difference between null hypothesis and alternative hypothesis

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Difference Between Null and Alternative Hypothesis

Null hypothesis implies a statement that expects no difference or effect. On the contrary, an alternative hypothesis is one that expects some difference or effect. Null hypothesis This article excerpt shed light on the fundamental differences between null and alternative hypothesis.

Content: Null Hypothesis Vs Alternative Hypothesis

Comparison chart, definition of null hypothesis.

A null hypothesis is a statistical hypothesis in which there is no significant difference exist between the set of variables. It is the original or default statement, with no effect, often represented by H 0 (H-zero). It is always the hypothesis that is tested. It denotes the certain value of population parameter such as µ, s, p. A null hypothesis can be rejected, but it cannot be accepted just on the basis of a single test.

Definition of Alternative Hypothesis

A statistical hypothesis used in hypothesis testing, which states that there is a significant difference between the set of variables. It is often referred to as the hypothesis other than the null hypothesis, often denoted by H 1 (H-one). It is what the researcher seeks to prove in an indirect way, by using the test. It refers to a certain value of sample statistic, e.g., x¯, s, p

The acceptance of alternative hypothesis depends on the rejection of the null hypothesis i.e. until and unless null hypothesis is rejected, an alternative hypothesis cannot be accepted.

Key Differences Between Null and Alternative Hypothesis

The important points of differences between null and alternative hypothesis are explained as under:

• A null hypothesis is a statement, in which there is no relationship between two variables. An alternative hypothesis is a statement; that is simply the inverse of the null hypothesis, i.e. there is some statistical significance between two measured phenomenon.
• A null hypothesis is what, the researcher tries to disprove whereas an alternative hypothesis is what the researcher wants to prove.
• A null hypothesis represents, no observed effect whereas an alternative hypothesis reflects, some observed effect.
• If the null hypothesis is accepted, no changes will be made in the opinions or actions. Conversely, if the alternative hypothesis is accepted, it will result in the changes in the opinions or actions.
• As null hypothesis refers to population parameter, the testing is indirect and implicit. On the other hand, the alternative hypothesis indicates sample statistic, wherein, the testing is direct and explicit.
• A null hypothesis is labelled as H 0 (H-zero) while an alternative hypothesis is represented by H 1 (H-one).
• The mathematical formulation of a null hypothesis is an equal sign but for an alternative hypothesis is not equal to sign.
• In null hypothesis, the observations are the outcome of chance whereas, in the case of the alternative hypothesis, the observations are an outcome of real effect.

There are two outcomes of a statistical test, i.e. first, a null hypothesis is rejected and alternative hypothesis is accepted, second, null hypothesis is accepted, on the basis of the evidence. In simple terms, a null hypothesis is just opposite of alternative hypothesis.

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Zipporah Thuo says

February 22, 2018 at 6:06 pm

The comparisons between the two hypothesis i.e Null hypothesis and the Alternative hypothesis are the best.Thank you.

Getu Gamo says

March 4, 2019 at 3:42 am

Thank you so much for the detail explanation on two hypotheses. Now I understood both very well, including their differences.

Jyoti Bhardwaj says

May 28, 2019 at 6:26 am

Thanks, Surbhi! Appreciate the clarity and precision of this content.

January 9, 2020 at 6:16 am

John Jenstad says

July 20, 2020 at 2:52 am

Thanks very much, Surbhi, for your clear explanation!!

Navita says

July 2, 2021 at 11:48 am

Thanks for the Comparison chart! it clears much of my doubt.

GURU UPPALA says

July 21, 2022 at 8:36 pm

Thanks for the Comparison chart!

Enock kipkoech says

September 22, 2022 at 1:57 pm

What are the examples of null hypothesis and substantive hypothesis

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Difference between Null and Alternate Hypothesis

Hypothesis is a statement or an assumption that may be true or false. There are six types of hypotheses mainly the Simple hypothesis, Complex hypothesis, Directional hypothesis, Associative hypothesis, and Null hypothesis. Usually, the hypothesis is the start point of any scientific investigation, It gives the right direction to the process of investigation. It avoids the blind search and gives direction to the search. It acts as a compass in the process.

Null hypothesis suggests that there is no relationship between the two variables. Null hypothesis is also exactly the opposite of the alternative hypothesis. Null hypothesis is generally what researchers or scientists try to disprove and if the null hypothesis gets accepted then we have to make changes in our opinion i.e. we have to make changes in our original opinion or statement in order to match null hypothesis. Null hypothesis is represented as H0. If my alternative hypothesis is that 55% of boys in my town are taller than girls then my alternative hypothesis will be that 55% of boys in my town are not taller than girls. 

Alternative hypothesis is a method for reaching a conclusion and making inferences and judgements about certain facts or a statement. This is done on the basis of the data which is available. Usually, the statement which we check regarding the null hypothesis is commonly known as the alternative hypothesis. Most of the times alternative hypothesis is exactly the opposite of the null hypothesis. This is what generally researchers or scientists try to approve. Alternative hypothesis is represented as Ha or H1. If my null hypothesis is that 55% of boys in my town are not taller than girls then my alternative hypothesis will be that 55% of boys in my town are taller than girls.

Following is the difference between the null hypothesis and alternate hypothesis:

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9.1 Null and Alternative Hypotheses

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

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

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

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

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

Mathematical Symbols Used in H 0 and H a :

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

Example 9.1

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

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

Example 9.2

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

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

• H 0 : μ __ 66
• H a : μ __ 66

Example 9.3

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

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

• H 0 : μ __ 45
• H a : μ __ 45

Example 9.4

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

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

• H 0 : p __ 0.40
• H a : p __ 0.40

Collaborative Exercise

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

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Null hypothesis and alternative hypothesis with 9 differences

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Null hypothesis definition

The null hypothesis is a general statement that states that there is no relationship between two phenomenons under consideration or that there is no association between two groups.

• A hypothesis, in general, is an assumption that is yet to be proved with sufficient pieces of evidence. A null hypothesis thus is the hypothesis a researcher is trying to disprove.
• A null hypothesis is a hypothesis capable of being objectively verified, tested, and even rejected.
• If a study is to compare method A with method B about their relationship, and if the study is preceded on the assumption that both methods are equally good, then this assumption is termed as the null hypothesis.
• The null hypothesis should always be a specific hypothesis, i.e., it should not state about or approximately a certain value.

Null hypothesis symbol

• The symbol for the null hypothesis is H 0, and it is read as H-null, H-zero, or H-naught.
• The null hypothesis is usually associated with just ‘equals to’ sign as a null hypothesis can either be accepted or rejected.

Null hypothesis purpose

• The main purpose of a null hypothesis is to verify/ disprove the proposed statistical assumptions.
• Some scientific null hypothesis help to advance a theory.
• The null hypothesis is also used to verify the consistent results of multiple experiments. For e.g., the null hypothesis stating that there is no relation between some medication and age of the patients supports the general effectiveness conclusion, and allows recommendations.

Null hypothesis principle

• The principle of the null hypothesis is collecting the data and determining the chances of the collected data in the study of a random sample, proving that the null hypothesis is true.
• In situations or studies where the collected data doesn’t complete the expectation of the null hypothesis, it is concluded that the data doesn’t provide sufficient or reliable pieces of evidence to support the null hypothesis and thus, it is rejected.
• The data collected is tested through some statistical tool which is designed to measure the extent of departure of the date from the null hypothesis.
• The procedure decides whether the observed departure obtained from the statistical tool is larger than a defined value so that the probability of occurrence of a high departure value is very small under the null hypothesis.
• However, some data might not contradict the null hypothesis which explains that only a weak conclusion can be made and that the data doesn’t provide strong pieces of evidence against the null hypothesis and the null hypothesis might or might not be true.
• Under some other conditions, if the data collected is sufficient and is capable of providing enough evidence, the null hypothesis can be considered valid, indicating no relationship between the phenomena.

When to reject null hypothesis?

• When the p-value of the data is less than the significant level of the test, the null hypothesis is rejected, indicating the test results are significant.
• However, if the p-value is higher than the significant value, the null hypothesis is not rejected, and the results are considered not significant.
• The level of significance is an important concept while hypothesis testing as it determines the percentage risk of rejecting the null hypothesis when H 0 might happen to be true.
• In other words, if we take the level of significance at 5%, it means that the researcher is willing to take as much as a 5 percent risk of rejecting the null hypothesis when it (H 0 ) happens to be true.
• The null hypothesis cannot be accepted because the lack of evidence only means that the relationship is not proven. It doesn’t prove that something doesn’t exist, but it just means that there are not enough shreds of evidence and the study might have missed it.

Null hypothesis examples

The following are some examples of null hypothesis:

• If the hypothesis is that “the consumption of a particular medicine reduces the chances of heart arrest”, the null hypothesis will be “the consumption of the medicine doesn’t reduce the chances of heart arrest.”
• If the hypothesis is that, “If random test scores are collected from men and women, does the score of one group differ from the other?” a possible null hypothesis will be that the mean test score of men is the same as that of the women.

H 0 : µ 1 = µ 2

H 0 = null hypothesis µ 1 = mean score of men µ 2 = mean score of women

Alternative hypothesis definition

An alternative hypothesis is a statement that describes that there is a relationship between two selected variables in a study.

• An alternative hypothesis is usually used to state that a new theory is preferable to the old one (null hypothesis).
• This hypothesis can be simply termed as an alternative to the null hypothesis.
• The alternative hypothesis is the hypothesis that is to be proved that indicates that the results of a study are significant and that the sample observation is not results just from chance but from some non-random cause.
• If a study is to compare method A with method B about their relationship and we assume that the method A is superior or the method B is inferior, then such a statement is termed as an alternative hypothesis.
• Alternative hypotheses should be clearly stated, considering the nature of the research problem.

Alternative hypothesis symbol

• The symbol of the alternative hypothesis is either H 1 or H a while using less than, greater than or not equal signs.

Alternative hypothesis purpose

• An alternative hypothesis provides the researchers with some specific restatements and clarifications of the research problem.
• An alternative hypothesis provides a direction to the study, which then can be utilized by the researcher to obtain the desired results.
• Since the alternative hypothesis is selected before conducting the study, it allows the test to prove that the study is supported by evidence, separating it from the researchers’ desires and values.
• An alternative hypothesis provides a chance of discovering new theories that can disprove an existing one that might not be supported by evidence.
• The alternative hypothesis is important as they prove that a relationship exists between two variables selected and that the results of the study conducted are relevant and significant.

Alternative hypothesis principle

• The principle behind the alternative hypothesis is similar to that of the null hypothesis.
• The alternative hypothesis is based on the concept that when sufficient evidence is collected from the data of random sample, it provides a basis for proving the assumption made by the researcher regarding the study.
• Like in the null hypothesis, the data collected from a random sample is passed through a statistical tool that measures the extent of departure of the data from the null hypothesis.
• If the departure is small under the selected level of significance, the alternative hypothesis is accepted, and the null hypothesis is rejected.
• If the data collected don’t have chances of being in the study of the random sample and are instead decided by the relationship within the sample of the study, an alternative hypothesis stands true.

Alternative hypothesis examples

The following are some examples of alternative hypothesis:

1. If a researcher is assuming that the bearing capacity of a bridge is more than 10 tons, then the hypothesis under this study will be:

Null hypothesis H 0 : µ= 10 tons Alternative hypothesis H a : µ>10 tons

2. Under another study that is trying to test whether there is a significant difference between the effectiveness of medicine against heart arrest, the alternative hypothesis will be that there is a relationship between the medicine and chances of heart arrest.

Null hypothesis vs Alternative hypothesis

• R. Kothari (1990) Research Methodology. Vishwa Prakasan. India.
• https://www.statisticssolutions.com/null-hypothesis-and-alternative-hypothesis/
• https://byjus.com/maths/null-hypothesis/
• https://en.wikipedia.org/wiki/Null_hypothesis
• https://keydifferences.com/difference-between-null-and-alternative-hypothesis.html
• 5% – https://en.wikipedia.org/wiki/Null_hypothesis
• 3% – https://keydifferences.com/difference-between-null-and-alternative-hypothesis.html
• 2% – https://byjus.com/maths/null-hypothesis/
• 1% – https://www.wisdomjobs.com/e-university/research-methodology-tutorial-355/procedure-for-hypothesis-testing-11525.html
• 1% – https://www.thoughtco.com/definition-of-null-hypothesis-and-examples-605436
• 1% – https://www.quora.com/What-are-the-different-types-of-hypothesis-and-what-are-some-examples-of-them
• 1% – https://www.dummies.com/education/math/statistics/what-a-p-value-tells-you-about-statistical-data/
• 1% – https://www.coursehero.com/file/p7jfbal5/These-are-hypotheses-capable-of-being-objectively-verified-and-tested-Thus-we/
• 1% – https://support.minitab.com/en-us/minitab/18/help-and-how-to/modeling-statistics/anova/how-to/one-way-anova/interpret-the-results/all-statistics-and-graphs/methods/
• 1% – https://stats.stackexchange.com/questions/105319/test-whether-there-is-a-significant-difference-between-two-groups
• 1% – https://statisticsbyjim.com/hypothesis-testing/failing-reject-null-hypothesis/
• 1% – https://quizlet.com/45299306/statistics-flash-cards/
• <1% – https://www.thoughtco.com/significance-level-in-hypothesis-testing-1147177
• <1% – https://www.thoughtco.com/null-hypothesis-vs-alternative-hypothesis-3126413
• <1% – https://www.sagepub.com/sites/default/files/upm-binaries/40007_Chapter8.pdf
• <1% – https://www.differencebetween.com/difference-between-hypothesis-and-vs-assumption/
• <1% – https://www.coursehero.com/file/18076181/introduction-to-hypothesis/
• <1% – https://statisticsbyjim.com/glossary/significance-level/
• <1% – https://quizlet.com/164755799/research-methods-midterm-2-flash-cards/
• <1% – https://online.stat.psu.edu/statprogram/reviews/statistical-concepts/hypothesis-testing/p-value-approach

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Hypothesis testing involves the careful construction of two statements: the null hypothesis and the alternative hypothesis. These hypotheses can look very similar but are actually different.

How do we know which hypothesis is the null and which one is the alternative? We will see that there are a few ways to tell the difference.

The Null Hypothesis

The null hypothesis reflects that there will be no observed effect in our experiment. In a mathematical formulation of the null hypothesis, there will typically be an equal sign. This hypothesis is denoted by H 0 .

The null hypothesis is what we attempt to find evidence against in our hypothesis test. We hope to obtain a small enough p-value that it is lower than our level of significance alpha and we are justified in rejecting the null hypothesis. If our p-value is greater than alpha, then we fail to reject the null hypothesis.

If the null hypothesis is not rejected, then we must be careful to say what this means. The thinking on this is similar to a legal verdict. Just because a person has been declared "not guilty", it does not mean that he is innocent. In the same way, just because we failed to reject a null hypothesis it does not mean that the statement is true.

For example, we may want to investigate the claim that despite what convention has told us, the mean adult body temperature is not the accepted value of 98.6 degrees Fahrenheit . The null hypothesis for an experiment to investigate this is “The mean adult body temperature for healthy individuals is 98.6 degrees Fahrenheit.” If we fail to reject the null hypothesis, then our working hypothesis remains that the average adult who is healthy has a temperature of 98.6 degrees. We do not prove that this is true.

If we are studying a new treatment, the null hypothesis is that our treatment will not change our subjects in any meaningful way. In other words, the treatment will not produce any effect in our subjects.

The Alternative Hypothesis

The alternative or experimental hypothesis reflects that there will be an observed effect for our experiment. In a mathematical formulation of the alternative hypothesis, there will typically be an inequality, or not equal to symbol. This hypothesis is denoted by either H a or by H 1 .

The alternative hypothesis is what we are attempting to demonstrate in an indirect way by the use of our hypothesis test. If the null hypothesis is rejected, then we accept the alternative hypothesis. If the null hypothesis is not rejected, then we do not accept the alternative hypothesis. Going back to the above example of mean human body temperature, the alternative hypothesis is “The average adult human body temperature is not 98.6 degrees Fahrenheit.”

If we are studying a new treatment, then the alternative hypothesis is that our treatment does, in fact, change our subjects in a meaningful and measurable way.

The following set of negations may help when you are forming your null and alternative hypotheses. Most technical papers rely on just the first formulation, even though you may see some of the others in a statistics textbook.

• Null hypothesis: “ x is equal to y .” Alternative hypothesis “ x is not equal to y .”
• Null hypothesis: “ x is at least y .” Alternative hypothesis “ x is less than y .”
• Null hypothesis: “ x is at most y .” Alternative hypothesis “ x is greater than y .”
• What 'Fail to Reject' Means in a Hypothesis Test
• Type I and Type II Errors in Statistics
• An Example of a Hypothesis Test
• The Runs Test for Random Sequences
• An Example of Chi-Square Test for a Multinomial Experiment
• The Difference Between Type I and Type II Errors in Hypothesis Testing
• What Level of Alpha Determines Statistical Significance?
• What Is the Difference Between Alpha and P-Values?
• What Is ANOVA?
• How to Find Critical Values with a Chi-Square Table
• Example of a Permutation Test
• Degrees of Freedom for Independence of Variables in Two-Way Table
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• How to Construct a Confidence Interval for a Population Proportion
• Degrees of Freedom in Statistics and Mathematics

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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 ) – 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 (H a ) – This is also known as the claim. This hypothesis should state what you expect the data to show, based on your research on the topic. This is your answer to your research question.

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.

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Null vs. Alternative Hypothesis

04.28.2023 • 5 min read

Sarah Thomas

Subject Matter Expert

Learn about a null versus alternative hypothesis and what they show with examples for each. Also go over the main differences and similarities between them.

In This Article

What Is a Null Hypothesis?

What is an alternative hypothesis, outcomes of a hypothesis test.

Main Differences Between Null & Alternative Hypothesis

Similarities Between Null & Alternative Hypothesis

Hypothesis Testing & Errors

In statistics, you’ll draw insights or “inferences” about population parameters using data from a sample. This process is called inferential statistics.

To make statistical inferences, you need to determine if you have enough evidence to support a certain hypothesis about the population. This is where null and alternative hypotheses come into play!

In this article, we’ll explain the differences between these two types of hypotheses, and we’ll explain the role they play in hypothesis testing.

Imagine you want to know what percent of Americans are vegetarians. You find a Gallup poll claiming ‌5% of the population was vegetarian in 2018, but your intuition tells you vegetarianism is on the rise and that ‌far more than 5% of Americans are vegetarian today.

To investigate further, you collect your own sample data by surveying 1,000 randomly selected Americans. You’ll use this random sample to determine whether it’s likely ‌the true population proportion of vegetarians is, in fact, 5% (as the Gallup data suggests) or whether it could be the case that the percentage of vegetarians is now higher.

Notice ‌that your investigation involves two rival hypotheses about the population. One hypothesis is that the proportion of vegetarians is 5%. The other hypothesis is that the proportion of vegetarians is greater than 5%. In statistics, we would call the first hypothesis the null hypothesis, and the second hypothesis the alternative hypothesis. The null hypothesis ( H 0 H_0 H 0 ​ ) represents the status quo or what is assumed to be true about the population at the start of your investigation.

Null Hypothesis

In hypothesis testing, the null hypothesis ( H 0 H_0 H 0 ​ ) is the default hypothesis.

It's what the status quo assumes to be true about the population.

The alternative hypothesis ( H a H_a H a ​ or H 1 H_1 H 1 ​ ) is the hypothesis that stands contrary to the null hypothesis. The alternative hypothesis ‌represents the research hypothesis—what you as the statistician are trying to prove with your data .

In medical studies, where scientists are trying to demonstrate whether a treatment has a significant effect on patient outcomes, the alternative hypothesis represents the hypothesis that the treatment does have an effect, while the null hypothesis represents the assumption that the treatment has no effect.

Alternative Hypothesis

The alternative hypothesis ( H a H_a H a ​ or H 1 H_1 H 1 ​ ) is the hypothesis being proposed in opposition to the null hypothesis.

Examples of Null and Alternative Hypotheses

In a hypothesis test, the null and alternative hypotheses must be mutually exclusive statements, meaning both hypotheses cannot be true at the same time. For example, if the null hypothesis includes an equal sign, the alternative hypothesis must state that the values being mentioned are “not equal” in some way.

Your hypotheses will also depend on the formulation of your test—are you running a one-sample T-test, a two-sample T-test, F-test for ANOVA , or a Chi-squared test? It also matters whether you are conducting a directional one-tailed test or a nondirectional two-tailed test.

Example 1: Two-Tailed T-test

Null Hypothesis: The population mean is equal to some number, x. 𝝁 = x

Alternative Hypothesis: The population mean is not equal to x. 𝝁 ≠ x

Example 2: One-tailed T-test (Right-Tailed)

Null Hypothesis: The population mean is less than or equal to some number, x. 𝝁 ≤ x Alternative Hypothesis: The population mean is greater than x. 𝝁 > x

Example 3: One-tailed T-test (Left-Tailed)

Null Hypothesis: The population mean is greater than or equal to some number, x. 𝝁 ≥ x

Alternative Hypothesis: The population mean is less than x. 𝝁 < x

By the end of a hypothesis test, you will have reached one of two conclusions.

You will run into either 2 outcomes:

Fail to reject the null hypothesis on the grounds that there's insufficient evidence to move away from the null hypothesis

Reject the null hypothesis in favor of the alternative.

If you’re ‌confused about the outcomes of a hypothesis test, a good analogy is a jury trial. In a jury trial, the defendant is innocent until proven guilty. To reach a verdict of guilt, the jury must find strong evidence (beyond a reasonable doubt) that the defendant committed the crime.

This is analogous to a statistician who must assume the null hypothesis is true unless they can uncover strong evidence ( a p-value less than or equal to the significance level) in support of the alternative hypothesis.

Notice also, that a jury never concludes a defendant is innocent—only that the defendant is guilty or not guilty. This is similar to how we never conclude that the null hypothesis is true. In a hypothesis test, we never conclude ‌that the null hypothesis is true. We can only “reject” the null hypothesis or “fail to reject” it.

In this video, let’s look at the jury example again, the reasoning behind hypothesis testing, and how to form a test. It starts by stating your null and alternative hypotheses.

Main Differences Between Null and Alternative Hypothesis

Here is a summary of the key differences between the null and the alternative hypothesis test.

The null hypothesis represents the status quo; the alternative hypothesis represents an alternative statement about the population.

The null and the alternative are mutually exclusive statements, meaning both statements cannot be true at the same time.

In a medical study, the null hypothesis represents the assumption that a treatment has no statistically significant effect on the outcome being studied. The alternative hypothesis represents the belief that the treatment does have an effect.

The null hypothesis is denoted by H_0 ; the alternative hypothesis is denoted by H_a H_1

You “fail to reject” the null hypothesis when the p-value is larger than the significance level. You “reject” the null hypothesis in favor of the alternative hypothesis when the p-value is less than or equal to your test’s significance level.

Similarities Between Null and Alternative Hypothesis

The similarities between the null and alternative hypotheses are as follows.

Both the null and the alternative are statements about the same underlying data.

Both statements provide a possible answer to a statistician’s research question.

The same hypothesis test will provide evidence for or against the null and alternative hypotheses.

Hypothesis Testing and Errors

Always remember that statistical inference provides you with inferences based on probability rather than hard truths. Anytime you conduct a hypothesis test, there is a chance that you’ll reach the wrong conclusion about your data.

In statistics, we categorize these wrong conclusions into two types of errors:

Type I Errors

Type II Errors

Type I Error (ɑ)

A Type I error occurs when you reject the null hypothesis when, in fact, the null hypothesis is true. This is sometimes called a false positive and is analogous to a jury that falsely convicts an innocent defendant. The probability of making this type of error is represented by alpha, ɑ.

Type II Error (ꞵ)

A Type II error occurs when you fail to reject the null hypothesis when, in fact, the null hypothesis is false. This is sometimes called a false negative and is analogous to a jury that reaches a verdict of “not guilty,” when, in fact, the defendant has committed the crime. The probability of making this type of error is represented by beta, ꞵ.

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Differences Between the Null Hypothesis and the Alternative Hypothesis in Statistical Analysis

Statistical hypotheses , consisting of the null hypothesis and the alternative hypothesis, play a crucial role in the process of testing and analyzing statistical data. Understanding the concept of a hypothesis is a critical first step in ensuring that research results are valid and scientifically accountable.

Statistical hypotheses help us to formulate research questions in a form that can be mathematically tested. Through hypotheses, we can also evaluate whether the research objectives have been met.

A proper understanding of these hypotheses allows us to draw accurate conclusions based on the data obtained during the research process. In this article, Kanda Data discusses the differences between the null hypothesis and the alternative hypothesis in statistical analysis.

Definition of a Hypothesis

A hypothesis is a proposed statement serving as a tentative explanation for a phenomenon or relationship observed during research activities. Additionally, we can define a hypothesis as a prediction or conjecture made before data is collected, which is then tested.

In research analyzed using inferential statistics, it is essential to incorporate hypothesis testing properly. In inferential statistical analysis, the formulation of a statistical hypothesis is vital for empirically proving the research questions or objectives.

Difference Between a Research Hypothesis and a Statistical Hypothesis

In research, we may encounter the term “hypothesis,” which at first glance seems similar but has different meanings. In statistics, we recognize both research hypotheses and statistical hypotheses. So, what is the difference between them?

Now, let’s distinguish between a research hypothesis and a statistical hypothesis. A research hypothesis is a statement made by a researcher based on theory or initial observations to explain a phenomenon.

On the other hand, a statistical hypothesis can be defined as a statement that can be mathematically tested using data collected during research activities. Subsequently, the statistical hypothesis we have created can be used to accept or reject the research hypothesis.

Understanding the Null Hypothesis and the Alternative Hypothesis

After understanding the difference between a research hypothesis and a statistical hypothesis, let’s delve deeper into statistical hypotheses. In hypothesis testing, there are two opposing types of hypotheses: the null hypothesis (H0) and the alternative hypothesis (H1 or Ha).

Next, let’s explore the differences between the null hypothesis and the alternative hypothesis more thoroughly. The Null Hypothesis (H0) is a statement that there is no significant effect/relationship/difference between the variables being tested.

The null hypothesis serves as the default statement assumed to be true until there is sufficient evidence to reject it. An example of a null hypothesis formulation might be: “There is no difference in the average rice production of farmers before and after participating in the extension program.”

So, what is the alternative hypothesis? The Alternative Hypothesis (H1 or Ha) states the opposite condition, namely that there is a significant effect/relationship/difference between the variables being tested. This hypothesis is the inverse of the null hypothesis and is proposed by the researcher to be tested for its truth. Example: “There is a difference in the average rice production of farmers before and after participating in the extension program.”

Based on the information I have provided, the main difference between these two hypotheses lies in their nature: the null hypothesis states that there is no effect/relationship/difference, while the alternative hypothesis states that there is an effect/relationship/difference.

Example of Statistical Hypothesis Formulation

To better understand the formulation of statistical hypotheses, I will provide an example. Suppose a researcher wants to test whether there is a difference in rice production among farmers before and after participating in the extension program. The statistical hypotheses can be formulated as follows:

Null Hypothesis (H0): The average rice production of farmers before and after participating in the extension program is not different (µ_before program = µ_after program). Alternative Hypothesis (H1): The average rice production of farmers before and after participating in the extension program is different (µ_before program ≠ µ_after program).

In this case, the null hypothesis states that there is no difference in rice production before and after participating in the extension program, while the alternative hypothesis states that there is a difference in rice production before and after participating in the extension program.

Understanding the differences between the null hypothesis and the alternative hypothesis is essential for us to grasp thoroughly during the process of statistical hypothesis testing. The null hypothesis serves as a basic statement that is tested to determine whether there is sufficient evidence to support the alternative hypothesis.

By formulating and testing hypotheses correctly, we hope to draw valid and significant conclusions from the data analysis we conduct. Well, that concludes the article I can write on this occasion. Stay tuned for updates from Kanda Data in the next educational article.

Difference Among Regression, Correlation, and Comparative Test

Hypothesis Test for Regression and Correlation Analysis