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The sign test

Specification: Introduction to statistical testing; the sign test.

When to use the sign test

The sign test is used when looking for a difference between paired data, i.e. repeated measures design (or matched pairs – counted as one person tested on two occasions) which generates nominal data.

A worked example

A slimming club believed that their new weight programme worked. They recorded the weights of ten members of the club when they first joined, and again after three months.

Use the sign test to work out whether the weight loss programme was effective for these members.

1. Is the hypothesis directional or non‐directional?

Directional since the hypothesis predicts that members will lose weight after three months on the programme.

2. Work out the sign.

Record each pair of data with a + or – (depending on whether the difference is positive or negative). If there is no difference (e.g. in the case of Jenny) then a nil sign ‘0’ is recorded.

3. Calculate the value of S

(S is the symbol for the sign test and is calculated by adding up the total number of pluses and minus and selecting the smaller value). In this case there are 7 minus and 2 pluses, therefore S = 2.

4. Calculate the value of N

(N is the total number of scores, minus any nil scores ‘0’). In this case there are 10 scores, but one is a 0, so N = 9.

5. Find the critical value

(see table) For a directional test for N = 9, the critical value = 1.

Note: For the sign test to be significant the calculated value of S must be equal to or less than the critical value.

6. Determine whether the results are significant or not (typically, the p ≤ 0.05 probability level is used unless otherwise stated).

For the sign test, the calculated value [2] must be equal to or less than the critical value [1] for the result to be significant. Therefore, these results are not significant as the calculated value of S is 2 which is higher than the critical value of S which is 1.

7. Reporting the conclusions of the sign test.

Once you have worked out the results of the sign test, you can draw a conclusion.

The result is not significant because the calculated value of S = 2 exceeds the critical value of 1 at a significance level of p ≤ 0.05 for a one‐tailed test.

Possible exam questions

Explain what N means in relation to statistical testing in psychology. (1 mark)
Identify the most commonly accepted level of probability (p) used in psychological research. (1 mark)

A 0.05

B 0.1

C 0.5

D 0.01

Calculate p ≤ 0.05 as a percentage. (1 mark)
A researcher has decided to use a sign test to assess the statistical significance of their results from an investigation which predicted that caffeine will enhance test performance compared to water. When looking at the table of critical values, the researcher notices that there are two headings: levels of significance for a one‐tailed test and levels of significance for a two‐tailed test.

Explain how the researcher will decide which to use and explain your reasoning. (2 marks)

Identify two factors a researcher must consider when deciding to use the sign test. (2 marks)
Suggest three reasons for using a sign test. (3 marks)
A psychologist was interested in investigating the power of advertising on consumer behaviour. He believed that television advertising had a positive effect on sales. The psychologist showed participants a new advert for an anti‐dandruff shampoo. He asked participants to then rate whether they were more likely or less likely to purchase the shampoo after seeing the new advert. Out of the ten participants, two said they were no more or no less likely (opinion stayed the same), six were more likely and two were less likely to buy the shampoo.
1. Calculate the value of S. (1 mark)
2. Using the most common significance level in psychology, decide if the results from this investigation are statistically significant. (2 marks)

Revision materials

Seneca learning

Sign Test

Online textbook

Year 1: 198-199

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