4.2.3.3 - Choosing a statistical test
Choosing a statistical test is a structured decision about the research question, design and level of measurement. You will use these three features to distinguish tests of difference from association and related from unrelated data, then select among the tests required for AQA Psychology. Applying the grid to unfamiliar studies will make the choice explainable rather than a matter of memorising isolated names.
Purpose, design and measurement
Inferential tests are not interchangeable. A psychologist chooses a test by matching the research question and the data to the assumptions of the test. Three linked decisions make the choice explainable. This is a useful order, not an additional exam requirement to state the factors in a prescribed sequence.
Statistical test
A statistical test is an inferential procedure that evaluates how unusual the observed result, or a more extreme result, would be if the null hypothesis were true.
Decision 1: is the study testing a difference or an association?
A test of difference compares two conditions or groups. Look for wording such as "whether there is a difference", "whether therapy reduces symptoms", or "whether group A scores higher than group B".
A test of association examines whether two co-variables are related. AQA often uses "association" and "correlation" in this area, although strictly Chi-Squared tests association between categories rather than a correlation coefficient. Look for wording such as "whether there is a relationship between sleep and memory score".
Decision 2: if it is a difference, is the design related or unrelated?
Related design
A related design is one where scores can be paired, either because the same participants are tested twice or because participants have been deliberately matched in pairs.
Unrelated design
An unrelated design is an independent groups design where different participants take part in each condition, so the scores in one group are not paired with scores in the other group.
For correlations, each participant normally supplies a value on each co-variable, so the two values are matched within that person. This is not a repeated-measures comparison between two conditions: the question is whether the variables vary together. For chi-squared association, each independent participant contributes to one cell formed from two categorical classifications.
Decision 3: what is the level of measurement?
Level of measurement
The level of measurement describes the kind of data collected. AQA requires nominal, ordinal and interval levels for choosing statistical tests.
- Nominal data are category frequencies, such as the number of participants who chose "yes" or "no".
- Ordinal data can be ranked, but the gaps between values are not known to be equal, such as anxiety ratings on a 1-10 scale.
- Interval data use equal units on a numerical scale, such as a temperature scale in degrees Celsius. Ratio measures also have a meaningful absolute zero: reaction time in milliseconds is an example. For this AQA test-selection grid, ratio measures use the interval row. A count of correct answers can be treated as equal-unit data when the question justifies that assumption; equal marks do not automatically prove equal psychological changes in ability.
A fast exam routine is: outcome, design, data. First ask difference or association. Then, for a difference, ask related or unrelated. Finally ask nominal, ordinal or interval.
Matching data to a test
The grid brings the three decisions together. Read across from the measurement level, then use the column that matches the research question. The study design selects the related or unrelated column only for a test of difference.
| Level of measurement | Test of difference: unrelated design | Test of difference: related design | Test of association/correlation |
|---|---|---|---|
| Nominal | Chi-Squared | Sign test for paired changes* | Chi-Squared |
| Ordinal | Mann-Whitney | Wilcoxon | Spearman's rho |
| Interval | Unrelated t-test | Related t-test | Pearson's r |
*The sign test counts the direction of paired changes, ignoring their sizes and excluding ties. Arbitrary category labels alone do not create a meaningful plus or minus. The neighbouring lesson teaches its calculation; this lesson concentrates on the other seven named tests. All choices still require suitable data and the relevant test assumptions.
Chi-Squared is used with nominal data. It can test whether there is a difference in category frequencies in an unrelated design, or whether two categorical variables are associated. For example, it could test whether different year groups are associated with preference for online or face-to-face revision.
Mann-Whitney is used for a test of difference with an unrelated design when the data are ordinal, ranked, or treated as the non-parametric alternative to an unrelated t-test.
Wilcoxon is used for a test of difference with a related design when the data are ordinal, ranked, or treated as the non-parametric alternative to a related t-test.
Spearman's rho
Spearman's rho is a non-parametric test of correlation used when data are ordinal or ranked. It assesses the strength and direction of an association between two ranked variables.
Pearson's r
Pearson's r is a parametric correlation test used when both co-variables are measured at interval level and the researcher is testing a linear relationship.
Unrelated t-test is used for a test of difference with an unrelated design and interval-level data. It compares the means of two independent groups.
Related t-test is used for a test of difference with a related design and interval-level data. It compares two related means, such as the same participants' scores before and after an intervention.
The names "related t-test" and "unrelated t-test" match AQA wording. In wider statistics sources they may also be called paired/dependent t-test and independent t-test.
Justifying a test choice
Good AO2 is not just "I remembered the table". It is showing how the scenario maps onto the table.
| Scenario clue | Decision | Likely test |
|---|---|---|
| "The same 20 students completed a stress scale before and after mindfulness." | Difference, related design, ordinal ratings | Wilcoxon |
| "Two different groups have equal-unit recovery times in days, with suitable distributions and similar variances." | Difference, unrelated design, interval-level measure | Unrelated t-test |
| "Researchers correlated rank position in a class with rank position in a competition." | Association/correlation, ordinal/ranked data | Spearman's rho |
| "Hours of revision and equal-unit exam scores show a linear relationship with suitable data and no influential outliers." | Association/correlation, interval-level co-variables | Pearson's r |
| "Researchers counted how many participants in each therapy group relapsed or did not relapse." | Difference or association using nominal category frequencies | Chi-Squared |
Pay attention to whether a number is a score or a category frequency. "Number of aggressive acts by each child" can be treated as an interval-level score in the AQA grid when each act is counted as an equal unit. A numerical label alone is insufficient; justify that measurement assumption. "Number of children classified as aggressive or not aggressive" is nominal because the researcher is counting category membership.
Likert-style scales are a common trap. A single "rate anxiety from 1 to 7" item is normally ordinal because the difference between 2 and 3 may not be psychologically equal to the difference between 6 and 7. If an exam scenario describes subjective ratings or ranks, choose the ordinal row unless the question gives a defensible reason to treat it as an equal-unit scale. “Standardised” means administered/scored consistently; that word alone does not establish interval measurement.
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