How to Report Effect Sizes in APA Format

APA Reporting Template

Use these templates to report effect sizes alongside your inferential statistics. Replace the bracketed placeholders with your values.

Cohen's d (Group Comparisons)

The difference was statistically significant, t([df]) = [t-value], p = [p-value], d = [Cohen's d], indicating a [small/medium/large] effect.

Hedges' g (Unequal or Small Samples)

The groups differed significantly, t([df]) = [t-value], p = [p-value], g = [Hedges' g], indicating a [small/medium/large] effect.

Eta-Squared ($\eta^2$) and Partial Eta-Squared ($\eta_p^2$)

There was a significant effect of [independent variable] on [dependent variable], F([df1], [df2]) = [F-value], p = [p-value], $\eta^2$ = [value] [or $\eta_p^2$ = [value]], a [small/medium/large] effect.

Pearson's r (Correlation as Effect Size)

[Variable 1] and [variable 2] were significantly correlated, r([df]) = [r-value], p = [p-value], representing a [small/medium/large] effect.

$R^2$ (Proportion of Variance Explained)

The model accounted for a significant proportion of variance in [outcome variable], $R^2$ = [value], F([df1], [df2]) = [F-value], p = [p-value].

Odds Ratio (Logistic Regression / 2 x 2 Tables)

Participants in [group 1] were [OR value] times [more/less] likely to [outcome] than participants in [group 2], OR = [value], 95% CI [[lower], [upper]], p = [p-value].

Worked Example

Scenario: A researcher conducted multiple analyses in a study comparing a new reading intervention to standard instruction among 120 elementary school students.

APA Write-Up with Multiple Effect Sizes:

An independent samples t-test indicated that the intervention group (M = 85.3, SD = 10.2) scored significantly higher than the control group (M = 78.1, SD = 11.6) on reading comprehension, t(118) = 3.67, p < .001, d = 0.66, indicating a medium-to-large effect.

A one-way ANOVA comparing reading comprehension across three dosage levels (low, medium, high) revealed a significant effect, F(2, 57) = 6.82, p = .002, $\eta^2$ = .19, a large effect. Post-hoc comparisons showed that the high-dosage group outperformed the low-dosage group (p = .001, d = 0.94).

Students in the intervention group were 3.2 times more likely to reach grade-level proficiency than students in the control group, OR = 3.20, 95% CI [1.58, 6.48], p = .001.

When to Use Each Effect Size

Effect Size Benchmarks

Cohen's d and Hedges' g

$\eta^2$ and $\eta_p^2$

Pearson's r

Odds Ratio

Note. These benchmarks are guidelines from Cohen (1988) and should be interpreted in the context of the specific research area. What counts as "large" in one field may be typical in another.

Reporting Checklist

• [ ] Reported at least one effect size measure for every inferential test
• [ ] Chose the correct effect size for the analysis (see table above)
• [ ] Reported the effect size value to two decimal places
• [ ] Interpreted the magnitude of the effect (small, medium, or large)
• [ ] Included a 95% confidence interval for the effect size when possible
• [ ] Used italics for statistical symbols (d, g, r, p)
• [ ] Used the correct notation ($\eta^2$ vs. $\eta_p^2$, d vs. g)
• [ ] Contextualized the effect size in practical terms when appropriate

Common Mistakes

1. Not reporting any effect size — APA 7th edition explicitly requires effect sizes. A p-value alone is not sufficient.
2. Confusing $\eta^2$ and $\eta_p^2$ — In factorial designs, partial eta-squared ($\eta_p^2$) removes variance from other factors. In one-way ANOVA they are the same, but always label them correctly.
3. Using Cohen's d with very unequal or small samples — Hedges' g corrects for small-sample bias. Use g when either group has fewer than 20 participants.
4. Interpreting benchmarks too rigidly — Cohen himself cautioned that his benchmarks are rough guidelines. A "small" effect can be practically important (e.g., in medical contexts), and a "large" effect may be trivial in a different domain.
5. Omitting confidence intervals — Whenever possible, report a 95% CI around the effect size to convey precision. For example: d = 0.66, 95% CI [0.29, 1.03].
6. Reporting effect sizes without the corresponding test statistic — Always pair the effect size with the full test result (t, F, $\chi^2$, etc.).

Non-Significant Results

Effect sizes should always be reported, even when results are not significant:

The intervention group (M = 80.1, SD = 10.8) did not score significantly higher than the control group (M = 78.4, SD = 11.2), t(118) = 0.87, p = .387, d = 0.15, indicating a small effect. Although the effect was not statistically significant, the small effect size suggests that any true difference between groups is likely negligible.

Non-significant results with small effect sizes strengthen the conclusion that no meaningful difference exists. Non-significant results with moderate-to-large effect sizes suggest the study may have been underpowered.