How to Report Cohen's d in APA 7

One of the most-typed statistics questions on the internet is whether Cohen's d takes a zero before the decimal point. The short answer is yes, and the reason is the same rule that keeps the zero off a p value. Reporting a d properly takes a little more than that zero, though: you have to say which standard deviation went into the denominator, attach a confidence interval, and decide whether the number you should be publishing is a d or a g. This is the writing-it-down half of the job; what the number means is covered in the effect size interpretation guide, and the shape of the whole section is in how to report results in APA 7.

Cohen's d is italicized, and it does take a leading zero

Two rules, no exceptions. d is italicized, because it is a Latin letter standing for a statistic, exactly like t, F, M and r. And d takes a leading zero: d = 0.66, not d = .66. If there is a d = .66 anywhere in your manuscript, that is the first thing an APA-literate reviewer will circle.

The leading zero is not a house preference, it is a rule with a reason behind it. APA 7 asks for the zero when a statistic can take values above 1 and drops it when the statistic cannot. Cohen's d can: two groups two standard deviations apart give d = 2.00, which is unremarkable in a trial with a waiting-list control. So d, g, M, SD, t, F and unstandardised B coefficients all take the zero, while p, r, R², alpha, omega, standardized beta, eta squared and Cramér's V do not, because they are bounded within 0 to 1 or −1 to 1.

The mirror-image mistake is just as common and usually appears in the same sentence: p = 0.013 sitting next to d = .66. Both zeros are on the wrong statistic. It should read p = .013, d = 0.66.

Decimal places. Two, like almost everything else in an APA results section. Write d = 0.66, not d = 0.6612 and not d = 0.7. Three decimals are reserved for the p value, the only number in the line that needs them.

Subscripts. When you write d_z, d_av or d_rm, the d stays italic and the subscript does not: it is a label naming the variant rather than a variable, so it is set upright. Spell out "Cohen's d" at first mention and use the bare d after that.

Which standard deviation goes in the denominator

A d is a difference between means divided by a standard deviation, and that is where the trouble starts: three different standard deviations are available, all three get labeled "Cohen's d" by some piece of software, and the resulting numbers are not the same. Your reader cannot tell which one you used unless you say so.

The pooled standard deviation. This is the classic between-groups Cohen's d: the two variances are weighted by their degrees of freedom, averaged, and the square root is taken. In the worked example below, SD = 5.85 in 31 people and SD = 5.95 in 29 pool to 5.90, giving d = 0.66. If you already have the test statistic there is an exact shortcut: d = t × √(1/n₁ + 1/n₂).

The standard deviation of the differences. This is the within-subjects case and it gives d_z, which also equals t/√n. With 28 participants measured twice, a mean change of 3.40 points and an SD of the differences of 4.55: t(27) = 3.95, p < .001, d_z = 0.75, 95% CI [0.33, 1.17].

The control group's standard deviation. This is Glass's delta, and it has a genuine use: when the intervention changes the spread of scores and not only their center, a pooled denominator is already contaminated by that change. Glass's delta standardizes on the variability of the group that received nothing.

The warning that saves a round of review: d_z is not comparable with a between-groups d. It depends on the correlation between the two measurements, so a strongly correlated pre-test and post-test can produce a d_z considerably larger than the between-groups d that the same raw difference would give. Putting both in one table, or one meta-analysis, adds up things that are not the same quantity. For repeated measures, the pre-post effect size calculator returns the correct variant and names it for you.

Since version 27, SPSS prints three rows in the same effect size table — "Cohen's d", "Hedges' correction" and "Glass's delta" — each with its own estimate and interval. Copying the wrong row takes a second. Say which one you used, in one sentence in the Method: "Effect sizes were calculated using the pooled standard deviation."

Hedges' g, and when d is not the number to publish

Cohen's d is biased upwards: in small samples it systematically overstates the population effect. Hedges' g is the same d multiplied by a correction factor of approximately 1 − 3/(4df − 1), where df are the degrees of freedom of the test. It always shrinks the estimate; it never inflates it.

How much it shrinks depends on sample size, and the numbers settle the question faster than the argument does. At df = 58 the factor is .99 and a d of 0.66 becomes g = 0.65, a difference no reader will ever act on. At df = 21 — a pilot with 11 and 12 participants — the factor is .96, and a d of 0.88 becomes g = 0.85. That is roughly 3% of an effect that was never there. The working rule that holds up: report g below about 20 participants per group, and stop worrying about it above 50.

Hedges' g is written exactly like d: italicized, with a leading zero, to two decimal places. g = 0.85. It is a Latin letter and it can exceed 1, so both rules from the first section apply unchanged. At first mention, call it "Hedges' g" and add that it is d corrected for small-sample bias, because plenty of readers assume it is a different index altogether.

What you should not do is report both for the same comparison. It reads as indecision and it duplicates numbers that carry identical information. Pick one, name it in the Method and keep it throughout the manuscript, tables included. If you are submitting somewhere that publishes meta-analyses, g is the safer choice, because that is the metric the literature expects. The effect size calculator returns d, g and both intervals from the means, standard deviations and group sizes.

The 95% confidence interval around d

A d without an interval is an estimate with no precision attached: it does not tell the reader whether it came from 30 people or 300. The APA 7 reporting standards ask for an effect size and, wherever it can be computed, its confidence interval, and there are journals that will send a manuscript back for the omission alone. The format is square brackets, a comma, no units: d = 0.66, 95% CI [0.14, 1.18]. Never a ± sign, which describes something else.

Read that example slowly, because it is the whole argument for including the interval. The point estimate is 0.66, but the data are compatible with an effect of 0.14 and with one of 1.18. In Cohen's vocabulary, the study cannot tell "small" apart from "large". Writing "d = 0.66, a medium effect" and stopping there hides the thing the interval is showing you, which is that the sample was never going to resolve the question that finely.

The exact interval for a d comes from the noncentral t distribution and it is not symmetric around the estimate: the longer arm usually runs toward the large-effect side. The back-of-envelope formulas in circulation give a reasonable normal approximation, fine for sanity-checking a number, but the interval you publish should come out of the software. SPSS has printed it in the effect size table since version 27, and the standard R effect size packages return it with no extra configuration.

One coherence check takes ten seconds and rescues whole paragraphs: if your p is below .05, the 95% CI for d cannot contain zero, and if your p is above .05, it must. A results section reporting p = .03 alongside a 95% CI of [−0.05, 0.88] has an error in one of the two. The small pilot from the previous section shows the same logic from the other side: t(21) = 2.10, p = .048, d = 0.88, 95% CI [0.02, 1.73]. The point estimate is large, the lower bound is barely clear of zero, and the p value is barely under .05. All three numbers are telling one story.

0.20, 0.50 and 0.80 are a convention, not a law

The three benchmarks come from Cohen (1988), and it is worth knowing how he introduced them: as a last resort, for use when a field offers nothing better to anchor a magnitude against. They are not constants of nature and they were never empirically validated. Nearly forty years later they get cited as though they were an official scale, which has turned them into a crutch.

For reporting, the practical consequence is specific: the label cannot stand in for the number or for what the number means in your own units. "d = 0.66, a medium effect" tells the reader nothing they can use. "d = 0.66, equivalent to 3.90 fewer points on the perceived stress scale, roughly two thirds of a standard deviation in this sample" does. The label can stay, but behind the translation, not instead of it.

The anchor worth having is your own literature. If trials in your area with an active comparator cluster in a particular range, that range is what your effect should be read against, and one sentence citing two or three comparable studies is worth more than Cohen's table. In clinical work the point sharpens: an effect below 0.50 can matter a great deal when the outcome is serious and the intervention is cheap, and one of 0.80 on a laboratory task may mean nothing outside the laboratory.

A small writing detail gives away the authors who have not thought about any of this: when you cite the benchmarks in your text, write them with leading zeros, because they are still values of d. It is 0.20, 0.50 and 0.80, not .20, .50 and .80. What to do with those values once you have them is worked through in the effect size interpretation guide; this article is only about how they are written.

A worked results paragraph you can copy

"Participants who used the guided breathing app reported lower perceived stress at follow-up (n = 31, M = 18.10, SD = 5.85) than those on the waiting list (n = 29, M = 22.00, SD = 5.95). The difference was statistically significant, t(58) = 2.56, p = .013, with a moderate standardized effect, d = 0.66, 95% CI [0.14, 1.18], calculated using the pooled standard deviation (SD_pooled = 5.90). The raw difference of 3.90 points is close to two thirds of a standard deviation in this sample, and the interval is compatible with effects from small to large, so the magnitude should be treated as poorly estimated at this sample size."

Notice the order, because it is the order any reviewer is reading for: the two groups described with their ns, then the test with its degrees of freedom and p value, then the effect size with its interval, then the sentence that translates the number back into the units of the study. That last sentence is the one that is almost never there, and it is the only part most readers will carry away.

The within-subjects version of the same paragraph changes two things and only two, the test statistic and the variant of d: "Perceived stress decreased from baseline to follow-up, t(27) = 3.95, p < .001, d_z = 0.75, 95% CI [0.33, 1.17]; the effect size was standardized on the standard deviation of the within-person differences." That closing clause about the denominator costs you thirteen words and heads off the reviewer's question.

If your test is a t test and you are still unsure how to assemble the full line with its degrees of freedom, the guide to reporting t tests and chi-square in APA 7 gives you the sentence pattern with the d already in position.

Frequently asked questions

Is Cohen's d italicized in APA 7?

Yes. It is a Latin letter standing for a statistic, so it is italicized in the same way as t, F, M and r: d = 0.66. Hedges' g is italicized too. Greek letters are not — standardized beta, eta squared and alpha stay upright — and neither are subscripts that act as labels, such as the z in d_z.

Does Cohen's d have a leading zero?

Yes, always: write d = 0.66, not d = .66. The APA 7 rule is that a statistic takes a zero before the decimal point when it can exceed 1, and d routinely can — two groups two standard deviations apart give d = 2.00. That is why p, r, R² and alpha are written without the zero, while d, g, M and t are written with it.

How do you report Cohen's d in APA format?

Immediately after the test statistic and the p value, italicized, with a leading zero, to two decimal places, and with its confidence interval: t(58) = 2.56, p = .013, d = 0.66, 95% CI [0.14, 1.18]. The interval goes in square brackets with a comma between the bounds, never with a ± sign, and the Method should state which standard deviation was used in the denominator.

When should you use Hedges' g instead of Cohen's d?

In small samples, because d overstates the population effect and g corrects it by multiplying by roughly 1 − 3/(4df − 1). Below about 20 participants per group the difference is visible: at df = 21, a d of 0.88 becomes g = 0.85. Above 50 per group the correction shifts the estimate by less than 1%, so either is fine as long as you report only one and say which.

How do you report a confidence interval for Cohen's d?

In square brackets with a comma, no units, straight after the estimate: d = 0.66, 95% CI [0.14, 1.18]. The exact interval comes from the noncentral t distribution and is not symmetric around d, so take it from your software rather than computing it by hand. Quick check: if p is below .05, the interval cannot contain zero.

How many decimal places should Cohen's d have?

Two, like the other statistics in an APA 7 results section: d = 0.66. Three decimals are reserved for the p value, and once p drops below .001 you write p < .001 rather than the number itself. The bounds of the confidence interval also take two decimals, so the whole line stays visually consistent.

If you are closing the results section of a thesis or a paper and the real doubt is not how d is written but whether the test underneath it was the right one, that question is far cheaper to settle before you write than after the manuscript comes back. Our statistical consultancy reviews the full analysis plan and puts in writing which test answers which hypothesis, which effect size belongs with it, and how every line should be reported.