How to Report Effect Size in APA Style

You ran your test, the p-value came out below .05, and you are tempted to write "the difference was significant" and move on. Resist. A p-value tells you whether an effect is likely to be non-zero given your sample size; it says almost nothing about how big that effect is or whether it matters in practice. With a large enough sample, a trivially small difference becomes "significant." Effect size is the number that answers the question your reader actually cares about: how much?

APA 7th edition makes this explicit. The Publication Manual requires authors to report effect sizes and, wherever possible, their confidence intervals alongside every inferential test. This guide shows you how to choose, compute, and report the right effect size for the test you ran, with copy-ready APA sentence templates and a worked example.

Why effect size and its confidence interval matter

A p-value confounds the magnitude of an effect with the precision of your estimate. Two studies can report p = .04, yet one describes a tiny, practically meaningless difference in a sample of 5,000 and the other a large difference in a sample of 30. Effect size separates the signal from the sample size.

The confidence interval then tells you how precisely you have pinned that effect down. A Cohen's d of 0.50 with a 95% CI of [0.10, 0.90] is a very different story from d = 0.50, 95% CI [0.45, 0.55]. The first is compatible with a near-trivial effect; the second is tight. Always pair a point estimate with its interval. A wide interval that crosses zero is itself a finding: your data simply cannot resolve the effect.

Cohen's d for t-tests

For comparing two means, the standard effect size is Cohen's d, a standardized mean difference. You take the difference between the two group means and divide by the pooled standard deviation:

d = (M1 − M2) / SDpooled

Dividing by the SD puts the difference in standard-deviation units, so it is comparable across studies and scales. Cohen's rough benchmarks are 0.2 (small), 0.5 (medium), and 0.8 (large), but treat these as conventions, not laws (more on that below).

Hedges' g for small samples

Cohen's d is slightly biased upward in small samples. Hedges' g applies a simple correction factor (roughly 1 − 3/(4df − 1)) that shrinks the estimate. For total sample sizes below about 50, report Hedges' g instead; for large samples d and g are practically identical. Note that the choice between a pooled and a Welch t-test does not change the recommended effect size, but it does affect which SD you should standardize against. See Welch's vs Student's t-Test: When Variances Differ for that decision.

Eta-squared and partial eta-squared for ANOVA

For ANOVA, effect size is expressed as the proportion of variance in the outcome explained by a factor. Eta-squared (η²) is the factor's sum of squares divided by the total sum of squares. In factorial designs, software usually reports partial eta-squared (η²_p), which divides the factor's SS by that factor's SS plus the error SS, removing the other factors from the denominator.

Cohen's benchmarks for η² are 0.01 (small), 0.06 (medium), and 0.14 (large). Be careful: partial eta-squared values from a multi-factor design are not comparable to eta-squared values from a one-way design, and they do not sum to 1. Report which one your software produced.

Why omega-squared is often better

Eta-squared is biased upward; it overstates the variance explained, especially in small samples. Omega-squared (ω²) applies a correction and is a less biased estimator of the population effect. If your software offers it, prefer ω² (or its partial version) for ANOVA. If you are choosing between ANOVA and a rank-based alternative, see ANOVA vs Kruskal-Wallis: Which Test to Use.

Pearson r for correlation

For a correlation, the coefficient Pearson r is itself the effect size: it is already standardized between −1 and +1. Cohen's benchmarks are 0.1 (small), 0.3 (medium), and 0.5 (large). Squaring it gives r² , the coefficient of determination, the proportion of variance the two variables share. An r of .30 means the variables share only 9% of their variance, a useful reality check against over-interpreting a "medium" correlation. Report r with its 95% CI. The choice of coefficient also matters; Pearson vs Spearman vs Kendall: Choosing a Correlation covers when Pearson is appropriate.

Effect size by test: a quick reference

APA sentence templates

The APA pattern is consistent: report the test statistic, its degrees of freedom, the exact p-value, and then the effect size with its confidence interval in brackets. Use italics for statistical symbols.

• t-test: "There was a significant difference, t(48) = 2.74, p = .009, d = 0.77, 95% CI [0.19, 1.35]."
• ANOVA: "The main effect of condition was significant, F(2, 87) = 6.41, p = .003, η²_p = .13, 90% CI [.03, .24]." (Convention uses a 90% CI for η²_p.)
• Correlation: "Anxiety and performance were negatively correlated, r(98) = −.34, p < .001, 95% CI [−.50, −.16]."

Worked example

Suppose a training group (M = 82.4, SD = 9.1, n = 25) outscores a control group (M = 75.8, SD = 10.2, n = 25). The pooled SD is about 9.66, so d = (82.4 − 75.8) / 9.66 ≈ 0.68. Because the total sample is 50, apply the Hedges correction (factor ≈ 0.984), giving g ≈ 0.67 — a medium-to-large effect. With the independent-samples t-test returning t(48) = 2.41, p = .020, you would write:

"The training group scored significantly higher than the control group, t(48) = 2.41, p = .020, Hedges' g = 0.67, 95% CI [0.10, 1.24]." Running this in MindStat returns d, g, and the CI automatically, so you can paste an APA-ready line without manual computation.

Common mistakes to avoid

Reporting only the p-value. This is the single most common reviewer complaint. A significant p with no effect size is an incomplete result.

Treating thresholds as absolute laws. Cohen himself called 0.2/0.5/0.8 arbitrary conventions for fields with no prior benchmarks. In a mature literature, a d of 0.2 may be large; in a noisy applied setting, 0.8 may be unremarkable. Interpret your effect against effects typical in your field, not a generic table.

Omitting the confidence interval. A point estimate without an interval hides your uncertainty. Always report both.

Key takeaways

• A p-value tells you whether; an effect size tells you how much. Report both, always.
• Use Cohen's d (or Hedges' g for small samples) for t-tests, η²/ω² for ANOVA, and Pearson r for correlation.
• Prefer the less-biased estimators (Hedges' g, omega-squared) when samples are small.
• Always pair the effect size with its confidence interval, and follow the APA order: statistic, df, p, then effect size + CI in brackets.
• Benchmarks are field-dependent guides, not universal laws.