Effect Size Quick Reference

What Are Effect Sizes?

Effect sizes measure the magnitude of a difference or relationship. Unlike p-values, effect sizes are not influenced by sample size and provide practical significance.

Interpretation Guidelines

Cohen's d (for t-tests)

Measures: Standardized difference between two means

d value	Interpretation	Example
0.0 - 0.2	Negligible	Barely noticeable difference
0.2 - 0.5	Small	Noticeable but modest effect
0.5 - 0.8	Medium	Moderate, visible difference
0.8+	Large	Substantial, important difference

In R:

library(effsize)
cohen.d(outcome ~ group, data = data)

η² (Eta Squared - for ANOVA)

Measures: Proportion of variance in outcome explained by the factor(s)

η² value	Interpretation	Variance Explained
0.01 - 0.06	Small	1-6% of variance
0.06 - 0.14	Medium	6-14% of variance
0.14+	Large	14%+ of variance

In R:

library(effectsize)
eta_squared(model)

R² (for Regression and Correlation)

Measures: Proportion of variance in outcome explained by predictor(s)

R² value	Interpretation	Practical Meaning
0.01 - 0.09	Small	Weak predictive power
0.09 - 0.25	Medium	Moderate predictive power
0.25+	Large	Strong predictive power

In R:

summary(model)$r.squared

Cramér's V (for Chi-Square)

Measures: Strength of association between categorical variables

V value	df = 1	df = 2	df = 3+
Small	0.10	0.07	0.06
Medium	0.30	0.21	0.17
Large	0.50	0.35	0.29

Note: df = min(rows-1, cols-1)

In R:

library(lsr)
cramersV(table(data$var1, data$var2))

r (Correlation Coefficient)

Measures: Strength and direction of linear relationship

r value	Interpretation	Relationship Strength
0.0 - 0.1	Negligible	No meaningful relationship
0.1 - 0.3	Small	Weak relationship
0.3 - 0.5	Medium	Moderate relationship
0.5 - 0.7	Large	Strong relationship
0.7+	Very Large	Very strong relationship

In R:

cor.test(data$var1, data$var2)

Important Notes

Statistical vs. Practical Significance

A result can be statistically significant (p < .05) but have a small effect size. Always report both!

Context Matters

Effect size interpretation depends on your field. A "small" effect in medicine might be life-saving.

Sample Size Independence

Unlike p-values, effect sizes are not inflated by large sample sizes.

APA Requirements

APA style requires reporting effect sizes for all inferential tests.

Direction Matters

For d and r, negative values indicate direction—magnitude is what matters for interpretation.

Quick Conversions

r² = R² (same thing)
d ≈ 2r (for similar sample sizes)
η² ≈ R² (for ANOVA vs. regression on same data)

When to Use Each

Test	Effect Size	R Package
One-Sample t-test	Cohen's d	`effsize`
Independent t-test	Cohen's d	`effsize`
Paired t-test	Cohen's d	`effsize`
One-Way ANOVA	η²	`effectsize`
Two-Way ANOVA	η²	`effectsize`
Regression	R²	Built-in
Correlation	r	Built-in
Chi-Square	Cramér's V	`lsr`

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