The Sign Test (AQA AS Psychology)

When to use the sign test

• The sign test is a method used in interferential statistics to determine whether or not an observed result (from a statistical test) is significant

• It is a non-parametric test which means that there is no assumption that the data will follow a normal distribution

• It is known as the Sign Test as it is based on the number of plus or minus signs present in the data after the calculations have taken place

• The criteria which determine the use of the Sign Test are

  • If the research investigates a difference

    • An experiment rather than a correlation (which investigates the relationship between variables)

  • Repeated measures design

    • Each participant experiences both conditions of the IV 

  • Nominal data

    • Data in categories (e.g. 'Exercised for 15 minutes/Did no exercise'

  • Whether the hypothesis is directional or non-directional

    • The type of hypothesis used will determine which critical value from the statistical tables to apply to the data

Calculation of the sign test

• Here is an example of how the Sign Test would be calculated using the results from a (fictional) study

• A researcher hypothesises that exercising before taking a test would improve concentration

• These are the results showing the test scores per participant

• Step 1:

  • Subtract the ‘exercise before test' score from the ‘no exercise' score and add the answer to the ‘difference’ column e.g.

    • 15 – 9 = 6

    • 7 - 12 = -5

• Step 2:

  • If the score after subtraction is positive, place a + before the number in the ‘difference’ column

  • If the score after subtraction is negative, place a - before the number in the 'difference' column

  • Note that scores of 0 difference do not have a positive or negative sign attached to them

• Step 3:

  • Count the number of + and – signs

    • Number of + signs = 3

    • Number of – signs = 5

  • Whichever number is lower becomes the observed value (S) for the test

    • Observed value of S = 3

• Step 4:

  • Identify the critical value using a statistical table

    • Look at the values which relate to whether the test is directional (one-tailed) or non-directional (two-tailed)

    • Select the correct level of significance at p = 0.05

• Step 5:

  • Use N to find your critical value (N refers to the number of participants in your data set)

    • If you have one participant who has scored the same in both conditions (i.e. difference is 0) you need to remove them from the data (this is true for participant number 4 in the above data set)

    • Therefore N = 8 for the above data set as participant 4 experienced no change

    • Using the N column (on the critical values table) find 8

    • Find the 0.05 critical value (according to whether it was a one-tailed or a two-tailed test)

• Step 6:

  • Consult your observed value (S) and ask, is the critical value at 0.05  more or less than the S value?

  • In this example let's say a directional (one-tailed) test was used in which case with a value of N = 8, the critical value is 1

  • As S = 3 is more than the critical value of 1, the researcher would have to accept the null hypothesis, there is no difference that exercising before taking a test would improve concentration

  • If the observed value had been equal to or less than the critical value, the researcher would be able to reject the null hypothesis and claim that there was a significant difference that exercising before taking a test would significantly improve concentration

Critical values table for The Sign Test

Accepting or rejecting the null hypothesis

• If the calculated S value is more than the critical value, the researcher would have to accept the null hypothesis

• If the calculated S value is equal to or less than the critical value, the researcher would be able to reject the null hypothesis and accept their alternative hypothesis