Sign Test – Inferential Statistics

Quantitative Data Analysis – Sign test

A non-parametric test used for experiments where the data is at least nominal and repeated measures has been used.

Statistical analysis, like the sign test, produces an observed value, which is compared to a critical value (on a table of values) in order to determine whether a set of results are significant to a specific level.

Key Definitions:

(1) Observed Value: The result of the statistical test (in this case, the result of the sign test).

(2) Critical Value: The table result (in which you will compare the observed value).

Calculating the sign test

Let’s suppose you want to find out whether students prefer a cooked or non-cooked breakfast (or neither).

You select 15 participants and complete the table below, if students prefer a non-cooked breakfast (cereal) put a -, if they prefer a cooked breakfast put a +.

Sign Test Table

To calculate the sign test; Insert the data into a table, use a plus or minus to indicate the direction of difference

1. To calculate the observed value add up the number of tallies for each option (+= -= ) ignore scores of participants who have not selected one of the options (i.e. those who selected neither)

2. Add up the number of times the less frequent sign occurs (e.g. identify which column has the fewest tallies) – the total of the less frequent sign is the observed value (s)

3. Next, you need to get the critical value from the critical value table (this will be provided in the exam). To get the critical value from the table you will need the value of N (the number of participants (omitting any participants responding ‘neither’ or ‘not with a ‘+’ or ‘-‘. In order to get the critical value from the table you will also need to know; the hypothesis type (one/two tailed) and the probability value.

4. In order for the ‘s’ value to be significant, you want the observed value (s) to be lower than the critical value (from the table). Remember – the important ‘r’ rule: When there is an ‘r’ in the name of the inferential test (e.g. spearman’s rho) you want the observed value to be greater than the critical value (from the table).

Exam Tip – when writing up your results, use the perfect paragraph outline on the inferential statistics page on this website.