How do psychologists choose and use an inferential test to decide whether results are significant?
Inferential statistics: probability and significance (), the null and alternative hypotheses, choosing the correct test (the binomial sign test, Mann-Whitney U, Wilcoxon, Spearman's rho, chi-square) from design and level of measurement, observed versus critical values, and Type I and Type II errors.
An Eduqas A-Level Psychology answer to inferential statistics in Component 2. Covers probability and the 0.05 significance level, the null hypothesis, how to choose between the binomial sign test, Mann-Whitney U, Wilcoxon, Spearman's rho and chi-square, comparing observed and critical values, and Type I and Type II errors.
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What this dot point is asking
Component 2 requires you to use inferential statistics: understand probability and significance, the null hypothesis, choose the correct test from the five named tests, compare observed and critical values, and understand Type I and Type II errors. This is examined every year.
The answer
Probability and significance
Choosing the test
Observed versus critical values and errors
The test gives an observed (calculated) value, compared with a critical value from a table for the sample size and significance level. Whether significance requires the observed value to be greater or less than the critical value depends on the test. Errors: a Type I error is a false positive (rejecting a true null, claiming an effect that is not real), more likely with a lenient level; a Type II error is a false negative (retaining a false null, missing a real effect), more likely with a strict level.
Examples in context
Example 1. Sign test in a simple before-and-after study. If participants rate their mood before and after an intervention as "better" or "worse" (nominal, related), the binomial sign test is correct. This shows how the three questions (difference, related, nominal) select the test.
Example 2. Chi-square for category counts. If you count how many men and women choose each of two options (frequencies in categories, unrelated, nominal), chi-square tests for an association. This illustrates the nominal, unrelated branch of the decision.
Try this
Q1. State the conventional significance level in psychology and what it means. [2 marks]
- Cue. : there is a 5 percent or smaller probability that the result is due to chance; below this the result is significant and the null hypothesis is rejected.
Q2. Name the test for a difference, with a repeated measures design and ordinal data. [1 mark]
- Cue. The Wilcoxon signed-ranks test.
Q3. Explain the difference between a Type I and a Type II error. [2 marks]
- Cue. A Type I error is a false positive (rejecting a true null, claiming an effect that is not real); a Type II error is a false negative (retaining a false null, missing a real effect).
Exam-style practice questions
Practice questions written in the style of WJEC Eduqas exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
Eduqas 20196 marksA study uses an independent groups design and produces ordinal data. Name the appropriate inferential test and justify your choice. [6 marks]Show worked answer →
A test-selection item (AO2). Maths content.
Test: the Mann-Whitney U test.
Justification: the test of difference is needed because the study compares two conditions. The design is independent groups (unrelated data, different participants in each condition), and the level of measurement is ordinal. A test of difference, with unrelated data, at ordinal level points to Mann-Whitney U.
Markers reward the correct test and a justification referencing all three decision criteria: difference (not correlation), unrelated design, and ordinal data.
Eduqas 20216 marksIn a study, the calculated value is compared with a critical value to decide significance. Explain how this decision is made and what a Type I error is. [6 marks]Show worked answer →
A knowledge item on significance and errors (AO1/AO3). Maths content.
Decision: the researcher sets a significance level, conventionally (a 5 percent risk that the result is due to chance). The calculated (observed) value is compared with the critical value from a table for the sample size and significance level. Depending on the test, the result is significant if the calculated value is either greater than or equal to, or less than or equal to, the critical value (the direction depends on the specific test). If significant, the null hypothesis is rejected.
Type I error: a false positive, rejecting a true null hypothesis (claiming a significant effect that does not really exist), made more likely by too lenient a significance level (for example ).
Markers reward the role of the significance level, the observed-versus-critical comparison, and a correct definition of a Type I error.
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Sources & how we know this
- Eduqas GCE A Level in Psychology (A290) specification — Eduqas (2015)