The Sign Test

• Statistical testing is used to find out whether differences found between variables in research are due to change, that is, its confidence in our findings.
• What is a null hypothesis?

  A statement of no difference or association or relationship between two variables. It predicts results are due to chance.
• Conditions for the sign test:

  • Level of measurement: Nominal
  • Test of difference (not a correlation)
  • Data should be related (e.g., either repeated measures or matched pairs)
• All studies employ a significance level in order to check for significant differences or relationships. The accepted level of probability in psychology is 0.05 or 5%. This is the level at which we decide whether to accept the experimental hypothesis or not.
• If the experimental hypothesis is accepted, this means there is less than 5% probability that the results occurred by chance. In simple terms, this means the researcher can be pretty certain that the difference found was because of the manipulation of the independent variable (though there will always be a 5% chance that results are due to chance factors, even if significance is found).
• In some circumstances, researchers need to be even more confident that results were not due to chance and so employ a more stringent significance level such as 0.01 (the 1% level). This is chosen when research may involve a human cost, such as when new drugs are being trialed on a vulnerable population, or when a particular investigation is a one-off and there is no possibility that it can be repeated in future.
• When the statistical test has been calculated, the researcher is left with a number. The calculated value needs to be compared with a critical value to decide whether the result is significant or not. The critical values for a sign test are given in a table of critical values (on page 73).

  You need the following information to use the table:

  1. The significance level (always 5% unless the research requires extreme stringency).
  2. The number of participants in the study (this is the N value).
  3. Whether the alternative hypothesis is directional (one-tailed) or non-directional (two-tailed).
• The sign test in 5 steps:

  1. Work out the 'sign.' Has the score going up (+) or down (-)
  2. Calculate the value of 's.' The lowest score, excluding any 'nil' scores.
  3. Calculate the value 'N.' The total number of participants (excluding any with no difference)
  4. Find the critical s value. Using the critical values table
  5. Determine whether the results are significant. Is your calculated value for s less than or equal to the critical value of s?

  Critical values of S for the sign test.