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Binomial Sign Test

When we think of statistics, the usual typical response is everyone's head starts spinning. But this doesn't have to be the case. Data handling and statistics can be simplified. Think of the word binomial; it may sound a bit daunting at first, but it can be pretty simple when broken down. Bi refers to two, and nominal refers to a type of data.

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# Binomial Sign Test

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When we think of statistics, the usual typical response is everyone's head starts spinning. But this doesn't have to be the case. Data handling and statistics can be simplified. Think of the word binomial; it may sound a bit daunting at first, but it can be pretty simple when broken down. Bi refers to two, and nominal refers to a type of data.

• We will start by covering binomial sign tests in psychology.
• Then we will explore the binomial sign test assumptions.
• Then we will explore some binomial sign test examples to learn how the statistic can be calculated. Here the binomial sign test significance table will be provided so that you can understand what it looks like and how it can be interpreted.
• Finally, we will learn the advantages and disadvantages of using the test.

## Binomial Sign Test Psychology

When analysing your data set, you must know which test you will use based on what the data initially tells you; this also considers how your information is distributed. So 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 interventions.

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

## Binomial Sign Test Assumptions

The binomial sign test assumptions are as follows:

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

• The statical test compares nominal data.

• 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 research that uses 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.

## The Binomial Sign Test and Hypotheses

The binomial sign test is useful because it identifies which hypothesis should be accepted when conducting 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.

If the analysis reveals non-significant results, 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

The binomial sign test example highlights how the binomial sign test can be calculated.

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.

The first step is identifying whether 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.

### The Variance of Binomial Distribution

The second step is calculating the number of participants who gained weight (+) and those who lost weight (-). During this step which 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.

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, and N is the number of participants included in the analysis.

In this research scenario:

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

### Hypothesis Test for Proportion using Binomial Distribution

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 must look at a binomial sign test significance table 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.

The 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 represents a 1% chance that the results are due to chance.

When asked to calculate a binomial sign test in your exam, you will be given the significance level.

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

In this example, the S value (2) is higher than the critical value (1). Therefore, the difference between participants before and after the intervention is insignificant. 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 insignificant.

The 95% certainty comes from calculating the probability from the .05 significance results reported.

## How to do Sign Test Psychology?

To recap simply, the steps of the sign test are as follows:

1. Calculate and assign whether there is a bigger (+) or smaller (-) difference in values in the two conditions. Identify how many there are for each + and - but ignore any participants that showed no difference.
2. Calculate S (least frequent size) and identify N (how many participants, not including any that showed no difference).
3. Finally, compare the S value to the critical value.

## Binomial Sign Test Significance Table

The table shows a binomial sign test significance table.

To find the critical value, you need to look for the number corresponding to the number of participants used in the analysis (N) against the significance value (p) 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.

The advantages of the binomial sign test are:

• 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.

However, the disadvantage of this test is:

• The sign test is non-parametric. Non-parametric tests are less powerful than their parametric alternatives because non-parametric tests use less information in their calculations, such as distributional information, making 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.
• A binomial sign test significance table is needed to calculate the binomial sign test;
• 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 to determine 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 used to identify the likelihood of an outcome of something happening.

The binomial sign test is a non-parametric statistical test used to test the probability of two outcomes.

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. A calculation can be done, or a statics programme can be used.

The sign test in psychology is another term for the binomial sign test. It is a non-parametric statistical test of whether there is a statistically significant difference between two conditions. The test is used when nominal data is collected, and the study uses a repeated measures design.

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.

## Test your knowledge with multiple choice flashcards

Which of the following statements is accurate?

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

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

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## Join over 22 million students in learning with our StudySmarter App

The first learning app that truly has everything you need to ace your exams in one place

• Flashcards & Quizzes
• AI Study Assistant
• Study Planner
• Mock-Exams
• Smart Note-Taking