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.

• 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.

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 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.

Binomial Sign Test Example

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

The first step is identifying whether values/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.

• 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.

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.

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.

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.

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 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.

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.

Binomial Sign Test in Psychology: Advantages and Disadvantages

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.