A standardized mean difference expresses the gap between two group means in units of their pooled standard deviation, so studies that used different scales can be compared on one footing. This calculator reports Cohen’s d, the basic standardized difference, and Hedges’ g, which applies a small-sample correction so the estimate is not biased upward in small studies. Each comes with its standard error and a 95% confidence interval for use in a meta-analysis.
Standardized mean difference calculator
Enter two groups' means, standard deviations, and sample sizes to get Cohen's d and the small-sample-corrected Hedges' g, each with a 95% confidence interval ready for pooling.
Hedges' g (bias-corrected)
0.475
95% CI 0.040 to 0.910, a small effect by conventional benchmarks
Effect size and components
Cohen's d0.479 (95% CI 0.040 to 0.918)
Glass's delta (group 2 SD as standardizer)0.462 (95% CI 0.017 to 0.906)
Mean difference (t interval, 80 degrees of freedom)0.600 (95% CI 0.049 to 1.151)
Pooled SD (sp)1.252
SE of Cohen's d0.2241
SE of Hedges' g0.2220
SE of Glass's delta0.2267
SE of the mean difference0.2767
Correction factor J0.9906
By conventional benchmarks Hedges’ g of 0.47 is a small effect (negligible under 0.2, small under 0.5, medium under 0.8, large at 0.8 and above). Treat these cut-offs as rough guides only; what counts as a meaningful effect depends on the field, the outcome, and the cost of the intervention. Glass’s delta standardizes on the group 2 standard deviation alone, so enter the control group as group 2 when the groups have unequal variability.
Meta-analysis ready
Hedges' g (estimate)0.4746
Standard error of g0.2220
Cohen's d (estimate)0.4791
Standard error of d0.2241
Paste Hedges’ g and its standard error into the meta-analysis calculator as one study line, for example “0.4746 0.2220” with the difference measure and the estimate plus standard error input selected.
Report-ready text
The intervention group (group 1) scored higher than the control group (group 2) (mean difference = 0.60, 95% CI 0.05 to 1.15; Hedges' g = 0.47, 95% CI 0.04 to 0.91), a small standardized effect.
Putting different scales on one footing
Continuous outcomes are rarely measured the same way twice. One depression trial uses a 0 to 27 questionnaire, another a 0 to 52 clinician rating, another a visual analogue scale. A raw difference of three points means completely different things on each. The standardized mean difference solves this by expressing the gap between two group means in units of the spread of the data itself, the pooled standard deviation. A standardized mean difference of 0.5 says the groups differ by half a standard deviation, a statement that travels across instruments and lets otherwise incompatible studies join one pooled meta-analysis.
This calculator reports two flavours. Cohen’s d is the plain mean difference divided by the pooled standard deviation. Hedges’ g multiplies d by a small correction factor that removes a known upward bias in small samples. Because included studies are often small, Hedges’ g is the conventional choice for synthesis, and the two converge as sample sizes grow. Our broader guide to effect sizes for continuous and binary outcomes sets these in context.
When to standardise, and when not to
Standardise only when you need to. If every included study used the exact same instrument, a raw mean difference is more transparent and easier for clinicians to act on, so prefer it. The standardized mean difference earns its place when the same underlying construct is measured on different scales. Be aware of its weakness too: the metric is sensitive to the spread of the populations studied, so a narrow, homogeneous sample inflates the standardized effect even when the raw difference is modest. Where studies report different metrics entirely, you may need our effect size conversion tool to bring binary and continuous results onto a single scale first.
Interpreting the magnitude
The familiar benchmarks treat a standardized mean difference near 0.2 as small, near 0.5 as medium, and near 0.8 as large. These are rough conventions, not laws, and they came from the social sciences rather than your field. A “small” effect on a hard clinical outcome can be enormously valuable, while a “large” effect on a soft surrogate may mean little. Read the estimate next to its confidence interval and judge clinical importance directly. The size label is a starting point for discussion, not a verdict.
A worked example
Suppose a trial reports a treatment mean of 18.0 with a standard deviation of 6.0 in 40 patients, and a control mean of 21.0 with a standard deviation of 7.0 in 42 patients, where lower scores are better. The pooled standard deviation combines the two, weighted by degrees of freedom, and lands near 6.52. Cohen’s d is the difference of minus 3.0 divided by 6.52, about minus 0.46, a medium-sized benefit. With a combined sample of 82, the Hedges’ correction factor is roughly 0.99, so Hedges’ g is about minus 0.45, barely different. If the 95 per cent confidence interval runs from minus 0.89 to minus 0.01, the effect is statistically clear but its lower bound is close to nothing, so you would temper the conclusion. Carry the Hedges’ g and its standard error into a random-effects pooling model to combine it with other trials.
Common mistakes
- Standardising when every study used one scale. You lose interpretability for no gain; report the raw mean difference instead.
- Using Cohen’s d in small studies. It is biased upward; Hedges’ g should be the default for synthesis.
- Reading the benchmarks as clinical thresholds. Small, medium, and large are statistical conventions, not statements about patient benefit.
- Pooling the wrong standard deviation. Mixing change-from-baseline and endpoint standard deviations across studies distorts the standardized effect; keep the basis consistent.
- Ignoring the spread of the source population. A standardized effect can look large simply because the sample was unusually homogeneous, an issue that also surfaces when reading a forest plot of standardized differences.
How it works
The two groups are first put on a common scale through the pooled standard deviation, which combines both groups’ standard deviations weighted by their degrees of freedom:
sp = sqrt( ((n1-1)*sd1^2 + (n2-1)*sd2^2) / (n1 + n2 - 2) )
Cohen’s d divides the mean difference by that pooled value:
d = (m1 - m2) / sp
SE(d) = sqrt( (n1 + n2) / (n1 * n2) + d^2 / (2 * (n1 + n2)) )
Hedges’ g applies a correction factor J that removes the small-sample upward bias in d:
J = 1 - 3 / (4 * (n1 + n2) - 9)
g = J * d
SE(g) = J * SE(d)
The 95% confidence interval for each estimate is symmetric on this scale:
95% CI = estimate +/- 1.96 * SE
The constant 1.96 is the standard normal value for a 95% interval. Hedges’ g and its standard error are the per-study inputs for inverse-variance pooling of standardized mean differences.
Frequently asked questions
- What is the difference between Cohen's d and Hedges' g?
- Both express the difference between two group means in pooled standard deviation units. Cohen's d slightly overestimates the true effect in small samples, so Hedges' g multiplies it by a correction factor that shrinks the estimate toward zero. The two are nearly identical once the combined sample size is large, but Hedges' g is preferred for meta-analysis because many included studies are small.
- When should I use a standardized mean difference?
- Use a standardized mean difference when the included studies measure the same underlying construct on different scales or instruments, for example different depression questionnaires. Standardizing by the pooled standard deviation puts every study on a common, unit-free scale so the estimates can be pooled. When all studies use the identical scale, a raw mean difference is easier to interpret and is preferable.
- How do I interpret the size of Cohen's d or Hedges' g?
- A common rough guide treats values around 0.2 as small, 0.5 as medium, and 0.8 as large, but these benchmarks are not absolute and depend on the field and the outcome. Always read the estimate next to its confidence interval, and judge whether the difference is clinically or practically meaningful rather than relying on the label alone.
- Can I compute these from a t test or p-value instead of means?
- Yes, in principle, because the standardized mean difference can be recovered from a t statistic and the group sizes, or from other summary statistics. This calculator uses the most direct inputs, the two means, their standard deviations, and the sample sizes. If you only have a t statistic, convert it to a standardized mean difference first, then enter the equivalent summaries here.
- What if a study reports a standard error or confidence interval instead of a standard deviation?
- You can recover the standard deviation before entering it here. Multiply a standard error by the square root of the group's sample size to get the standard deviation, or derive the standard deviation from the width of a confidence interval and the relevant critical value. Extracting these correctly is a routine but error-prone part of data extraction, so double-check each conversion against the original paper.
- Why does Hedges' g make so little difference in large studies?
- The correction factor that turns Cohen's d into Hedges' g depends on the combined degrees of freedom, and it approaches one as the total sample size grows. With a few hundred participants the shrinkage is well under one per cent, so the two estimates are practically identical. The correction only bites in genuinely small studies, which is exactly where the upward bias in Cohen's d would otherwise matter.
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