Effect Size Calculator

Figran

Get Cohen's d, Hedges' g and related effect sizes, with confidence intervals, from what your paper reports.

  • Means, t, F, r or odds ratio
  • Confidence intervals
  • Overlap plot
Reference SD
Export width
Reference only: |d| of 0.2, 0.5 and 0.8 are often called small, medium and large.

Cohen's d

0.905

95% CI [0.370, 1.434]

Overlap: 0.651 · U3: 0.817 · Probability of superiority: 0.739

ControlControlTreatmentTreatmentd = 0.905 · g = 0.894−2024Standardized valueDensity
The overlap plot assumes normally distributed groups with equal variance.

Results

MeasureEstimateConfidence intervalStandard errorVariance
Cohen's d 0.9050.370, 1.4340.2710.073
Hedges' g 0.8940.365, 1.4150.2680.072
Glass Δ (group 2 SD) 0.8330.321, 1.3460.2620.068
Correlation r Converted from Means and SDs0.4180.185, 0.5890.1030.011
Odds ratio Converted from Means and SDs5.1661.955, 13.4750.492 (log-OR scale)0.242 (log-OR scale)
Method notes
The variance of g is J²·Vd (Borenstein, 2009); metafor’s default can be slightly larger for small samples (0.246 vs 0.273 with n = 8 per group).Sampling variances and the Glass Δ interval use large-sample approximations.Input r uses the Fisher z scale for SE and variance; converted r uses the r scale.Odds ratio SE and variance use the log-OR scale.Independent-group d and its noncentral-t interval assume equal population variances.Correlation r is calculated from the test statistic and its degrees of freedom.

APA report sentence

Cohen's d = 0.91, 95% CI [0.37, 1.43]

Effect size examples

Start with a design close to your study, then replace the values.

ControlControlTreatmentTreatmentd = 0.905 · g = 0.894−2024Standardized valueDensity

Independent groups

Compare two group means and standard deviations.

30 participants per group

−0.500.511.5dz (95% CI)dz = 0.55995% CI [0.080, 1.025]

A paired t statistic

Convert a paired or one-sample t statistic to a standardized difference.

t = 2.5 · 20 pairs

BeforeBeforeAfterAfterdav = 0.566−2024Standardized valueDensity

Paired observations

Compare repeated measurements using their correlation.

24 pairs · r = 0.5

00.10.20.30.4Partial η² (95% CI)Partial η² = 0.14995% CI [0.010, 0.300]

ANOVA F statistic

Estimate partial eta squared from an omnibus F test.

F(2, 57) = 5

ControlControlTreatmentTreatmentd = 0.382−202Standardized valueDensity

Odds ratio conversion

Convert an odds ratio to an approximate standardized difference.

OR = 2 · log-OR SE = 0.25

Study AStudy AStudy BStudy BStudy CStudy CStudy DStudy D−2−10123Hedges' g (95% CI)

Several studies

Calculate effects and sampling variances for a meta-analysis.

4 studies · n = 16–80 per study

How to calculate effect size online

Choose the information you have and take the result into your report.

  1. 1Choose an input

    Select the statistic or data reported by your study.

  2. 2Enter the values

    Enter group summaries, raw data or a test statistic.

  3. 3Inspect the result

    Read the estimate, interval and plot.

  4. 4Export or copy

    Download the plot or copy the report sentence.

Which effect size should I report?

Choose the measure that matches the study design and research question.

DesignMeasureWhen to use it
Independent groupsd, gUse Hedges' g for small samples or meta-analysis; d is the uncorrected difference.
Paired measurementsdz, davdz uses the SD of differences; dav uses the square root of the average variance. State the definition.
ANOVAη²pPartial η² is the effect's variance relative to effect plus error variance; it equals η² only in one-way designs.

Effect size formulas and conversions

Use these definitions as an effect size converter between d, r and odds ratios; the formulas depend on the input and design.

d=M1−M2spooled

Cohen's d formula uses the pooled within-group SD.

g=Jd,r=dd2+aa=(n1+n2)2n1n2

Use a = 4 when group sizes are unavailable.

ln(OR)=πd3

The odds ratio conversion uses a logistic approximation.

ηp2=Fdf1Fdf1+df2

Partial eta squared uses the F statistic and its degrees of freedom.

r=tt2+df

For a t test, r follows directly from t and its degrees of freedom.

Paired standardizers

dav=M1−M2SD12+SD222

Here dav uses the square root of the average variance; Lakens (2013) uses the average SD.

drm=dz2(1−r)

Here drm uses the formula shown.

Source: Borenstein et al. (2009), Converting Among Effect Sizes

Effect size FAQ

What is an effect size?

An effect size describes the magnitude of a difference or association, independently of a significance decision.

How is Cohen's d calculated?

Subtract the group means and divide by their pooled within-group standard deviation.

How do d and Hedges' g differ?

Hedges’ g applies a small-sample correction to d; this calculator uses the exact gamma-function correction.

Are 0.2, 0.5 and 0.8 universal cutoffs?

No. These are rough reference points; interpret an effect in its scientific context, as discussed by Lakens (2013).

Which d should I use for paired data?

Choose a standardizer for the question: dz uses the SD of differences and dav uses the square root of the average variance. The paired-standardizer formula also defines drm.

Is partial eta squared the same as eta squared?

Not always. Partial eta squared excludes variance associated with other effects, so it can be larger than eta squared.

Can I calculate an effect from t or F?

Yes. For independent groups use t and both group sizes; for a paired or one-sample t use t and n. F and its degrees of freedom yield partial eta squared.

How should I report the result?

Report the measure, estimate, confidence interval and the study design; explain the standardizer for paired data.

Can I use these results in a meta-analysis?

Yes. The multiple-study mode exports g, its approximate variance and confidence limits for independent groups.

Are my data uploaded?

No. Calculations and downloads run in your browser; the draft stays in session storage.

Can this calculate statistical power?

Use the power analysis calculator to estimate power or sample size. Power analysis calculator

What is rank-biserial correlation?

It is a signed effect size for the Mann-Whitney test; with the group 1 U convention it equals Cliff's delta. Ties count as half a win.

Calculate your effect size

Turn your study statistics into an interpretable estimate.

Calculate your effect size