How to Report Cohen's d in APA 7 (With Example)

Cohen's d is the effect size that goes with a t-test: the difference between two means in standard deviation units. Marks are lost on the italics, the leading zero, a missing confidence interval, and above all on not saying which d you computed, because there are several. This guide covers the format, the choice of d, and a worked example you can reproduce.

What you need before you write a single word

An APA 7 report of Cohen's d needs:

1. The test it belongs to, usually a t-test, with its t, df and exact p.
2. The means and standard deviations of the groups or conditions.
3. The value of d, and the standardizer you divided by (pooled SD, SD of the differences, or the average SD).
4. A 95% confidence interval for d, and the method used to compute it.

Is Cohen's d italicised in APA?

Yes. APA 7 italicises statistical symbols written with Latin letters, so the d is italic; the name "Cohen's" is not. The same goes for Hedges' g, named after Larry Hedges (so not "Hedge's g").

The APA 7 format template

The effect size goes at the end of the test result, after p, followed by its interval:

[Group 1] scored higher on [outcome] (M = X.XX, SD = X.XX) than [group 2] (M = X.XX, SD = X.XX), t(df) = X.XX, p = .XXX, d = X.XX, 95% CI [X.XX, X.XX].

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Formatting rules reviewers actually check:

• Keep the leading zero on d. Cohen's d has no upper bound, so APA 7 keeps the zero: d = 0.95, never d = .95. The same applies to Hedges' g.
• No leading zero on p, because p cannot exceed 1.
• Report d to two decimals, the usual choice for effect sizes.
• Put the confidence interval in square brackets with its level: 95% CI [0.09, 1.79].
• Say in words which group was higher, so the sign of d is never ambiguous.

Which d did you compute?

"Cohen's d" is a family. Name the member you used in the Method or the Results.

Independent groups. The standard d divides the mean difference by the pooled standard deviation of the two groups (Cohen, 1988). The worked example below uses it.

Paired or repeated measures. Here two versions are common, and they can give very different numbers from the same data (Lakens, 2013):

• d_z divides the mean of the difference scores by the standard deviation of the difference scores. It follows directly from the paired t-test (d_z = t divided by the square root of n), so it is the natural input for a power analysis.
• d_av divides the mean difference by the average of the two conditions' standard deviations. It ignores the correlation between the measures, so it is easier to compare with a between-groups d.

In a typeset manuscript the z and av are subscripts. When the two measures are strongly correlated, d_z can be much larger than d_av, so an unlabelled d from a paired design tells the reader very little. See the paired t-test guide for the rest of that write-up.

Hedges' g: the small-sample correction

Cohen's d overestimates the population effect in small samples. Hedges' g applies a correction factor (Hedges & Olkin, 1985). A widely used approximation (Lakens, 2013) is:

g = d × (1 - 3 / (4(n1 + n2) - 9))

The correction shrinks d by a few percent with 20 to 30 participants and becomes negligible in large samples. With small groups, report g and keep its leading zero.

A worked example

Twenty-four students (fictional data) learned a 30-word list with spaced or massed practice, 12 per group. Words recalled a week later:

• Spaced practice: 21, 18, 24, 19, 23, 17, 22, 20, 25, 19, 16, 22
• Massed practice: 18, 15, 21, 18, 14, 20, 17, 19, 19, 22, 15, 18

From those numbers:

• Spaced practice: M = 20.50, SD = 2.81
• Massed practice: M = 18.00, SD = 2.45
• Student's independent-samples t-test: t(22) = 2.32, p = .030
• Pooled SD = 2.64, so d = 2.50 / 2.64 = 0.95
• 95% CI for d: [0.09, 1.79], computed with the noncentral t distribution
• Hedges' g = 0.92, 95% CI [0.09, 1.72]

The noncentral t method finds the noncentrality values that put the observed t at the 2.5th and 97.5th percentiles, then converts them to the d scale. It is exact under the t-test's assumptions; the large-sample approximation gives a slightly different interval, so say which you used.

Written up in APA 7:

Students who used spaced practice recalled more words (M = 20.50, SD = 2.81) than students who used massed practice (M = 18.00, SD = 2.45), t(22) = 2.32, p = .030, d = 0.95, 95% CI [0.09, 1.79].

Add in the Method: "Cohen's d uses the pooled standard deviation; its confidence interval uses the noncentral t distribution." With 12 per group, the corrected value is equally correct:

..., t(22) = 2.32, p = .030, Hedges' g = 0.92, 95% CI [0.09, 1.72].

Look at the interval before you write "large effect": the data are consistent with anything from a trivial effect to a huge one.

Interpreting d: use Cohen's benchmarks with caution

Cohen (1988) suggested 0.20 as small, 0.50 as medium and 0.80 as large, as a fallback for when nothing better is known, not as a grading scale. Used mechanically, they cause two problems:

• They ignore the field. A small effect from a cheap, scalable intervention can matter more than a large one on a lab task.
• They ignore the interval. In the example, d = 0.95 is "large" by the benchmark, but the lower limit of 0.09 is not even "small".

Compare d with effects in your own literature instead, and describe the interval. The effect size guide lists the benchmarks for other statistics.

Mistakes reviewers catch

• Dropping the leading zero. d = .95 is wrong because d can exceed 1. Write 0.95.
• Not italicising d, or italicising "Cohen's" as well.
• Not saying which d. In a paired design, d_z and d_av can differ by a factor of two. Name the one you report.
• An unlabelled confidence interval. If you also report the CI of the mean difference (here [0.27, 4.73] words), make clear which is which.
• "Hedge's g". The name is Hedges.
• Reporting d without the means and SDs, so the reader cannot see the raw difference.

Before you report: did the test's assumptions hold?

The pooled-SD d inherits the Student's t-test assumptions: independent observations, roughly normal outcomes, similar variances. In the example, Levene's test gave no sign of unequal variances, F(1, 22) = 0.70, p = .41. If the variances clearly differ, the pooled SD is a poor standardizer; say so and consider the Welch test. The assumptions guide shows how to check each one, and the independent t-test guide covers the rest of the write-up.

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Frequently asked questions

Does Cohen's d need a leading zero in APA 7? Yes. It can exceed 1, so write d = 0.95, not d = .95.

Should I report Cohen's d or Hedges' g? With small groups, Hedges' g, because d is biased upward. In large samples they are practically identical; just name the one you report.

Where does d go in the sentence? After the p value, followed by its confidence interval: t(22) = 2.32, p = .030, d = 0.95, 95% CI [0.09, 1.79].

Which related guides might I need? Often these: confidence intervals, Welch's t-test and p values.

References

American Psychological Association. (2020). Publication manual of the American Psychological Association (7th ed.).

Cohen, J. (1988). Statistical power analysis for the behavioral sciences (2nd ed.). Lawrence Erlbaum Associates.

Hedges, L. V., & Olkin, I. (1985). Statistical methods for meta-analysis. Academic Press.

Lakens, D. (2013). Calculating and reporting effect sizes to facilitate cumulative science: A practical primer for t-tests and ANOVAs. Frontiers in Psychology, 4, 863. https://doi.org/10.3389/fpsyg.2013.00863