Effect Size Measures in SPSS: Cohen's d, Eta Squared, and r Explained

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📸 Effect size in SPSS — Cohen's d from t-test output (SPSS 27+)

Why Effect Sizes Are Mandatory

A p-value only tells you whether a result is likely due to chance. It says nothing about practical importance. A study with n=10,000 can detect a trivially small difference at p<.001. Effect sizes answer the question: "How big is the effect?" APA 7 and most journals now require effect sizes alongside p-values.

Effect Size by Test Type

• Independent/Paired t-test → Cohen's d: Small=.20, Medium=.50, Large=.80
• ANOVA → Eta squared (η²): Small=.01, Medium=.06, Large=.14
• ANOVA → Partial η² (η²p): SPSS Options → Estimates of effect size
• Correlation → r: Small=.10, Medium=.30, Large=.50
• Chi-square → Cramer's V / φ: Same benchmarks as r

📸 Cohen's d automatically reported in SPSS 27+ t-test output

Computing Cohen's d Manually (Older SPSS)

d = (M₁ - M₂) / SD_pooled, where SD_pooled = √[(SD₁² + SD₂²)/2]. From t-test output you can also compute: d = t × √(1/n₁ + 1/n₂).

APA Reporting

Group A (M=74.2, SD=10.3) scored significantly higher than Group B (M=65.8, SD=11.2), t(91)=3.84, p<.001, d=0.78, 95% CI [0.40, 1.16], indicating a large effect.

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