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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.

• At this point we can write hypotheses for a single mean (\(\mu\)), paired means(\(\mu_d\)), a single proportion (\(p\)), the difference between two independent means (\(\mu_1-\mu_2\)), the difference between two proportions (\(p_1-p_2\)), a simple linear regression slope (\(\beta\)), and a correlation (\(\rho\)). 
• The research question will give us the information necessary to determine if the test is two-tailed (e.g., "different from," "not equal to"), right-tailed (e.g., "greater than," "more than"), or left-tailed (e.g., "less than," "fewer than").
• The research question will also give us the hypothesized parameter value. This is the number that goes in the hypothesis statements (i.e., \(\mu_0\) and \(p_0\)). For the difference between two groups, regression, and correlation, this value is typically 0.

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., =).

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AP®︎/College Statistics

Course: ap®︎/college statistics   >   unit 10.

• Idea behind hypothesis testing

Examples of null and alternative hypotheses

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

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Video transcript

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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Hypothesis Testing with One Sample

Null and Alternative Hypotheses

OpenStaxCollege

[latexpage]

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.

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 .

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 (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

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

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

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

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

<!– ??? –>

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.

Chapter 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:

Formula Review

H 0 and H a are contradictory.

If α ≤ p -value, then do not reject H 0 .

If α > p -value, then reject H 0 .

α is preconceived. Its value is set before the hypothesis test starts. The p -value is calculated from the data.

You are testing that the mean speed of your cable Internet connection is more than three Megabits per second. What is the random variable? Describe in words.

The random variable is the mean Internet speed in Megabits per second.

You are testing that the mean speed of your cable Internet connection is more than three Megabits per second. State the null and alternative hypotheses.

The American family has an average of two children. What is the random variable? Describe in words.

The random variable is the mean number of children an American family has.

The mean entry level salary of an employee at a company is 💲58,000. You believe it is higher for IT professionals in the company. State the null and alternative hypotheses.

A sociologist claims the probability that a person picked at random in Times Square in New York City is visiting the area is 0.83. You want to test to see if the proportion is actually less. What is the random variable? Describe in words.

The random variable is the proportion of people picked at random in Times Square visiting the city.

A sociologist claims the probability that a person picked at random in Times Square in New York City is visiting the area is 0.83. You want to test to see if the claim is correct. State the null and alternative hypotheses.

In a population of fish, approximately 42% are female. A test is conducted to see if, in fact, the proportion is less. State the null and alternative hypotheses.

Suppose that a recent article stated that the mean time spent in jail by a first–time convicted burglar is 2.5 years. A study was then done to see if the mean time has increased in the new century. A random sample of 26 first-time convicted burglars in a recent year was picked. The mean length of time in jail from the survey was 3 years with a standard deviation of 1.8 years. Suppose that it is somehow known that the population standard deviation is 1.5. If you were conducting a hypothesis test to determine if the mean length of jail time has increased, what would the null and alternative hypotheses be? The distribution of the population is normal.

A random survey of 75 death row inmates revealed that the mean length of time on death row is 17.4 years with a standard deviation of 6.3 years. If you were conducting a hypothesis test to determine if the population mean time on death row could likely be 15 years, what would the null and alternative hypotheses be?

• H 0 : __________
• H a : __________
• H 0 : μ = 15
• H a : μ ≠ 15

The National Institute of Mental Health published an article stating that in any one-year period, approximately 9.5 percent of American adults suffer from depression or a depressive illness. Suppose that in a survey of 100 people in a certain town, seven of them suffered from depression or a depressive illness. If you were conducting a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult American population, what would the null and alternative hypotheses be?

Some of the following statements refer to the null hypothesis, some to the alternate hypothesis.

State the null hypothesis, H 0 , and the alternative hypothesis. H a , in terms of the appropriate parameter ( μ or p ).

• The mean number of years Americans work before retiring is 34.
• At most 60% of Americans vote in presidential elections.
• The mean starting salary for San Jose State University graduates is at least 💲100,000 per year.
• Twenty-nine percent of high school seniors get drunk each month.
• Fewer than 5% of adults ride the bus to work in Los Angeles.
• The mean number of cars a person owns in her lifetime is not more than ten.
• About half of Americans prefer to live away from cities, given the choice.
• Europeans have a mean paid vacation each year of six weeks.
• The chance of developing breast cancer is under 11% for women.
• Private universities’ mean tuition cost is more than 💲20,000 per year.
• H 0 : μ = 34; H a : μ ≠ 34
• H 0 : p ≤ 0.60; H a : p > 0.60
• H 0 : μ ≥ 100,000; H a : μ < 100,000
• H 0 : p = 0.29; H a : p ≠ 0.29
• H 0 : p = 0.05; H a : p < 0.05
• H 0 : μ ≤ 10; H a : μ > 10
• H 0 : p = 0.50; H a : p ≠ 0.50
• H 0 : μ = 6; H a : μ ≠ 6
• H 0 : p ≥ 0.11; H a : p < 0.11
• H 0 : μ ≤ 20,000; H a : μ > 20,000

Over the past few decades, public health officials have examined the link between weight concerns and teen girls’ smoking. Researchers surveyed a group of 273 randomly selected teen girls living in Massachusetts (between 12 and 15 years old). After four years the girls were surveyed again. Sixty-three said they smoked to stay thin. Is there good evidence that more than thirty percent of the teen girls smoke to stay thin? The alternative hypothesis is:

• p < 0.30
• p > 0.30

A statistics instructor believes that fewer than 20% of Evergreen Valley College (EVC) students attended the opening night midnight showing of the latest Harry Potter movie. She surveys 84 of her students and finds that 11 attended the midnight showing. An appropriate alternative hypothesis is:

• p > 0.20
• p < 0.20

Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test. The null and alternative hypotheses are:

• H o : \(\overline{x}\) = 4.5, H a : \(\overline{x}\) > 4.5
• H o : μ ≥ 4.5, H a : μ < 4.5
• H o : μ = 4.75, H a : μ > 4.75
• H o : μ = 4.5, H a : μ > 4.5

Data from the National Institute of Mental Health. Available online at http://www.nimh.nih.gov/publicat/depression.cfm.

Null and Alternative Hypotheses Copyright © 2013 by OpenStaxCollege is licensed under a Creative Commons Attribution 4.0 International License , except where otherwise noted.

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• Knowledge Base
• Methodology
• How to Write a Strong Hypothesis | Guide & Examples

How to Write a Strong Hypothesis | Guide & Examples

Published on 6 May 2022 by Shona McCombes .

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.

Table of contents

What is a hypothesis, developing a hypothesis (with example), hypothesis examples, 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).

Variables in hypotheses

Hypotheses propose a relationship between two or more variables . An independent variable is something the researcher changes or controls. A dependent variable is something the researcher observes and measures.

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 .

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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.

Step 2: Do some preliminary research

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 identify which variables you will study and what you think the relationships are between them. Sometimes, you’ll have to operationalise more complex constructs.

Step 3: Formulate your hypothesis

Now you should have some idea of what you expect to find. Write your initial answer to the question in a clear, concise sentence.

Step 4: Refine your hypothesis

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:

• The relevant variables
• The specific group being studied
• The predicted outcome of the experiment or analysis

Step 5: Phrase your hypothesis in three ways

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.

Step 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 .

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 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).

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

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

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McCombes, S. (2022, May 06). How to Write a Strong Hypothesis | Guide & Examples. Scribbr. Retrieved 9 June 2024, from https://www.scribbr.co.uk/research-methods/hypothesis-writing/

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8.1.1: Null and Alternative Hypotheses

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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.

\(H_{0}\) 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.

Example \(\PageIndex{1}\)

• \(H_{0}\): No more than 30% of the registered voters in Santa Clara County voted in the primary election. \(p \leq 30\)
• \(H_{a}\): More than 30% of the registered voters in Santa Clara County voted in the primary election. \(p > 30\)

Exercise \(\PageIndex{1}\)

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%. \(p \neq 0.25\)

Example \(\PageIndex{2}\)

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:

• \(H_{0}: \mu = 2.0\)
• \(H_{a}: \mu \neq 2.0\)

Exercise \(\PageIndex{2}\)

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 \((=, \neq, \geq, <, \leq, >)\) for the null and alternative hypotheses.

• \(H_{0}: \mu \_ 66\)
• \(H_{a}: \mu \_ 66\)
• \(H_{0}: \mu = 66\)
• \(H_{a}: \mu \neq 66\)

Example \(\PageIndex{3}\)

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:

• \(H_{0}: \mu \geq 5\)
• \(H_{a}: \mu < 5\)

Exercise \(\PageIndex{3}\)

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.

• \(H_{0}: \mu \_ 45\)
• \(H_{a}: \mu \_ 45\)
• \(H_{0}: \mu \geq 45\)
• \(H_{a}: \mu < 45\)

Example \(\PageIndex{4}\)

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.

• \(H_{0}: p \leq 0.066\)
• \(H_{a}: p > 0.066\)

Exercise \(\PageIndex{4}\)

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 (\(=, \neq, \geq, <, \leq, >\)) for the null and alternative hypotheses.

• \(H_{0}: p \_ 0.40\)
• \(H_{a}: p \_ 0.40\)
• \(H_{0}: p = 0.40\)
• \(H_{a}: p > 0.40\)

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.

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 \((=, \leq \text{or} \geq)\)
• Always write the alternative hypothesis , typically denoted with \(H_{a}\) or \(H_{1}\), using less than, greater than, or not equals symbols, i.e., \((\neq, >, \text{or} <)\).
• 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.

Formula Review

\(H_{0}\) and \(H_{a}\) are contradictory.

• If \(\alpha \leq p\)-value, then do not reject \(H_{0}\).
• If\(\alpha > p\)-value, then reject \(H_{0}\).

\(\alpha\) is preconceived. Its value is set before the hypothesis test starts. The \(p\)-value is calculated from the data.References

Data from the National Institute of Mental Health. Available online at http://www.nimh.nih.gov/publicat/depression.cfm .

Hypothesis Testing (cont...)

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:

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:

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.

Significance levels

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).

One- and two-tailed predictions

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:

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:

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.

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. 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.

How to Write a Null and Alternative Hypothesis: A Guide With Examples

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When undertaking a qualitative or quantitative research project, researchers must first formulate a research question, from which they develop a hypothesis. By definition, a hypothesis is a prediction that a researcher makes about the research question and can either be affirmative or negative. In this case, a research question has three main components: variables (independent and dependent), a population sample, and the relation between the variables. When the prediction contradicts the research question, it is referred to as a null hypothesis. In short, a null hypothesis is a statement that implies there is no relationship between independent and dependent variables. Hence, researchers need to learn how to write a good null and alternative hypothesis to present quality studies.

General Aspect of Writing a Null and Alternative Hypothesis

Students with qualitative or quantitative research assignments must learn how to formulate and write a good research question and hypothesis. By definition, a hypothesis is an assumption or prediction that a researcher makes before undertaking an experimental investigation. Basically, academic standards require such a prediction to be a precise and testable statement, meaning that researchers must prove or disapprove of it in the course of the assignment. In this case, the main components of a hypothesis are variables (independent and dependent), a population sample, and the relation between the variables. Therefore, a research hypothesis is a prediction that researchers write about the relationship between two or more variables. In turn, the research inquiry is the process that seeks to answer the research question and, in the process, test the hypothesis by confirming or disapproving it.

Types of Hypotheses

There are several types of hypotheses, including an alternative hypothesis, a null hypothesis, a directional hypothesis, and a non-directional hypothesis. Basically, the directional hypothesis is a prediction of how the independent variable affects the dependent variable. In contrast, the non-directional hypothesis predicts that the independent variable influences the dependent variable, but does not specify how. Regardless of the type, all hypotheses are about predicting the relationship between the independent and dependent variables.

What Is a Null and Alternative Hypothesis

A null hypothesis, usually symbolized as “H0,” is a statement that contradicts the research hypothesis. In other words, it is a negative statement, indicating that there is no relationship between the independent and dependent variables. By testing the null hypothesis, a researcher can determine whether the inquiry results are due to the chance or the effect of manipulating the dependent variable. In most instances, a null hypothesis corresponds with an alternative hypothesis, a positive statement that covers a relationship that exists between the independent and dependent variables. Also, it is highly recommended that a researcher should write the alternative hypothesis first before the null hypothesis.

10 Examples of Research Questions Цith H0 and H1 Hypotheses

Before developing a hypothesis, a researcher must formulate the research question. Then, the next step is to transform the question into a negative statement that claims the lack of a relationship between the independent and dependent variables. Alternatively, researchers can change the question into a positive statement that includes a relationship that exists between the variables. In turn, this latter statement becomes the alternative hypothesis and is symbolized as H1. Hence, some of the examples of research questions and hull and alternative hypotheses are as follows:

1. Do physical exercises help individuals to age gracefully?

A Null Hypothesis (H0): Physical exercises are not a guarantee for graceful old age.

An Alternative Hypothesis (H1): Engaging in physical exercises enables individuals to remain healthy and active into old age.

2. What are the implications of therapeutic interventions in the fight against substance abuse?

H0: Therapeutic interventions are of no help in the fight against substance abuse.

H1: Exposing individuals with substance abuse disorders to therapeutic interventions helps to control and even stop their addictions.

3. How do sexual orientation and gender identity affect the experiences of late adolescents in foster care?

H0: Sexual orientation and gender identity have no effects on the experiences of late adolescents in foster care.

H1: The reality of stereotypes in society makes sexual orientation and gender identity factors complicate the experiences of late adolescents in foster care.

4. Does income inequality contribute to crime in high-density urban areas?

H0: There is no correlation between income inequality and incidences of crime in high-density urban areas.

H1: The high crime rates in high-density urban areas are due to the incidence of income inequality in those areas.

5. Does placement in foster care impact individuals’ mental health?

H0: There is no correlation between being in foster care and having mental health problems.

H1: Individuals placed in foster care experience anxiety and depression at one point in their life.

6. Do assistive devices and technologies lessen the mobility challenges of older adults with a stroke?

H0: Assistive devices and technologies do not provide any assistance to the mobility of older adults diagnosed with a stroke.

H1: Assistive devices and technologies enhance the mobility of older adults diagnosed with a stroke.

7. Does race identity undermine classroom participation?

H0: There is no correlation between racial identity and the ability to participate in classroom learning.

H1: Students from racial minorities are not as active as white students in classroom participation.

8. Do high school grades determine future success?

H0: There is no correlation between how one performs in high school and their success level in life.

H1: Attaining high grades in high school positions one for greater success in the future personal and professional lives.

9. Does critical thinking predict academic achievement?

H0: There is no correlation between critical thinking and academic achievement.

H1: Being a critical thinker is a pathway to academic success.

10. What benefits does group therapy provide to victims of domestic violence?

H0: Group therapy does not help victims of domestic violence because individuals prefer to hide rather than expose their shame.

H1: Group therapy provides domestic violence victims with a platform to share their hurt and connect with others with similar experiences.

Summing Up on How to Write a Null and Alternative Hypothesis

The formulation of research questions in qualitative and quantitative assignments helps students develop a hypothesis for their experiment. In this case, learning how to write a good hypothesis helps students and researchers to make their research relevant. Basically, the difference between a null and alternative hypothesis is that the former contradicts the research question, while the latter affirms it. In short, a null hypothesis is a negative statement relative to the research question, and an alternative hypothesis is a positive statement. Moreover, it is important to note that developing the null hypothesis at the beginning of the assignment is for prediction purposes. As such, the research work answers the research question and confirms or disapproves of the hypothesis. Hence, some of the tips that students and researchers need to know when developing a null hypothesis include:

• Formulate a research question that specifies the relationship between an independent variable and a dependent variable.
• Develop an alternative hypothesis that says a relationship that exists between the variables.
• Develop a null hypothesis that says a relationship that does not exist between the variables.
• Conduct the research to answer the research question, which allows the confirmation of a disapproval of a null hypothesis.

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Alternative Hypothesis

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Diving deep into the realm of scientific research, the alternative hypothesis plays a pivotal role in steering investigations. It stands contrary to the null hypothesis , providing a different perspective or direction. This essential component often sets the foundation for groundbreaking discoveries. If you’re keen on understanding this concept further, our collection of alternative hypothesis statement examples, combined with a thorough writing guide and insightful tips, will serve as your comprehensive roadmap.

What is an Alternative hypothesis?

An alternative hypothesis is a statement used in statistical testing that indicates the presence of an effect, relationship, or difference. It stands in direct contrast to the null hypothesis, which posits that there is no effect or relationship. The alternative causual hypothesis provides a specific direction to the research and can be directional (e.g., one value is greater than another) or non-directional (e.g., two values are not equal).

What is an example of an Alternative hypothesis statement?

If a researcher is studying the effect of a new teaching method on student performance, the null hypothesis might be: “The new teaching method has no effect on student performance.” An example of an alternative hypothesis could be:

Directional: “Students exposed to the new teaching method will perform better than those who were not.” Non-directional: “Student performance will be different for those exposed to the new teaching method compared to those who were not.”

100 Alternative Hypothesis Statement Examples

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The alternative hypothesis symbolizes a statement of what a statistical hypothesis test is set to establish. Often contrasted with a null hypothesis, it indicates the expected direction of the tested relation. Dive into these varied thesis statement examples showcasing the core essence of alternative hypotheses.

• Smoking and Cancer : Smoking is positively related to lung cancer incidence.
• Diet and Weight Loss : The Atkins diet results in more weight loss than a conventional diet.
• Medication Efficiency : Drug A is more effective than Drug B in treating migraines.
• Exercise Duration : Engaging in physical activity for more than 30 minutes daily reduces depression symptoms.
• Class Size and Learning : Smaller class sizes lead to higher student test scores.
• Sugar Intake : Consuming more than 50 grams of sugar daily increases the risk of diabetes.
• Vitamin C and Cold : Vitamin C intake reduces the duration of the common cold.
• Sleep Duration : Sleeping less than 6 hours results in decreased cognitive function.
• Training Methods : Method X training increases employee productivity more than Method Y.
• Pollution Levels : Higher levels of industrial activity correlate with increased air pollution.
• Stress and Disease : Chronic stress has a positive relationship with heart diseases.
• Alcohol and Reaction Time : Alcohol consumption slows down reaction time.
• Meditation and Blood Pressure : Regular meditation lowers blood pressure.
• Organic Food : Consuming organic food leads to better gut health.
• Advertising : Increased advertising results in higher sales figures.
• Salary and Job Satisfaction : A higher salary correlates with job satisfaction.
• Age and Memory : As age increases, short-term memory retention decreases.
• Temperature and Aggression : Higher temperatures are associated with increased aggressive behavior.
• Social Media : Spending more than 2 hours on social media daily increases feelings of loneliness.
• Music and Concentration : Listening to classical music improves concentration during studies. …
• Recycling Habits : Communities with mandatory recycling policies have higher recycling rates.
• Urban Areas : Living in urban areas increases the likelihood of asthma.
• Pets and Loneliness : Owning a pet decreases feelings of loneliness.
• Reading Habits : Reading more than 3 books a month correlates with increased empathy.
• Green Spaces : Having access to green spaces reduces stress levels.
• Vaccination : Vaccination reduces the incidence of specific diseases.
• Chocolate and Mood : Consuming chocolate elevates mood.
• Remote Work : Working remotely improves overall work satisfaction.
• Financial Literacy : Financial literacy education reduces personal debt.
• Mindfulness and Anxiety : Practicing mindfulness decreases symptoms of anxiety. …
• Dietary Fiber : Higher dietary fiber intake is associated with lower risks of bowel cancer.
• Travel and Creativity : People who travel frequently are more creative.
• Education Level and Income : Individuals with higher education levels earn more income.
• Technology Adoption : People who receive technology training adapt to new devices faster.
• Parental Involvement and Academic Performance : Increased parental involvement enhances students’ academic performance.
• Exercise Frequency and Heart Health : Exercising at least five times a week improves heart health.
• Gender and Leadership Roles : Men are more likely to hold leadership positions in corporate settings.
• Social Support and Mental Health : Strong social support networks reduce the risk of depression.
• Quality of Sleep and Productivity : Better sleep quality leads to higher productivity levels.
• High-Fat Diet and Cholesterol Levels : A high-fat diet increases cholesterol levels.
• Caffeine Intake and Alertness : Higher caffeine intake enhances alertness and cognitive function.
• Online Shopping Habits : People who frequently shop online spend more money than in-store shoppers. …
• Education and Political Views : Higher education levels are associated with more liberal political views.
• Gender and Risk-Taking Behavior : Men are more likely to engage in risky behaviors.
• Temperature and Ice Cream Sales : Higher temperatures increase ice cream sales.
• Artificial Sweeteners and Weight Loss : Consuming products with artificial sweeteners aids in weight loss.
• Exercise and Stress Reduction : Regular exercise reduces stress levels.
• Music Genres and Mood : Listening to upbeat music improves mood.
• Online Learning and Engagement : Online learners are more engaged in virtual classroom discussions.
• Personality Traits and Job Performance : Extroverted individuals perform better in sales roles.
• Environmental Awareness and Recycling : Higher environmental awareness leads to more recycling practices.
• Social Media Usage and Self-Esteem : Excessive social media usage correlates with lower self-esteem. …
• Sleep Deprivation and Reaction Time : Sleep-deprived individuals have slower reaction times.
• Breakfast Consumption and Metabolism : Eating breakfast kickstarts metabolism for the day.
• Leadership Style and Employee Satisfaction : Transformational leadership style increases employee job satisfaction.
• Bilingualism and Cognitive Abilities : Bilingual individuals possess enhanced cognitive abilities.
• Video Game Playing and Aggression : Playing violent video games increases aggressive behavior.
• Hydration and Cognitive Function : Staying hydrated improves cognitive function.
• Parental Support and Academic Achievement : Supportive parenting leads to higher academic achievement.
• Workplace Flexibility and Work-Life Balance : Jobs with flexible schedules enhance work-life balance.
• Digital Learning and Knowledge Retention : Digital learning methods improve long-term knowledge retention.
• Art Exposure and Creativity : Exposure to various forms of art fosters creative thinking.
• Solar Energy Adoption and Utility Bills : Homes with solar energy systems experience lower utility bills.
• Parental Involvement and Student Behavior : Increased parental involvement reduces student behavioral issues.
• Team Diversity and Creativity : Diverse teams generate more creative solutions.
• Social Media Marketing and Brand Awareness : Social media marketing boosts brand awareness more than traditional methods.
• Morning Routine and Productivity : Following a structured morning routine enhances overall productivity.
• Music Training and Cognitive Development : Music training improves cognitive abilities in children.
• Employee Training and Job Satisfaction : Comprehensive employee training programs lead to higher job satisfaction.
• Eating Before Bed and Sleep Quality : Consuming heavy meals before bed negatively affects sleep quality.
• Financial Incentives and Employee Performance : Offering financial incentives increases employee performance.
• Parental Attachment and Emotional Well-being : Strong parental attachment fosters better emotional well-being in children.
• Social Interaction and Mental Well-being : Frequent social interaction correlates with improved mental health.
• Education and Crime Rates : Higher education levels result in lower crime rates within communities.
• Diet and Acne : A diet high in dairy products exacerbates acne.
• Leadership Style and Employee Motivation : Autocratic leadership style hampers employee motivation.
• Urban Green Spaces and Stress Reduction : Access to urban green spaces lowers stress levels.
• Sleep Duration and Athletic Performance : Adequate sleep duration enhances athletic performance.
• Financial Literacy and Investment Success : Individuals with high financial literacy make more successful investments.
• Team Collaboration and Project Success : Effective team collaboration leads to more successful project outcomes.
• Media Exposure and Body Image : Increased media exposure contributes to negative body image perceptions.
• Gender Representation and Film Success : Movies with more balanced gender representation achieve higher box office success. …
• Meditation and Anxiety Reduction : Regular meditation practice reduces symptoms of anxiety.
• Cognitive Training and Memory Enhancement : Cognitive training programs improve memory retention.
• Positive Affirmations and Self-Confidence : Repeating positive affirmations enhances self-confidence.
• Physical Fitness and Longevity : Being physically fit is linked to increased lifespan.
• Parental Guidance and Online Safety : Strong parental guidance promotes responsible online behavior in children.
• Artificial Intelligence and Job Displacement : Increased AI integration leads to more job displacement.
• Public Transportation Usage and Air Quality : Increased public transportation usage improves air quality in cities.
• Social Support and Addiction Recovery : Strong social support networks aid in addiction recovery.
• Gender Diversity and Company Performance : Companies with diverse gender representation outperform others.
• Mindfulness Meditation and Pain Management : Mindfulness meditation reduces perception of pain.
• Music Therapy and Autism : Music therapy improves social interaction skills in children with autism.
• Social Media Usage and Academic Performance : Excessive social media usage negatively impacts academic performance.
• Employee Engagement and Organizational Success : Higher employee engagement leads to greater organizational success.
• Healthy Eating and Longevity : A diet rich in fruits and vegetables contributes to a longer lifespan.
• Gender Stereotypes and Career Choice : Gender stereotypes influence career choices among young adults.
• Environmental Conservation Efforts and Biodiversity : Increased conservation efforts positively affect biodiversity.
• Volunteerism and Personal Well-being : Engaging in volunteer activities enhances personal well-being.
• Artificial Intelligence and Customer Service : AI-driven customer service improves user satisfaction.

Alternative Hypothesis Statement Examples in Research

In alternative research hypothesis propel investigations beyond the null. Examples span diverse fields, revealing the direction researchers expect their findings to take.

• Effect of Music on Concentration : Listening to classical music enhances concentration during study.
• Green Tea and Weight Loss : Green tea consumption leads to more significant weight loss than water intake.
• Parental Involvement and Academic Achievement : Active parental involvement boosts student academic achievement.
• Social Media Usage and Self-Esteem : Frequent social media use correlates with lower self-esteem.

Alternative Hypothesis Statement Examples in Business Research

Business research thrives on alternative hypotheses. Dive into these business-oriented examples that challenge null assumptions.

• Marketing Campaign Impact : Marketing campaign A generates higher conversion rates than campaign B.
• Employee Training and Productivity : Comprehensive employee training enhances workplace productivity.
• Work-Life Balance and Employee Satisfaction : Improved work-life balance increases employee job satisfaction.
• Customer Service Channel Effectiveness : Online chat support results in higher customer satisfaction compared to phone support.
• Branding Influence on Purchase Intent : Strong brand presence leads to increased purchase intent.

Directional Alternative Hypothesis Statement Examples

Directional hypothesis add clarity to research expectations. Explore these examples that predict specific outcomes.

• Exercise Frequency and Heart Health : Engaging in physical activity five times a week improves heart health.

Alternative Hypothesis Statement Examples in Psychology

Psychological studies benefit from well-crafted alternative hypotheses. These psychology hypothesis examples delve into the realm of human behavior and cognition.

• Mindfulness Meditation and Anxiety Reduction : Regular mindfulness practice reduces symptoms of anxiety.

Alternative Null Hypothesis Statement Examples

Explore alternative null hypothesis —statements asserting the absence of specific effects or differences.

• Coffee Consumption and Weight Gain : Increased coffee consumption does not lead to weight gain.
• Smartphone Usage and Sleep Quality : Using smartphones before bed does not impact sleep quality.
• Music Genre and Study Performance : Studying with rock music does not affect academic performance.
• Green Spaces and Stress Reduction : Access to green spaces does not decrease stress levels.
• Team Diversity and Project Success : Team diversity does not influence project success rates.

Alternative Hypothesis Statement Examples in Medical Research

Medical research relies on robust alternative hypotheses to drive scientific inquiry. These examples explore hypotheses in the realm of healthcare.

• Exercise and Diabetes Prevention : Regular exercise decreases the risk of developing type 2 diabetes.
• Medication A and Blood Pressure Reduction : Medication A leads to greater reduction in blood pressure compared to medication B.
• Nutritional Intake and Heart Disease : Higher intake of fruits and vegetables lowers the risk of heart disease.
• Stress Reduction Techniques and Anxiety Levels : Practicing stress reduction techniques decreases anxiety levels.
• Alternative Medicine and Pain Management : Alternative medicine therapies alleviate chronic pain more effectively than traditional treatments.

Alternative Hypothesis Statement Examples in Education Research

Education research thrives on alternative hypotheses to investigate innovative approaches. Explore examples that challenge conventional notions.

• Technology Integration and Student Engagement : Integrating technology enhances student engagement in the classroom.
• Project-Based Learning and Knowledge Retention : Project-based learning improves long-term knowledge retention.
• Teacher Professional Development and Student Performance : Effective teacher professional development positively impacts student academic performance.
• Inclusive Classroom Environment and Learning Outcomes : Inclusive classrooms lead to better learning outcomes for diverse students.
• Feedback Frequency and Writing Improvement : Frequent feedback results in greater improvement in student writing skills.

These examples showcase the pivotal role of alternative hypotheses across various disciplines, serving as the driving force behind scientific exploration and advancement.

What is the Alternative Hypothesis Formula?

The alternative hypothesis, denoted as “Ha” or “H1,” represents the assertion researchers aim to support through evidence. It stands in contrast to the null hypothesis (Ho), which suggests no effect or relationship. The formula for the alternative hypothesis varies based on the nature of the study:

• Directional Hypothesis : For studies with an expected direction, the formula takes the form of a prediction. For instance, “The new drug increases patient recovery rates.”
• Non-Directional Hypothesis : For exploratory studies, the formula reflects the possibility of any difference or effect. For example, “There is a difference in recovery rates between the two drugs.”

How do you start an Alternative Hypothesis?

Starting an alternative simple hypothesis involves framing a clear research statement that highlights the anticipated effect, relationship, or difference. To begin:

• Identify the Research Question: Determine the specific aspect you intend to explore or compare.
• Formulate a Hypothesis: Craft a statement that directly addresses the expected outcome.
• Include Variables: Introduce the relevant variables and their predicted connection.
• Be Clear and Specific: Ensure the alternative hypothesis is concise and unambiguous.

Is the Alternative Hypothesis a Claim or Statement?

The alternative hypothesis is both a claim and a statement. It claims that there is a measurable effect, relationship, or difference in the variables being studied. It is also a statement that researchers work to validate through evidence.

How do you write an Alternative Hypothesis Statement? – Step by Step Guide

Creating a robust alternative hypothesis statement involves structured steps:

• Identify Variables : Clearly define the independent and dependent variables in your study.
• State Expected Effect : Express the anticipated impact, relationship, or difference between variables.
• Be Precise : Use specific language to convey the exact nature of the expected outcome.
• Include Direction (if applicable) : If your hypothesis is directional, specify the expected direction.
• Avoid Ambiguity : Make sure your statement is clear and leaves no room for confusion.

Tips for Writing an Alternative Hypothesis Statement

• Be Specific : Clearly define the variables and the predicted relationship.
• Use Measurable Terms : Incorporate quantifiable terms to indicate the magnitude of the effect.
• Testability : Ensure the hypothesis can be tested empirically.
• Conciseness : Keep the statement concise and to the point.
• Alignment with Research Question : Ensure the hypothesis directly answers your research question.
• Avoid Value Judgments : Avoid value judgments or personal biases in the hypothesis.
• Review Literature : Consult existing literature to align your hypothesis with prior research.

Crafting a strong alternative hypothesis statement is essential for guiding your research and forming the basis for causual hypothesis testing. It directs the focus of your investigation and lays the foundation for drawing meaningful conclusions.

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Module 9: Hypothesis Testing With One Sample

Null and alternative hypotheses, learning outcomes.

• Describe hypothesis testing in general and in practice

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.

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 .

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 adecision. 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 (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

• 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

• 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

• H 0 : p = 0.40
• H a : p > 0.40

Concept 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 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.

Formula Review

H 0 and H a are contradictory.

• OpenStax, Statistics, Null and Alternative Hypotheses. Provided by : OpenStax. Located at : http://cnx.org/contents/[email protected]:58/Introductory_Statistics . License : CC BY: Attribution
• Introductory Statistics . Authored by : Barbara Illowski, Susan Dean. Provided by : Open Stax. Located at : http://cnx.org/contents/[email protected] . License : CC BY: Attribution . License Terms : Download for free at http://cnx.org/contents/[email protected]
• Simple hypothesis testing | Probability and Statistics | Khan Academy. Authored by : Khan Academy. Located at : https://youtu.be/5D1gV37bKXY . License : All Rights Reserved . License Terms : Standard YouTube License

Statistics Made Easy

How to Write Hypothesis Test Conclusions (With Examples)

A   hypothesis test is used to test whether or not some hypothesis about a population parameter is true.

To perform a hypothesis test in the real world, researchers obtain a random sample from the population and perform a hypothesis test on the sample data, using a null and alternative hypothesis:

• Null Hypothesis (H 0 ): The sample data occurs purely from chance.
• Alternative Hypothesis (H A ): The sample data is influenced by some non-random cause.

If the p-value of the hypothesis test is less than some significance level (e.g. α = .05), then we reject the null hypothesis .

Otherwise, if the p-value is not less than some significance level then we fail to reject the null hypothesis .

When writing the conclusion of a hypothesis test, we typically include:

• Whether we reject or fail to reject the null hypothesis.
• The significance level.
• A short explanation in the context of the hypothesis test.

For example, we would write:

We reject the null hypothesis at the 5% significance level.   There is sufficient evidence to support the claim that…

Or, we would write:

We fail to reject the null hypothesis at the 5% significance level.   There is not sufficient evidence to support the claim that…

The following examples show how to write a hypothesis test conclusion in both scenarios.

Example 1: Reject the Null Hypothesis Conclusion

Suppose a biologist believes that a certain fertilizer will cause plants to grow more during a one-month period than they normally do, which is currently 20 inches. To test this, she applies the fertilizer to each of the plants in her laboratory for one month.

She then performs a hypothesis test at a 5% significance level using the following hypotheses:

• H 0 : μ = 20 inches (the fertilizer will have no effect on the mean plant growth)
• H A : μ > 20 inches (the fertilizer will cause mean plant growth to increase)

Suppose the p-value of the test turns out to be 0.002.

Here is how she would report the results of the hypothesis test:

We reject the null hypothesis at the 5% significance level.   There is sufficient evidence to support the claim that this particular fertilizer causes plants to grow more during a one-month period than they normally do.

Example 2: Fail to Reject the Null Hypothesis Conclusion

Suppose the manager of a manufacturing plant wants to test whether or not some new method changes the number of defective widgets produced per month, which is currently 250. To test this, he measures the mean number of defective widgets produced before and after using the new method for one month.

He performs a hypothesis test at a 10% significance level using the following hypotheses:

• H 0 : μ after = μ before (the mean number of defective widgets is the same before and after using the new method)
• H A : μ after ≠ μ before (the mean number of defective widgets produced is different before and after using the new method)

Suppose the p-value of the test turns out to be 0.27.

Here is how he would report the results of the hypothesis test:

We fail to reject the null hypothesis at the 10% significance level.   There is not sufficient evidence to support the claim that the new method leads to a change in the number of defective widgets produced per month.

Additional Resources

The following tutorials provide additional information about hypothesis testing:

Introduction to Hypothesis Testing 4 Examples of Hypothesis Testing in Real Life How to Write a Null Hypothesis

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Hypothesis Testing | A Step-by-Step Guide with Easy Examples

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:

• 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 and discussion section.

Though the specific details might vary, the procedure you will use when testing a hypothesis will always follow some version of these steps.

Table of contents

Step 1: state your null and alternate hypothesis, step 2: collect data, step 3: perform a statistical test, step 4: decide whether to reject or fail to reject your null hypothesis, step 5: present your findings, other interesting articles, frequently asked questions about hypothesis testing.

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.

• H 0 : Men are, on average, not taller than women. H a : Men are, on average, taller than women.

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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 .

• an estimate of the difference in average height between the two groups.
• a p -value showing how likely you are to see this difference if the null hypothesis of no difference is true.

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 ).

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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.

• Normal distribution
• Descriptive statistics
• Measures of central tendency
• Correlation coefficient

Methodology

• Cluster sampling
• Stratified sampling
• Types of interviews
• Cohort study
• Thematic analysis

Research bias

• Implicit bias
• Cognitive bias
• Survivorship bias
• Availability heuristic
• Nonresponse bias
• Regression to the mean

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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Writing Null Hypotheses in Research and Statistics

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 High School 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 26,330 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.

Things You Should Know

• Write a research null hypothesis as a statement that the studied variables have no relationship to each other, or that there's no difference between 2 groups.

• 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.

What is a null hypothesis?

• Research hypothesis: States in plain language that there's no relationship between the 2 variables or there's no difference between the 2 groups being studied.
• Statistical hypothesis: States the predicted outcome of statistical analysis through a mathematical equation related to the statistical method you're using.

Examples of Null Hypotheses

Null Hypothesis vs. Alternative Hypothesis

• For example, your alternative hypothesis could state a positive correlation between 2 variables while your null hypothesis states there's no relationship. If there's a negative correlation, then both hypotheses are false.

• You need additional data or evidence to show that your alternative hypothesis is correct—proving the null hypothesis false is just the first step.
• In smaller studies, sometimes it's enough to show that there's some relationship and your hypothesis could be correct—you can leave the additional proof as an open question for other researchers to tackle.

How do I test a null hypothesis?

• Group means: Compare the mean of the variable in your sample with the mean of the variable in the general population. [6] X Research source
• Group proportions: Compare the proportion of the variable in your sample with the proportion of the variable in the general population. [7] X Research source
• Correlation: Correlation analysis looks at the relationship between 2 variables—specifically, whether they tend to happen together. [8] X Research source
• Regression: Regression analysis reveals the correlation between 2 variables while also controlling for the effect of other, interrelated variables. [9] X Research source

Templates for Null Hypotheses

• Research null hypothesis: There is no difference in the mean [dependent variable] between [group 1] and [group 2].

• Research null hypothesis: The proportion of [dependent variable] in [group 1] and [group 2] is the same.

• Research null hypothesis: There is no correlation between [independent variable] and [dependent variable] in the population.

• Research null hypothesis: There is no relationship between [independent variable] and [dependent variable] in the population.

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Thanks for reading our article! If you’d like to learn more about physics, check out our in-depth interview with Joseph Quinones .

• ↑ https://online.stat.psu.edu/stat100/lesson/10/10.1
• ↑ https://online.stat.psu.edu/stat501/lesson/2/2.12
• ↑ https://support.minitab.com/en-us/minitab/21/help-and-how-to/statistics/basic-statistics/supporting-topics/basics/null-and-alternative-hypotheses/
• ↑ https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5635437/
• ↑ https://online.stat.psu.edu/statprogram/reviews/statistical-concepts/hypothesis-testing
• ↑ https://education.arcus.chop.edu/null-hypothesis-testing/
• ↑ https://sphweb.bumc.bu.edu/otlt/mph-modules/bs/bs704_hypothesistest-means-proportions/bs704_hypothesistest-means-proportions_print.html

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How to Insert the Null Hypothesis Symbol in Microsoft Word

In Microsoft Word you can type the null hypothesis symbol, which is the letter H followed by the numeral 0 as a subscript using the subscript button in the Home tab, or you can use a keyboard shortcut to apply the subscript format. Note that after typing the zero as a subscript, any punctuation immediately after it will also appear as a subscript unless you disable the subscript formatting.

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Typing the Symbol

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To type the null hypothesis symbol, type the letter "H" and then click the subscript icon in the Font section of the Home tab. Your cursor will appear smaller, and you can now type the numeral "0." When you press the space bar, your font will change back to your default font size and you can continue typing.

Using a Keyboard Shortcut

After you've typed the letter "H," press and hold the Ctrl key, then press the equal sign and then release both. You can now type the numeral "0," which will appear as a subscript. When you press space, your font size will revert to what it was formerly and you can continue typing.

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• New York University: Elementary Statistics Tests of Hypothesis: Means

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

Julia Simkus

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On This Page:

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

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

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

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

How to Write a Null Hypothesis

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

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

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

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

Examples of Null Hypotheses

When Do We Reject The Null Hypothesis? 

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

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

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

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

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

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

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

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

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

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

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

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

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

Why Do We Never Accept The Null Hypothesis?

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

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

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

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

Why Do We Use The Null Hypothesis?

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

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

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

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

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

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

Purpose of a Null Hypothesis 

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

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

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

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

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

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

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

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

What are some problems with the null hypothesis?

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

Why can a null hypothesis not be accepted?

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

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

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

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

Is a null hypothesis directional or non-directional?

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

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

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

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

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

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

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

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

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

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6 Best Free Alternatives to Microsoft Word

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• Best for sharing and real time collaboration: Google Docs
• Best for long and complex documents: Apache OpenOffice Writer
• Best for automation: Zoho Writer
• Best for customization: LibreOffice Writer
• Best for advanced features: WPS Office Writer
• Best for users who prefer Microsoft Word's interface: Microsoft Office Word Online

Microsoft Word has its devotees, but find one person who loves it, and you’ll probably find several who don’t. From redesigns that hide familiar menu items to overly complicated and often unused features, there’s a lot to be desired in a simple word processor that Microsoft Word doesn’t deliver due to its complex nature.

Microsoft Word as a part of Microsoft Office is expensive — for instance, Microsoft 365 Business Premium costs $22 for each user per month.

SEE: Discover the best free alternatives to Microsoft Excel .

If you don’t need all the features that Microsoft Word offers, it can be hard to justify paying that price, especially in a small business environment where you just need a word processor. Don’t pay for what you won’t use and take a look at one of these six free Microsoft Word alternatives instead.

Alternatives to Microsoft Word comparison

This chart provides a general overview of Microsoft Word capabilities. We evaluated each tool further to determine which might suit your needs best.

Google Docs: Best for sharing and real time collaboration

Google Docs, which is easily the most popular Microsoft Word alternative on this list, is free to everyone with a Google account.

If you want the basic features of Microsoft Word, you don’t need to look any further than Google Doc — it supports all your basic word processing needs and is tightly integrated with Google Drive and other products. Since everything is saved in Google’s cloud, you don’t need to worry about losing your work ( Figure A ). Docs automatically save after every single keystroke, so in the event of a crash, you should be able to pick up right where you left off, down to the letter. Google Docs also supports Microsoft Word’s .doc and .docx formats, so you shouldn’t have any problems importing and editing those files.

One of its best features for business users is real-time collaboration. If you share a document with another Google user, both of you can be in the document simultaneously, see the other user’s cursor position, watch what they’re typing, and chat with each other. It’s a great collaboration tool that stands out among word processors.

Advanced users may find the features lacking — it really is a bare-bones word processor.

Standout features

• Real-time collaboration capability.
• Pageless view.
• Table templates.
• Watermarks.
• Document summary.
• Google Meet integration.
• Menu shortcut that lets you tag people, add elements and perform other actions.
• Commenting, notes and suggestions.
• Meeting notes.
• Email draft.
• Checklists.
• Customizable templates.
• In-doc chat capability.
• Table of contents sidebar.
• Find and replace capability.
• Intuitive, easy to learn and use.
• Easy sharing and collaboration.
• Easy track changes.
• Versatile and user friendly.
• Limited offline capability.
• Some users reported that it has limited advanced formatting and editing capabilities.
• Sometimes crashes occur when too many people are working on the same document.

SEE: Become a Google Docs power user .

Apache OpenOffice Writer: Best for long and complex documents

If you hate Microsoft Word because of its ribbon, then Apache’s OpenOffice Writer is the 2003 throwback you want. It has a classic interface that, while it can look a bit cluttered, mimics the menus that Microsoft tossed out when Office 2007 was released ( Figure B ). It will definitely feel familiar to Office 2003 users, with the added perk of still receiving updates and security patches, which is important for a business software suite.

OpenOffice Writer has its own document format, but it also supports .doc and .docx files, and it does a great job of maintaining formatting when importing those types of files. Many of the advanced features of Microsoft Word are included in OpenOffice Writer as well, so editing complex Word documents won’t be an issue.

If online collaboration or native cloud support is a selling point, then you may want to pass on OpenOffice Writer because it includes neither. It’s possible to store files in a cloud drive and access them using OpenOffice, but you’ll need the desktop client of Google Drive , Microsoft OneDrive or Apple iCloud installed so that you can open your cloud storage like a local computer folder.

• Table of contents and references.
• AutoCorrect dictionary.
• AutoComplete capability.
• Multi-page display.
• HTML, PDF, and MediaWiki formats.
• Supports .docx and .doc.
• Familiar, Microsoft-like interface.
• Over 900 templates.
• Commenting/Notes.
• It doesn’t have mobile apps.
• The user interface isn’t intuitive.

Zoho Writer: Best for automation

Zoho Writer is a free document creation tool with a clean writing interface and powerful built-in capabilities. Writing documents in Writer is largely distraction-free, while important text tools are still within reach. The native features of Writer, many of which leverage the capabilities of other Zoho apps, really set it apart from the rest. Use the built-in AI tool, Zia, for better quality content, fast grammar fixes and insight into the document’s readability for different audiences ( Figure C ).

The Document Sign tool puts e-signature tools right in the doc so that teams can go from draft to approval to signature, all in the same space. Document Fillable tools also put forms right in your documents, giving them a professional feel that’s ready for embedding anywhere you need a form.

Not to be outdone by Google Docs or Microsoft Word, Zoho Writer’s real-time collaboration has granular controls, including comments, suggestions, text masking to hide some items from collaborators and even content locks for blocks of text. Zoho Writer is built for corporate collaboration, legal approvals and creative teams.

• WordPress integration.
• Comments and notes.
• Lock or mask sensitive information.
• Post to WordPress from Zoho Writer.
• Word document import.
• Export to .docx and .pdf.
• Document automation.
• Document fillable.
• Real-time collaboration.
• Offline editing capability.
• Integrates well with Zoho WorkDrive and other products in the Zoho suite.
• Users say the editor gets slow when working with large documents.
• Zoho Writer spell checker could be improved.

LibreOffice Writer: Best for customization

The Document Foundation’s LibreOffice Writer, like OpenOffice, is a completely free and open-source product that offers word processing, support for .doc and .docx file formats and all the tools the average Microsoft Word user will need in a word processor. LibreOffice Writer and OpenOffice Writer are similar in a lot of ways: interface style, file format support, lack of cloud integration and real-time collaboration, and general word processing features ( Figure D ). Both are solid choices for those looking for a free alternative to Microsoft Word, and selecting one over the other largely comes down to preference.

One aspect of LibreOffice stands out, and it is’’t what’s in the app — it’s the community-driven nature of the platform. Collaborating with users and developers to improve the product is front and center on LibreOffice’s website, and that focus has grown LibreOffice into a thriving community of users and coders that keep making it better .

• Desktop publishing.
• Integrated calculation function.
• Drawing tools.
• Spellchecker, thesaurus, AutoCorrect and hyphenation.
• Works well with MS Office files.
• Installs on Windows, Linux and Mac.
• Supports drag-and-drop.
• Some users reported that the tool is sometimes slow.
• Limited documentation.

WPS Office Writer: Best for advanced features

If you want a word processor as feature-packed as Word but don’t want to pay a premium, check out WPS Office Writer. It’s a full-featured application suite that feels premium.

WPS Office Writer does most of the same things as Microsoft Word, and it includes native cloud support to make storing documents online a snap; however, it does lack real-time collaboration ( Figure E ). Look at any review of WPS Office Writer, and you’ll find statements that attest to how much it’s like Word. With its inclusion of more features than other free suites like OpenOffice, this might be the one to go for — especially considering it’s free.

With anything free and high quality, there’s usually a catch, and you might be able to guess what it is in our modern age of “freemium” apps: Ads. Don’t let that dissuade you from trying WPS Writer — you might not see an ad. There’s no banner across the top of the app; ads only appear when you want to use select features like printing or exporting to PDF. If you need to do one of those things, you’ll have to sit through a roughly 10-second ad, which unlocks the feature for 30 minutes. If you like what WPS Writer offers, you can eliminate ads by paying a yearly subscription fee of $29.99 or $9.99 for three months.

Key features

• PDF file support.
• File format conversion.
• PDF to Word conversion.
• Document to picture export.
• Picture to text conversion.
• Skins and design customization.
• Supports Windows, macOS, Linux, Android and iOS.
• Supports 13 languages on PC and 46 languages on mobile.
• 20GB of cloud storage.
• WPS Office is compatible with 47 common document formats.
• The free version contains ads.
• Some users say the app is a bit slow.

Microsoft Office Word Online: Best for users who prefer Microsoft Word's interface

Don’t overlook Microsoft’s free alternative to the paid version of Word: Office Online. Like Google Docs, Microsoft Word Online is a simplified, cloud-based version of Word ( Figure F ). It lacks many of the advanced features of a locally-installed version of Word, but this is as close as you can get for users who want a free version of Word.

Similarities between Google Docs and Word Online are present all the way down to the interface, but with a few tweaks you can make it feel more like the Microsoft ribbon instead of the dropdown menus Google Docs uses. Documents created in Word Online are saved in Microsoft OneDrive, and real-time collaboration features like those in Google Docs are available as well. One big plus in Word Online’s favor is formatting: If you create a document in Word Online and then import it to a local version of Microsoft Word, it’s going to retain the formatting way better than a Google Docs file.

• .docm, .docx, .pptm, .pptx, .xlsm, and. xlsx support.
• 5GB of cloud storage.
• Templates, fonts, icons and stickers.
• Spelling and grammar.
• Auto-save function.
• Dictation and voice command capability.
• Familiar environment for Microsoft Office users.
• Limited features compared to the offline version.
• It may contain ads.

SEE: Explore everything Microsoft 365 has to offer.

How to choose the best free alternatives to Microsoft Word

When selecting the best free alternatives to Microsoft Word, there are a few key factors to consider.

• Assess your specific requirements and determine the features and functionalities you need from word processing software. This could include document formatting options, collaboration capabilities, compatibility with various file formats and available templates.
• Conduct thorough research on popular options such as Google Docs, LibreOffice Writer, Apache OpenOffice Writer, Zoho Writer and WPS Office Writer.
• Read user reviews, compare features and test the software to see how well it meets your requirements.
• Consider factors like compatibility with Microsoft Word formats, integration with cloud storage and ongoing support and updates.

By evaluating these criteria, you can make an informed decision and choose the alternative that best suits your needs.

Review methodology

We analyzed each Microsoft Word alternative based on five key data points: free, support for Microsoft Word format, offline access, templates and ability to meet needs. All the tools in our comparison group satisfy these criteria. We evaluated how well each alternative fulfills users’ needs in terms of functionality, ease of use, formatting capabilities and other relevant factors. This criterion helps assess the overall suitability of the tool for different types of users and their specific requirements.

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Scientific Method For Kids With Examples

Kids have questions about the world around them every day, and there is so much to learn through experimentation with simple materials. You can begin using the scientific method with elementary kids. Below we’ll share with you how and when to introduce the scientific method, the steps of the scientific method, and some easy scientific method experiments. There are so many great ways to enjoy science projects with kids!

What Is The Scientific Method?

The scientific method is a process or method of research. A problem is identified, information about the problem is gathered, a hypothesis or question is formulated from the information, and the hypothesis is put to the test with an experiment to prove or disprove its validity.

Sounds heavy… What in the world does that mean?!? It means you don’t need to try and solve the world’s biggest science questions! The scientific method is all about studying and learning things right around you.

As children develop practices that involve creating, gathering data evaluating, analyzing, and communicating, they can apply these critical thinking skills to any situation.

Note: The use of the best Science and Engineering Practices is also relevant to the topic of using the scientific method. Read more here and see if it fits your science planning needs.

Can Young Kids Use the Scientific Method?

Kids are great scientists at any age, and can use the scientific method in context to what they are learning. It can be adapted for any age!

The scientific method is a valuable tool for introducing kids to a logical way to solve scientific problems. Scientists use the scientific method to study, learn, and come up with an answer!

The scientific method is a process that helps double-check that answers are correct and the correct results are obtained through careful planning. Sometimes the guesses and questions change as you run your experiments.

Kids can use the scientific method too on questions that are relevant to them!

Let’s break the scientific method for kids down into six parts, and you can quickly see how each can be incorporated into your next science experiment.

What Are The Steps In The Scientific Method?

• Make initial observations.
• Come up with a question of interest that is based on the observations.
• Develop a hypothesis or prediction to go along with the question.
• Experiment and test.
• Gather and record results of tests and experiments and draw conclusions.
• Share and discuss results.

Whoa… Wait A  Minute! That sounds like a lot for a young kid!

You are correct. Depending on your kid’s abilities, following all the scientific method steps precisely will not go well. Someone will get frustrated, bored, and turned off by just how cool science can be. We do not want that to happen!

Using The Scientific Method For Preschool and Kindergarten

Use the scientific method steps as a guideline in the back of your mind. You can cover most of the steps by talking with your kids about…

• What do they think will happen?
• What is happening ?
• What happened compared to what they thought would happen ?

No writing is required! It’s also best to pick pretty straightforward ideas that aren’t overly involved or complicated to set up and test. Kids always have burning questions and “what ifs.”

See if you can tackle their next “what if” using the scientific method by listening carefully to their conversations. You can even have them keep a journal with their “what if” questions for your next science time.

Learn more about Science Activities For Preschoolers and Kindergarten Science Experiments .

Now on to how to apply the scientific method for elementary kiddos and beyond.

Scientific Method Steps In Action

Learn more about the steps of the scientific method below, which are great for science at home with your kids or in the classroom! We have also included some simple scientific method experiments for you to enjoy.

Ice Science Experiments are perfect for this! Try these 3 today !

STEP 1: Make Observations

Tons of everyday activities would make for cool science experiments using the scientific method. Listen to what your kids talk about and see happening. My son noticed that ice melted pretty fast in his water.

Observation is simply noticing what’s happening through our senses or with tools like a magnifying glass. Observation is used to collect and record data, enabling scientists to construct and test hypotheses and theories.

Learn more about observations in science.

STEP 2: Come Up With A Question 

Your kids’ observations should lead to some sort of question. For my son and his ice observations, he came up with questions. Does ice melt faster in different liquids? His curiosity about what happens to the ice in liquids is a simple science experiment perfect for using the scientific method.

Next! Do some research and come up with ideas!

STEP 3: Develop A Prediction or Hypothesis

You have made your observations, you have your question, and now you need to make a prediction about what you think will happen.

A prediction is a guess at what might happen in an experiment based on observation or other information.

A hypothesis is not simply a guess! It’s a statement of what you believe will happen based on the information you have gathered.

My son hypothesizes that ice will melt faster in juice than in water.

STEP 4: Conduct An Experiment

We made a prediction that ice will melt faster in juice than it will in water, and now we have to test our hypothesis. We set up an experiment with a glass of juice, a glass of water, and an ice cube for each.

For the best experiments, only one thing should change! All the things that can be changed in a science experiment are called variables. There are three types of variables; independent, dependent, and controlled.

The independent variable is the one that is changed in the experiment and will affect the dependent variable. Here we will use different types of liquids to melt our ice cube in.

The dependent variable is the factor that is observed or measured in the experiment. This will be the melting of the ice cubes. Set up a stopwatch or set a time limit to observe the changes!

The controlled variable stays constant in the experiment. The liquids should be roughly the same temperature (as close as possible) for our ice melting experiment and measured to the same amount. So we left them out to come to room temperature. They could also be tested right out of the fridge!

You can find simple science experiments here with dependent and controlled variables.

STEP 5: Record Results and Draw Conclusions

Make sure to record what is happening as well as the results—note changes at specific time intervals or after one set time interval.

For example…

• Record when each ice cube is completely melted.
• Add drawings if you wish of the setup up and the end results.
• Was your prediction accurate? If it was inaccurate, record why.
• Write out a final conclusion to your experiment.

STEP 6: Communicate Your Results

This is the opportunity to talk about your hypothesis, experiment, results, and conclusion!

ALTERNATIVE IDEAS: Switch out an ice cube for a lollipop or change the liquids using vinegar and cooking oil.

Now you have gone through the steps of the scientific method, read on for more fun scientific method experiments to try!

Free printable scientific method worksheets!

Fun Scientific Method Experiments

Sink or float experiment.

A Sink or Float experiment is great for practicing the steps of the scientific method with younger kids.

Grab this FREE printable sink or float experiment

Here are a few of our favorite scientific method experiments, which are great for elementary-age kids . Of course, you can find tons more awesome and doable science projects for kids here!

Magic Milk Experiment

Start with demonstrating this delightful magic milk experiment. Then get kids to apply the steps of the scientific method by coming up with a question to investigate. What happens when you change the type of milk used?

What Dissolves In Water

Investigate  what solids dissolve in water  and what do not. Here’s a super fun science experiment for kids that’s very easy to set up! Learn about solutions, solutes, and solvents through experimenting with water and common kitchen ingredients.

Apple Browning Experiment

Investigate how to keep apples from turning brown with this apple oxidation experiment . What can you add to cut apples to stop or slow the oxidation process?

Freezing Water Experiment

Will it freeze? What happens to the freezing point of water when you add salt?

Viscosity Experiment

Learn about the viscosity of fluids with a simple  viscosity experiment . Grab some marbles and add them to different household liquids to find out which one will fall to the bottom first. 

Seed Germination Experiment

Set up a simple seed germination experiment .

Catapult Experiment

Make a simple popsicle stick catapult and use one of our experiment ideas to investigate from rubber band tension to changes in launch angle and more. How far can you fling your objects? Take measurements and find out.

Floating Orange

Investigate whether an orange floats or sinks in water, and what happens if you use different types of oranges. Learn about buoyancy and density with a simple ingredient from the kitchen, an orange.

Bread Mold Experiment

Grow mold on bread for science, and investigate how factors such as moisture, temperature, and air affect mold growth. 

Eggshell Strength Experiment

Test how strong an egg is with this eggshell strength experiment . Grab some eggs, and find out how much weight an egg can support.

Free Printable Science Fair Starter Guide

Are you looking to plan a science fair project, make a science fair board, or want an easy guide to set up science experiments?

Learn more about prepping for a science fair and grab this free printable science fair project pack here!

If you want a variety of science fair experiments with instructions, make sure to pick up a copy of our Science Project Pack in the shop.

Bonus STEM Projects For Kids

STEM activities include science, technology, engineering, and mathematics. As well as our kids science experiments, we have lots of fun STEM activities for you to try. Check out these STEM ideas below…

• Building Activities
• Engineering Projects For Kids
• What Is Engineering For Kids?
• LEGO Engineering Projects
• Coding Activities For Kids
• STEM Worksheets
• Top 10 STEM Challenges For Kids

Printable Science Projects Pack

If you’re looking to grab all of our printable science projects in one convenient place plus exclusive worksheets and bonuses like a STEAM Project pack, our Science Project Pack is what you need! Over 300+ Pages!

• 90+ classic science activities  with journal pages, supply lists, set up and process, and science information.  NEW! Activity-specific observation pages!
• Best science practices posters  and our original science method process folders for extra alternatives!
• Be a Collector activities pack  introduces kids to the world of making collections through the eyes of a scientist. What will they collect first?
• Know the Words Science vocabulary pack  includes flashcards, crosswords, and word searches that illuminate keywords in the experiments!
• My science journal writing prompts  explore what it means to be a scientist!!
• Bonus STEAM Project Pack:  Art meets science with doable projects!
• Bonus Quick Grab Packs for Biology, Earth Science, Chemistry, and Physics

19 Comments

A great post and sure to help extend children’s thinking! I would like to download the 6 steps but the blue download button doesn’t seem to be working for me.

Thank you! All fixed. You should be able to download now!

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it is so great, thanks a lot.

This helped for a science project.Thanks so much.

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