared to the second half. But in the alternative hypothesis, the quality of water is poor in the second half when observed.
|
|
It denotes there is no relationship between two measured phenomena. | It’s a hypothesis that a random cause may influence the observed data or sample. |
It is represented by H | It is represented by H or H |
Example: Rohan will win at least Rs.100000 in lucky draw. | Example: Rohan will win less than Rs.100000 in lucky draw. |
Basically, there are three types of the alternative hypothesis, they are;
Left-Tailed : Here, it is expected that the sample proportion (π) is less than a specified value which is denoted by π 0 , such that;
H 1 : π < π 0
Right-Tailed: It represents that the sample proportion (π) is greater than some value, denoted by π 0 .
H 1 : π > π 0
Two-Tailed: According to this hypothesis, the sample proportion (denoted by π) is not equal to a specific value which is represented by π 0 .
H 1 : π ≠ π 0
Note: The null hypothesis for all the three alternative hypotheses, would be H 1 : π = π 0 .
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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 of no difference between the variables—they are not related. This can often be considered the status quo and as a result if you cannot accept the null it requires some action.
H a : The alternative hypothesis: It is a claim about the population that is contradictory to H 0 and what we conclude when we reject H 0 . This is usually what the researcher is trying to prove.
Since the null and alternative hypotheses are contradictory, you must examine evidence to decide if you have enough evidence to reject the null hypothesis or not. The evidence is in the form of sample data.
After you have determined which hypothesis the sample supports, you make a decision. There are two options for a decision. They are "reject H 0 " if the sample information favors the alternative hypothesis or "do not reject H 0 " or "decline to reject H 0 " if the sample information is insufficient to reject the null hypothesis.
Mathematical Symbols Used in H 0 and H a :
equal (=) | not equal (≠) greater than (>) less than (<) |
greater than or equal to (≥) | less than (<) |
less than or equal to (≤) | more than (>) |
H 0 always has a symbol with an equal in it. H a never has a symbol with an equal in it. The choice of symbol depends on the wording of the hypothesis test. However, be aware that many researchers (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.
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.
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.
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.
Bring to class a newspaper, some news magazines, and some Internet articles . In groups, find articles from which your group can write null and alternative hypotheses. Discuss your hypotheses with the rest of the class.
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Statistics By Jim
Making statistics intuitive
By Jim Frost 6 Comments
The null hypothesis in statistics states that there is no difference between groups or no relationship between variables. It is one of two mutually exclusive hypotheses about a population in a hypothesis test.
In every study or experiment, researchers assess an effect or relationship. This effect can be the effectiveness of a new drug, building material, or other intervention that has benefits. There is a benefit or connection that the researchers hope to identify. Unfortunately, no effect may exist. In statistics, we call this lack of an effect the null hypothesis. Researchers assume that this notion of no effect is correct until they have enough evidence to suggest otherwise, similar to how a trial presumes innocence.
In this context, the analysts don’t necessarily believe the null hypothesis is correct. In fact, they typically want to reject it because that leads to more exciting finds about an effect or relationship. The new vaccine works!
You can think of it as the default theory that requires sufficiently strong evidence to reject. Like a prosecutor, researchers must collect sufficient evidence to overturn the presumption of no effect. Investigators must work hard to set up a study and a data collection system to obtain evidence that can reject the null hypothesis.
Related post : What is an Effect in Statistics?
Null hypotheses start as research questions that the investigator rephrases as a statement indicating there is no effect or relationship.
Does the vaccine prevent infections? | The vaccine does not affect the infection rate. |
Does the new additive increase product strength? | The additive does not affect mean product strength. |
Does the exercise intervention increase bone mineral density? | The intervention does not affect bone mineral density. |
As screen time increases, does test performance decrease? | There is no relationship between screen time and test performance. |
After reading these examples, you might think they’re a bit boring and pointless. However, the key is to remember that the null hypothesis defines the condition that the researchers need to discredit before suggesting an effect exists.
Let’s see how you reject the null hypothesis and get to those more exciting findings!
So, you want to reject the null hypothesis, but how and when can you do that? To start, you’ll need to perform a statistical test on your data. The following is an overview of performing a study that uses a hypothesis test.
The first step is to devise a research question and the appropriate null hypothesis. After that, the investigators need to formulate an experimental design and data collection procedures that will allow them to gather data that can answer the research question. Then they collect the data. For more information about designing a scientific study that uses statistics, read my post 5 Steps for Conducting Studies with Statistics .
After data collection is complete, statistics and hypothesis testing enter the picture. Hypothesis testing takes your sample data and evaluates how consistent they are with the null hypothesis. The p-value is a crucial part of the statistical results because it quantifies how strongly the sample data contradict the null hypothesis.
When the sample data provide sufficient evidence, you can reject the null hypothesis. In a hypothesis test, this process involves comparing the p-value to your significance level .
Reject the null hypothesis when the p-value is less than or equal to your significance level. Your sample data favor the alternative hypothesis, which suggests that the effect exists in the population. For a mnemonic device, remember—when the p-value is low, the null must go!
When you can reject the null hypothesis, your results are statistically significant. Learn more about Statistical Significance: Definition & Meaning .
Conversely, when the p-value is greater than your significance level, you fail to reject the null hypothesis. The sample data provides insufficient data to conclude that the effect exists in the population. When the p-value is high, the null must fly!
Note that failing to reject the null is not the same as proving it. For more information about the difference, read my post about Failing to Reject the Null .
That’s a very general look at the process. But I hope you can see how the path to more exciting findings depends on being able to rule out the less exciting null hypothesis that states there’s nothing to see here!
Let’s move on to learning how to write the null hypothesis for different types of effects, relationships, and tests.
Related posts : How Hypothesis Tests Work and Interpreting P-values
The null hypothesis varies by the type of statistic and hypothesis test. Remember that inferential statistics use samples to draw conclusions about populations. Consequently, when you write a null hypothesis, it must make a claim about the relevant population parameter . Further, that claim usually indicates that the effect does not exist in the population. Below are typical examples of writing a null hypothesis for various parameters and hypothesis tests.
Related posts : Descriptive vs. Inferential Statistics and Populations, Parameters, and Samples in Inferential Statistics
T-tests and ANOVA assess the differences between group means. For these tests, the null hypothesis states that there is no difference between group means in the population. In other words, the experimental conditions that define the groups do not affect the mean outcome. Mu (µ) is the population parameter for the mean, and you’ll need to include it in the statement for this type of study.
For example, an experiment compares the mean bone density changes for a new osteoporosis medication. The control group does not receive the medicine, while the treatment group does. The null states that the mean bone density changes for the control and treatment groups are equal.
Proportions tests assess the differences between group proportions. For these tests, the null hypothesis states that there is no difference between group proportions. Again, the experimental conditions did not affect the proportion of events in the groups. P is the population proportion parameter that you’ll need to include.
For example, a vaccine experiment compares the infection rate in the treatment group to the control group. The treatment group receives the vaccine, while the control group does not. The null states that the infection rates for the control and treatment groups are equal.
Some studies assess the relationship between two continuous variables rather than differences between groups.
In these studies, analysts often use either correlation or regression analysis . For these tests, the null states that there is no relationship between the variables. Specifically, it says that the correlation or regression coefficient is zero. As one variable increases, there is no tendency for the other variable to increase or decrease. Rho (ρ) is the population correlation parameter and beta (β) is the regression coefficient parameter.
For example, a study assesses the relationship between screen time and test performance. The null states that there is no correlation between this pair of variables. As screen time increases, test performance does not tend to increase or decrease.
For all these cases, the analysts define the hypotheses before the study. After collecting the data, they perform a hypothesis test to determine whether they can reject the null hypothesis.
The preceding examples are all for two-tailed hypothesis tests. To learn about one-tailed tests and how to write a null hypothesis for them, read my post One-Tailed vs. Two-Tailed Tests .
Related post : Understanding Correlation
Neyman, J; Pearson, E. S. (January 1, 1933). On the Problem of the most Efficient Tests of Statistical Hypotheses . Philosophical Transactions of the Royal Society A . 231 (694–706): 289–337.
January 11, 2024 at 2:57 pm
Thanks for the reply.
January 10, 2024 at 1:23 pm
Hi Jim, In your comment you state that equivalence test null and alternate hypotheses are reversed. For hypothesis tests of data fits to a probability distribution, the null hypothesis is that the probability distribution fits the data. Is this correct?
January 10, 2024 at 2:15 pm
Those two separate things, equivalence testing and normality tests. But, yes, you’re correct for both.
Hypotheses are switched for equivalence testing. You need to “work” (i.e., collect a large sample of good quality data) to be able to reject the null that the groups are different to be able to conclude they’re the same.
With typical hypothesis tests, if you have low quality data and a low sample size, you’ll fail to reject the null that they’re the same, concluding they’re equivalent. But that’s more a statement about the low quality and small sample size than anything to do with the groups being equal.
So, equivalence testing make you work to obtain a finding that the groups are the same (at least within some amount you define as a trivial difference).
For normality testing, and other distribution tests, the null states that the data follow the distribution (normal or whatever). If you reject the null, you have sufficient evidence to conclude that your sample data don’t follow the probability distribution. That’s a rare case where you hope to fail to reject the null. And it suffers from the problem I describe above where you might fail to reject the null simply because you have a small sample size. In that case, you’d conclude the data follow the probability distribution but it’s more that you don’t have enough data for the test to register the deviation. In this scenario, if you had a larger sample size, you’d reject the null and conclude it doesn’t follow that distribution.
I don’t know of any equivalence testing type approach for distribution fit tests where you’d need to work to show the data follow a distribution, although I haven’t looked for one either!
February 20, 2022 at 9:26 pm
Is a null hypothesis regularly (always) stated in the negative? “there is no” or “does not”
February 23, 2022 at 9:21 pm
Typically, the null hypothesis includes an equal sign. The null hypothesis states that the population parameter equals a particular value. That value is usually one that represents no effect. In the case of a one-sided hypothesis test, the null still contains an equal sign but it’s “greater than or equal to” or “less than or equal to.” If you wanted to translate the null hypothesis from its native mathematical expression, you could use the expression “there is no effect.” But the mathematical form more specifically states what it’s testing.
It’s the alternative hypothesis that typically contains does not equal.
There are some exceptions. For example, in an equivalence test where the researchers want to show that two things are equal, the null hypothesis states that they’re not equal.
In short, the null hypothesis states the condition that the researchers hope to reject. They need to work hard to set up an experiment and data collection that’ll gather enough evidence to be able to reject the null condition.
February 15, 2022 at 9:32 am
Dear sir I always read your notes on Research methods.. Kindly tell is there any available Book on all these..wonderfull Urgent
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About this unit.
Significance tests give us a formal process for using sample data to evaluate the likelihood of some claim about a population value. Learn how to conduct significance tests and calculate p-values to see how likely a sample result is to occur by random chance. You'll also see how we use p-values to make conclusions about hypotheses.
A hypothesis test uses sample data to determine whether or not some claim about a population parameter is true.
Whenever we perform a hypothesis test, we always write a null hypothesis and an alternative hypothesis, which take the following forms:
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.
Alternative hypothesis: The sample data does provide sufficient evidence to support the claim being made by an individual.
For example, suppose it’s assumed that the average height of a certain species of plant is 20 inches tall. However, one botanist claims the true average height is greater than 20 inches.
To test this claim, she may go out and collect a random sample of plants. She can then use this sample data to perform a hypothesis test using the following two hypotheses:
H 0 : μ ≤ 20 (the true mean height of plants is equal to or even less than 20 inches)
H A : μ > 20 (the true mean height of plants is greater than 20 inches)
If the sample data gathered by the botanist shows that the mean height of this species of plants is significantly greater than 20 inches, she can reject the null hypothesis and conclude that the mean height is greater than 20 inches.
Read through the following examples to gain a better understanding of how to write a null hypothesis in different situations.
A biologist wants to test whether or not the true mean weight of a certain species of turtles is 300 pounds. To test this, he goes out and measures the weight of a random sample of 40 turtles.
Here is how to write the null and alternative hypotheses for this scenario:
H 0 : μ = 300 (the true mean weight is equal to 300 pounds)
H A : μ ≠ 300 (the true mean weight is not equal to 300 pounds)
It’s assumed that the mean height of males in a certain city is 68 inches. However, an independent researcher believes the true mean height is greater than 68 inches. To test this, he goes out and collects the height of 50 males in the city.
H 0 : μ ≤ 68 (the true mean height is equal to or even less than 68 inches)
H A : μ > 68 (the true mean height is greater than 68 inches)
A university states that 80% of all students graduate on time. However, an independent researcher believes that less than 80% of all students graduate on time. To test this, she collects data on the proportion of students who graduated on time last year at the university.
H 0 : p ≥ 0.80 (the true proportion of students who graduate on time is 80% or higher)
H A : μ < 0.80 (the true proportion of students who graduate on time is less than 80%)
A food researcher wants to test whether or not the true mean weight of a burger at a certain restaurant is 7 ounces. To test this, he goes out and measures the weight of a random sample of 20 burgers from this restaurant.
H 0 : μ = 7 (the true mean weight is equal to 7 ounces)
H A : μ ≠ 7 (the true mean weight is not equal to 7 ounces)
A politician claims that less than 30% of citizens in a certain town support a certain law. To test this, he goes out and surveys 200 citizens on whether or not they support the law.
H 0 : p ≥ .30 (the true proportion of citizens who support the law is greater than or equal to 30%)
H A : μ < 0.30 (the true proportion of citizens who support the law is less than 30%)
Introduction to Hypothesis Testing Introduction to Confidence Intervals An Explanation of P-Values and Statistical Significance
Hey there. My name is Zach Bobbitt. I have a Masters of Science degree in Applied Statistics and I’ve worked on machine learning algorithms for professional businesses in both healthcare and retail. I’m passionate about statistics, machine learning, and data visualization and I created Statology to be a resource for both students and teachers alike. My goal with this site is to help you learn statistics through using simple terms, plenty of real-world examples, and helpful illustrations.
you are amazing, thank you so much
Say I am a botanist hypothesizing the average height of daisies is 20 inches, or not? Does T = (ave – 20 inches) / √ variance / (80 / 4)? … This assumes 40 real measures + 40 fake = 80 n, but that seems questionable. Please advise.
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The null and alternative hypotheses offer competing answers to your research question. When the research question asks "Does the independent variable affect the dependent variable?": The null hypothesis ( H0) answers "No, there's no effect in the population.". The alternative hypothesis ( Ha) answers "Yes, there is an effect in the ...
Null hypothesis: µ ≥ 70 inches. Alternative hypothesis: µ < 70 inches. A two-tailed hypothesis involves making an "equal to" or "not equal to" statement. For example, suppose we assume the mean height of a male in the U.S. is equal to 70 inches. The null and alternative hypotheses in this case would be: Null hypothesis: µ = 70 inches.
The null and alternative hypotheses are two competing claims that researchers weigh evidence for and against using a statistical test: Null hypothesis (H0): There's no effect in the population. Alternative hypothesis (HA): There's an effect in the population. The effect is usually the effect of the independent variable on the dependent ...
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.
10.1 - Setting the Hypotheses: Examples. A significance test examines whether the null hypothesis provides a plausible explanation of the data. The null hypothesis itself does not involve the data. It is a statement about a parameter (a numerical characteristic of the population). These population values might be proportions or means or ...
It is the opposite of your research hypothesis. The alternative hypothesis--that is, the research hypothesis--is the idea, phenomenon, observation that you want to prove. If you suspect that girls take longer to get ready for school than boys, then: Alternative: girls time > boys time. Null: girls time <= boys time.
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.
5.2 - Writing Hypotheses. The first step in conducting a hypothesis test is to write the hypothesis statements that are going to be tested. For each test you will have a null hypothesis ( H 0) and an alternative hypothesis ( H a ). When writing hypotheses there are three things that we need to know: (1) the parameter that we are testing (2) the ...
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.
Example As in the previous example, consider a test about the mean of a normal distribution, where we test .Suppose that we exclude a priori that can be negative. In other words, the statistical model includes all the normal distributions with mean .It follows that includes all the normal distributions with and the alternative hypothesis is .
Thus, our alternative hypothesis is the mathematical way of stating our research question. If we expect our obtained sample mean to be above or below the null hypothesis value, which we call a directional hypothesis, then our alternative hypothesis takes the form: HA: μ > 7.47 or HA: μ < 7.47 H A: μ > 7.47 or H A: μ < 7.47.
The alternative hypothesis is often denoted as H 1 or H A. If you are performing a two-tailed hypothesis test, the alternative hypothesis states that the population parameter does not equal the null hypothesis value. For example, when the alternative hypothesis is H A: μ ≠ 0, the test can detect differences both greater than and less than ...
Alternative hypothesis is often denoted as H a or H 1. In statistical hypothesis testing, to prove the alternative hypothesis is true, it should be shown that the data is contradictory to the null hypothesis. Namely, there is sufficient evidence against null hypothesis to demonstrate that the alternative hypothesis is true. Example
There are 5 main steps in hypothesis testing: State your research hypothesis as a null hypothesis and alternate hypothesis (H o) and (H a or H 1 ). Collect data in a way designed to test the hypothesis. Perform an appropriate statistical test. Decide whether to reject or fail to reject your null hypothesis. Present the findings in your results ...
These conclusions are all based upon a level of probability, a significance level, that is set by the analyst. Table 9.1 presents the various hypotheses in the relevant pairs. For example, if the null hypothesis is equal to some value, the alternative has to be not equal to that value. H0. Ha. equal (=) not equal (≠) greater than or equal to ...
Writing null and alternative hypotheses. A ketchup company regularly receives large shipments of tomatoes. For each shipment that is received, a supervisor takes a random sample of 500 tomatoes to see what percent of the sample is bruised and performs a significance test. If the sample shows convincing evidence that more than 10 % of the entire ...
The alternative hypothesis is a hypothesis used in significance testing which contains a strict inequality. A test of significance will result in either rejecting the null hypothesis (indicating ...
Null Hypothesis (H0) - This can be thought of as the implied hypothesis. "Null" meaning "nothing.". This hypothesis states that there is no difference between groups or no relationship between variables. The null hypothesis is a presumption of status quo or no change. Alternative Hypothesis (Ha) - This is also known as the claim.
The alternative hypothesis is a statement used in statistical inference experiment. It is contradictory to the null hypothesis and denoted by H a or H 1. We can also say that it is simply an alternative to the null. In hypothesis testing, an alternative theory is a statement which a researcher is testing.
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 of no difference between the variables—they are not related. This can often be considered the status quo and as a result if you cannot accept the null it requires some action.
Alternative Hypothesis H A: The correlation in the population is not zero: ρ ≠ 0. For all these cases, the analysts define the hypotheses before the study. After collecting the data, they perform a hypothesis test to determine whether they can reject the null hypothesis. The preceding examples are all for two-tailed hypothesis tests.
Statistics and probability. 16 units · 157 skills. Unit 1. Analyzing categorical data. ... Examples of null and alternative hypotheses (Opens a modal) P-values and significance tests ... (Opens a modal) Using P-values to make conclusions (Opens a modal) Practice. Simple hypothesis testing Get 3 of 4 questions to level up! Writing null and ...
Example 1: Weight of Turtles. A biologist wants to test whether or not the true mean weight of a certain species of turtles is 300 pounds. To test this, he goes out and measures the weight of a random sample of 40 turtles. Here is how to write the null and alternative hypotheses for this scenario: H0: μ = 300 (the true mean weight is equal to ...
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 of no difference between the variables—they are not related. This can often be considered the status quo and as a result if you cannot accept the null it requires some action.