Effect Size Calculator

What an effect size calculator does

A standardized effect size answers the question a p-value cannot: not whether two groups differ, but by how much. An effect size calculator turns means, standard deviations, and sample sizes into Cohen’s d, Hedges’ g, or Glass’s delta, each on a scale that compares cleanly across studies. Journals and thesis committees increasingly ask for one alongside every test, with a confidence interval attached.

If you are computing effect sizes across a dozen studies for a meta-analysis, Fynman handles the search and screening upstream, so the studies reaching this calculator are already the ones that met your inclusion criteria.

How standardized effect sizes work

An effect size in the standardized mean difference family takes the raw gap between two means and divides it by a measure of spread, producing a unitless number. The original measurement scale drops out. A blood-pressure trial measured in mmHg and a depression trial measured in PHQ-9 points report effects on incompatible scales; converted to Cohen’s d, both sit on common ground.

That is why every meta-analysis of continuous outcomes runs on standardized effect sizes rather than raw differences. The standardized mean difference is the workhorse of intervention research, and the three estimators this calculator returns are the ones reviewers expect to see.

How to use this calculator

Pick an input mode at the top. Summary stats is the default: enter each group’s mean, standard deviation, and sample size. Raw data takes two pasted columns of scores and computes the summary statistics for you. From a test statistic recovers an effect size when a published paper reports only a t, F, or r value.

Set a confidence level (90, 95, or 99 percent) and submit. The result panel leads with one estimator, and the Estimator chips switch the headline between Cohen’s d, Hedges’ g, and Glass’s delta without recomputing. The Interpret for chips reframe the same number against a chosen discipline’s benchmark. Open the method section for the pooled standard deviation, the correction factor, and the formula with your values substituted.

Group 2 is the control or comparison group. The sign of the effect follows the order you enter the groups in; the interpretation uses the magnitude.

Cohen’s d, Hedges’ g, or Glass’s delta: which to report

All three standardize the same mean difference. They differ in what goes in the denominator and in whether they correct for small-sample bias.

The pooled standard deviation is where calculators quietly disagree. The correct weighted formula is:

sp = √[ ((n₁−1)·s₁² + (n₂−1)·s₂²) / (n₁+n₂−2) ]

A common shortcut averages the two standard deviations instead. That shortcut equals the weighted formula only when the groups are the same size; with unequal groups it produces a different, biased d. This calculator always uses the weighted form and prints the pooled SD in the method section so the value is never hidden.

Hedges’ g exists because Cohen’s d has a known upward bias in small samples. Hedges’ g multiplies d by a correction factor, J ≈ 1 − 3/(4·df − 1), that pulls the estimate back toward the population value. Once the total sample size is comfortably past 50, d and g are nearly identical and the choice stops mattering.

How to interpret your effect size

Cohen’s 1988 benchmarks of 0.2, 0.5, and 0.8 are conventions for when no field-specific value exists. They are not universal cutoffs. Cohen himself wrote that they were for use “when no other basis” for judging the effect was available, and he set 0.5 as the level “likely to be visible to the naked eye of a careful observer.” A d of 0.4 reads as merely “small” on that table and as a perfectly publishable effect against the benchmarks researchers in several fields actually use.

The psychology row converts Gignac and Szodorai’s correlation guidelines (r of .10, .20, and .30) into d units, because published effects in individual-differences research cluster well below Cohen’s table. The education row uses Hattie’s synthesis of more than 800 meta-analyses, which places the hinge point for a worthwhile educational effect at d ≈ 0.40. In medicine, a standardized effect is only meaningful next to a minimal clinically important difference; a statistically large d can still be clinically trivial.

The Interpret for chips in the result panel apply each of these benchmarks to your own number, so the verdict you cite matches the field you publish in.

Effect size from a t-value, F-value, or correlation

When a paper reports a test statistic but not the group means and SDs, you can still recover an effect size. The test-statistic mode handles three routes:

• From t: d = t · √(1/n₁ + 1/n₂), for an independent-samples t-test.
• From F: d = √(F · (1/n₁ + 1/n₂)), valid for a two-group one-way ANOVA, where F has one numerator degree of freedom and equals t².
• From r: d = 2r / √(1 − r²), converting a point-biserial correlation to a standardized mean difference.

This is the common case when building a meta-analysis extraction sheet from heterogeneous papers. Glass’s delta is unavailable in this mode, because it needs the control group’s raw standard deviation, and a test statistic does not carry it.

How the confidence interval is calculated

The interval is the estimate plus or minus a critical value times the standard error. For Cohen’s d the large-sample standard error is:

SE(d) = √[ (n₁+n₂)/(n₁·n₂) + d² / (2(n₁+n₂)) ]

The bounds are then d ± z · SE(d), with z from the standard normal (1.96 for 95 percent). For Hedges’ g, the standard error is the d standard error scaled by the same correction factor J. For Glass’s delta, the second term of the variance uses the control group’s degrees of freedom.

These are the standard estimators from Hedges and Olkin (1985) and Borenstein and colleagues (2009). They are the formulas behind R’s effsize and metafor packages, so the values this calculator returns agree with those packages to ordinary rounding. The method section shows the correction factor and the pooled SD for every result, so a reviewer can trace each number.

Reporting effect size in your manuscript

APA 7 reports a standardized effect size with its interval inline, for example Cohen's d = 0.54, 95% CI [0.18, 0.91]. Hedges’ g uses the same shape with the label g, and Glass’s delta uses Δ. The paste-ready sentence panel switches between APA and a Vancouver-style parenthetical and copies the line in one click.

Report the interval, not just the point estimate. Daniel Lakens’ 2013 guide to calculating and reporting effect sizes is the practical reference most methods sections lean on, and it is explicit that the interval belongs next to the number. For the additive-measure case, where you want a CI on a raw mean or proportion rather than a standardized one, use the confidence interval calculator; for ratio measures from a 2×2 table, the odds ratio calculator is the sibling tool. The broader interpretation framework sits in the research methodology guide.

Fynman extracts the reported effect size and its interval from every included paper automatically, so the meta-analysis extraction sheet builds itself instead of being retyped study by study.

Worked example

A two-arm trial reports a treatment group (n = 60, mean = 12.4, SD = 3.1) against a control group (n = 60, mean = 10.6, SD = 3.5).

Enter those six values in Summary stats mode at 95 percent confidence. The pooled SD is 3.31, giving Cohen’s d = 0.54, 95% CI [0.18, 0.91]. With J = 0.994 the small-sample correction barely moves it: Hedges’ g = 0.54, 95% CI [0.18, 0.90]. Glass’s delta, using only the control SD of 3.5, is 0.51, 95% CI [0.14, 0.88].

By Cohen’s 1988 benchmarks a d of 0.54 is a medium effect. Against the empirical psychology bands it is also medium, and against Hattie’s education benchmark it sits above the 0.40 hinge, inside the zone of desired effects. The interval excludes zero in every case, but its lower bound near 0.18 is a reminder that the true effect could be modest. The paste-ready APA sentence reads Cohen's d = 0.54, 95% CI [0.18, 0.91].

Frequently asked questions