Select an appropriate statistical test (to include: selecting a suitable…

The idea

Three questions settle the choice. Is the researcher testing for a difference between conditions or for an association between two co-variables? If a difference, was the design related (repeated measures or matched pairs) or unrelated (independent groups)? What level of measurement did the dependent variable produce? Nominal and unrelated gives Chi-Square, ordinal and unrelated gives Mann-Whitney U, interval and unrelated gives the unrelated t-test. Nominal and related gives the sign test, ordinal and related gives Wilcoxon, interval and related gives the related t-test. A correlation takes Spearman's rho for ranked data and Pearson's r for interval data. Chi-Square is also used for an association between two nominal variables.

What earns the marks

• Naming the test exactly as AQA names it, so Chi-Square, the sign test, Mann-Whitney U, Wilcoxon signed ranks, the related t-test, the unrelated t-test, Spearman's rho or Pearson's r.
• Justifying the choice in three parts: the hypothesis predicts a difference or a correlation/association, the design is related or unrelated, and the data are nominal, ordinal or interval.
• Adding the condition Chi-Square carries, namely that the data must be independent frequencies in categories with each participant appearing in one cell only.
• Saying what the chosen test then delivers, which is an observed value to be compared with a critical value at the stated level of significance.

Common mistakes and how to put them right

• Choosing Chi-Square for two sets of scores from the same participants, when a repeated measures design breaks the requirement that the frequencies be independent.

• Reaching for Spearman's rho whenever two sets of scores appear, even though a study that manipulates an independent variable is testing a difference and needs a difference test.

• Naming a test and stopping, which usually caps a three mark item at one mark because the two justification marks are for the design and the level of measurement.

• Calling a matched pairs design unrelated on the grounds that the participants are different people, when the matching is precisely what makes it related.

Exam tips

• Name the inferential test, then justify it separately from the research aim, experimental design and level of measurement given in the scenario.
• Underline the three cues in the stem before you answer: difference or correlation/association, related or unrelated, and the units the dependent variable was measured in.
• If the stem gives a table of frequencies in unordered categories, the data are nominal, so the answer is Chi-Square for an unrelated design or association, and the sign test for a related design. However, ordered frequency categories (e.g., low/medium/high) are ordinal data and require ordinal tests.
• Learn the table by its rows rather than by rote lists, because the examiner can ask the same question backwards by giving you the test and asking what the design and the data must have been.