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# Binomial Sign Test

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When analysing your data set, you must know which test you will use based on what the data is initially telling you. This also takes into account how your information is distributed, all so that you can confidently declare if your results are significant or not.

The binomial sign test is also referred to as the sign test, a statistical test used to test the probability of two outcomes.

For instance, the binomial sign test may identify the likelihood of people’s success or failure in planned diet intervention.

This test is a non-parametric test in which the data collected from the two groups do not need to be normally distributed.

Statistics, flaticon.com/Freepik

## Binomial Sign Test Assumptions

The binomial sign test assumptions are as follows:

• It should be used when testing a difference between values.

• The experiment should use a related design (repeated measures or matched-pairs design)

• This test relies on comparisons, which can be from the same or different participants as long as it is acceptable to compare them, such as being tested after being identified to share a similar characteristic (this is a matched-pairs design)

• Non-normal data – the data of participants should not be equally distributed.

The equivalent parametric test should be used if data points are normally distributed.

It compares the data you have in your set and changes it into nominal data.

## The Binomial Sign Test and Hypotheses

The binomial sign test is useful because it can identify which hypothesis should be accepted when carrying out analyses on non-normally distributed data. This process is known as hypothesis testing.

If significant findings are found, the alternative hypothesis can be accepted, and the null hypothesis should be rejected. Whereas, if the analysis reveals non-significant findings, then the alternative hypothesis should be rejected, and the null hypothesis should be accepted.

The null hypothesis is when a researcher proposes that there will be no difference before and after the intervention.

The alternative hypothesis is when a researcher predicts that they expect to observe a difference before and after the intervention.

## Binomial Sign Test Example

This research scenario shows how a binomial sign test formula should be worked out.

The researchers proposed and designed an experiment to test the following two-tailed hypothesis – there will be a difference in participants’ weight before and after the tailored diet programme.

### Step 1

The first step is to identify if values/scores increased or decreased after the intervention.

 Weight before intervention Weight after intervention Difference Participant 1 65 68 + Participant 2 72 70 - Participant 3 83 82 - Participant 4 72 68 - Participant 5 81 77 - Participant 6 69 67 - Participant 7 73 69 - Participant 8 70 73 + Participant 9 75 70 - Participant 10 72 72 0

You do not need to calculate the difference between the group; you just need to assign a + or - sign correctly. The sign indicates whether scores increased or decreased after the intervention.

### Step 2

The second step is to calculate the number of participants who gained weight (+) and those who lost weight (-). During this step who showed no difference (0) should be ignored.

In this research scenario:
• Two participants gained weight (+)

• Seven participants lost weight (-)

• One participant had no difference in weight (0). Hereafter, this participant will no longer be included in the analysis.

### Step 3

In the third step, the S value needs to be calculated, and N also needs to be identified.

The S value is the least frequent sign when the difference (sign) is calculated before and after the intervention.

N is the number of participants included in the analysis.

In this research scenario:

• The positive sign is the least common, and there are two of them. Therefore, the S value is two.
• S = 2
• There are nine participants because seven participants weighed less after the intervention, and two had increased in weight. The one participant that showed no difference was not included in the analysis; therefore, they are not added when calculating the N value.
• N = 9

### Step 4

In the final stage of calculating the binomial sign test, the S value must be compared against the critical value.

The critical value is a statistical value used to determine whether a hypothesis should be accepted or rejected.

You need to look at a binomial sign test significance to find the critical value. The significance level and the number of participants tested in the analysis determine the critical value. If you look at a binomial sign test critical values table you can see that N can be compared against .05 or .01. This value is the significance value.

Significance value (p) is the likelihood that the critical value results from an error/ chance. A significance value of .05 means a 5% chance that the results are due to chance. Furthermore, a p-value of .01 means a 1% chance that the results are due to chance.

In your exam, you will be given the significance level that was found when asked to calculate a binomial sign test.

The purpose of statistical analyses is to identify if the calculations are significant. If the results are significant, then the alternative hypothesis can be accepted.

In the binomial sign test, for the S value to be significant, it must be equal to or less than the critical value.

In this research scenario:

S = 2

N = 9

p = .05

The critical value is 1

The S value (2) is higher than the critical value (1). Therefore, the difference between participants before and after the intervention is not significant. S (2) > Critical value (1). The researcher will reject the alternative hypothesis and accept the null hypothesis.

The null hypothesis in this research scenario is that there will be no significant difference between participants’ weight before and after the diet intervention. The researcher can say with 95% certainty that the results are not significant. The 95% certainty comes from calculating the probability from the .05 significance results reported.

## Binomial Sign Test Significance Table

This table shows what a binomial sign test significance table looks like.

To find the critical value you need to look for the number that corresponds with the number of participants used in the analysis (N) against the significance value (p) that was calculated in the analysis.

 N 0.05 .01 5 0 - 6 0 0 7 0 0 8 1 0 9 1 1 10 1 1 11 2 1 12 2 2 13 3 2 14 3 2

If you are asked to calculate the binomial sign test, the binomial sign test significance table will be given to you.

Let’s discuss the advantages and disadvantages of the binomial sign test in psychology.

### Advantages of the binomial sign test

• When researchers collect data, it is not always possible to collect data from a normally-distributed sample.

• Researchers can statistically calculate whether the null or alternative hypothesis should be accepted.

### Disadvantages of the binomial sign test

• The sign test is a non-parametric test. Non-parametric tests are known to be less powerful than their parametric alternatives because non-parametric tests use less information in their calculations, such as distributional information, which makes them less sensitive.

## Binomial Sign Test - Key Takeaways

• The binomial sign test is a statistical test used to test the probability of an occurrence happening.
• A binomial sign test is a form of a non-parametric test. It can be used when testing a difference between values and uses a related design (repeated measures or matched-pairs design). It changes values into nominal data.
• There are four steps to calculating binomial sign tests.
• To calculate the binomial sign test, a binomial sign test significance table is needed;
• This table identifies if the calculated S value is significant by comparing it against a critical value.
• The number of participants used in the analysis (N) and the significance value (p) calculated during analyses determine the critical value.
• An advantage of the binomial sign test is that it allows researchers what hypothesis should be accepted when data are non-normally distributed.
• A disadvantage of the binomial sign test is that it is considered less powerful than its parametric alternative.

The binomial sign test is a non-parametric statistical test.

An example of how the binomial sign test may be used in psychology is identifying the likelihood of people’s success or failure in planned diet intervention.

The sign test in psychology is another term for the binomial sign test.

There are four steps to calculate the binomial sign test:

1. Identify the number of increases or decreases before and after intervention/between participants
2. Calculate the number of increases (+) and decreases (-)
3. Calculate the S and N- value
4. Identify if the S value is significant after comparing the data against the value in the binomial sign test significance test..

The binomial sign test is used to identify the likelihood of an outcome of something happening.

## Final Binomial Sign Test Quiz

Question

What type of test is the binomial sign test?

Parametric test

Show question

Question

What is an advantage of the binomial sign test?

• When researchers collect data, it is not always possible to collect data from a normally-distributed sample.
• Researchers can statistically calculate whether the null or alternative hypothesis should be accepted.

Show question

Question

What is the disadvantage of using a binomial sign test?

The sign test is a non-parametric test. Non-parametric tests are known to be less powerful than their parametric alternatives because non-parametric tests use less information in their calculations, such as distributional information, which makes them less sensitive.

Show question

Question

How many steps are there when calculating the binomial sign test?

2

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Question

What is the purpose of the binomial sign test?

The binomial sign test is a statistical test that is used to test the probability of an occurrence happening.

Show question

Question

Which of the following statements is accurate?

The binomial sign test may be used to identify the likelihood of people’s success or failure in planned diet intervention.

Show question

Question

What are the binomial sign test assumptions?

The binomial sign test assumptions are as follows:

• It should be used when testing a difference between values.
• The experiment should use a related design (repeated measures or matched-pairs design)
• This test relies on comparisons, which can be from the same or different participants as long as it is acceptable to compare them, such as being tested after being identified to share a similar characteristic (this is a matched-pairs design)
• Non-normal data – the data of participants should not be equally distributed.

Show question

Question

What would the N be in the following research scenario when calculating the binomial sign test values, ‘the researcher recruited nine participants, but the two showed no difference’?

9

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Question

Should the researcher accept the research findings as significant if the S value is calculated to be higher than the critical value?

No

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Question

If the S value is calculated to be lower than the critical value, then which hypothesis should the researcher accept?

Alternative hypothesis

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Question

Which values are included in the binomial sign test significance table?

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Question

What does a p-value of .05 indicate?

A p-value of .05 means the researcher can say with 95% the results observed/calculated are not due to chance.

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Question

What does N stand for in statistical analyses?

N is the number of participants that are included in the analysis.

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Question

What is the S value in the binomial sign test?

The S value is the sign that is the least frequent when the difference (sign) is calculated before and after the intervention.

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Question

Are participants who show no difference included in the analysis of the binomial sign test?

Yes

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