Effect size — Edexcel A-Level Statistics
Test yourself on Effect size with PEARSON EDEXCEL A-Level practice questions.
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Effect size explained
Effect size measures the strength of a phenomenon, complementing significance tests which only assess evidence against a null hypothesis.
Read the full explanation
A small p-value does not imply a large or important effect; effect size quantifies magnitude. Common measures include Cohen's d for mean differences, Pearson's r for correlation, and eta-squared (η²) or omega-squared (ω²) for ANOVA. In authentic contexts, you calculate an effect size from sample data and interpret it using benchmarks (e.g., Cohen's d: 0.2 small, 0.5 medium, 0.8 large). You also apply effect size by comparing it across studies or contexts, and by reporting it alongside p-values. For example, a new teaching method may produce a statistically significant improvement in test scores, but if Cohen's d is 0.1, the practical benefit is small. Effect size helps decide whether a finding matters in real-world settings.
Your focus
- Define effect size and explain how it complements significance testing.
- Calculate and interpret an appropriate effect size measure for a given context.
- Apply effect size to evaluate the practical importance of a finding in an authentic scenario.
Effect size exam tips
Marking Points
- Definition: effect size quantifies the magnitude of a difference or relationship, independent of sample size.
- Complementarity: significance testing addresses whether an effect exists; effect size addresses how large it is.
- Common measures: Cohen's d for two means, Pearson's r for association, η² for ANOVA.
- Calculation: for Cohen's d, d = (mean difference) / (pooled standard deviation); for η², η² = SS_between / SS_total.
- Interpretation: use context-specific benchmarks; Cohen's benchmarks are guidelines, not strict rules.
- Application: report effect size with confidence intervals and p-values to give a complete picture.
Examiner Tips
- 💡When asked to interpret an effect size, state the measure (e.g., Cohen's d), its value, and what it means in the context (e.g., 'a small effect on test scores').
- 💡If you calculate an effect size, show the formula and substitute the correct values; keep units consistent.
- 💡In multiple-choice questions, eliminate options that confuse significance with effect size or that misstate the direction of a formula.
- 💡Remember that effect size can be reported with a confidence interval to show precision.
Common Mistakes
- Misunderstanding: 'A statistically significant result is always practically important.' Correction: significance depends on sample size; a tiny effect can be significant in a large sample, so always report effect size.
- Misunderstanding: 'Effect size is the same as the p-value.' Correction: p-value measures evidence against the null; effect size measures magnitude; they answer different questions.
- Misunderstanding: 'Cohen's benchmarks (0.2, 0.5, 0.8) apply universally.' Correction: benchmarks are context-dependent; in education, even 0.2 may be meaningful, while in physics, larger values may be needed.
- Misunderstanding: 'Effect size can only be used with two groups.' Correction: effect size measures exist for correlations, ANOVA, and more; choose the measure that matches the design.