Effect Size Calculation: Cohen’s d vs. Hedges’ g

When studies measure the same underlying construct using different instruments -- one trial using a 0 to 100 anxiety scale, another using a completely different validated questionnaire -- you cannot pool their raw mean differences directly. Effect size calculation using a standardized measure like Cohen's d or Hedges' g solves this by expressing each study's effect in units of standard deviation rather than the original, incompatible scales.

What standardization actually does

A standardized mean difference divides the raw difference between two group means by a pooled standard deviation, producing a unitless number that represents how many standard deviations apart the two groups are. This makes a study using a 100-point scale and a study using a 7-point scale directly comparable, provided both are genuinely measuring the same underlying construct in a reasonably similar population.

Cohen's d: the more commonly known version

Cohen's d is calculated as the difference between two group means divided by the pooled standard deviation of both groups. It's the version most researchers learn first, and conventional interpretive bands exist -- roughly 0.2 for a small effect, 0.5 for a medium effect, 0.8 for a large effect -- though these thresholds are rough conventions from a specific research context and should not be applied rigidly to every field without consideration of what a meaningful effect actually looks like in that specific area.

Hedges' g: the same idea, corrected for small samples

Hedges' g applies a small but specific correction factor to Cohen's d, addressing a known upward bias in Cohen's d when sample sizes are small. This correction shrinks the effect size slightly, more so for smaller studies, bringing the estimate closer to the true population effect size. For studies with reasonably large samples, the difference between d and g is negligible; for a meta-analysis including several small trials, the difference can matter enough to affect your pooled estimate meaningfully.

Which one to actually use

Given that Hedges' g corrects a real, known bias and converges to essentially the same value as Cohen's d in larger samples, most current meta-analysis guidance and software defaults recommend using Hedges' g as the standard choice rather than uncorrected Cohen's d, particularly when your included studies have a mix of sample sizes or include any genuinely small trials. Some fields and some older meta-analysis traditions still default to Cohen's d out of convention rather than a specific methodological reason, and it's worth checking what your target journal or field commonly expects, while being prepared to justify Hedges' g as the more statistically defensible default if asked.

A common and avoidable mistake

A frequent error in practice is calculating Cohen's d correctly for each individual study but then failing to note in the methods section which specific correction, if any, was applied -- leaving readers unable to tell whether the reported "d" values in your forest plot are actually Hedges'-corrected or not. State explicitly which formula you used, since the two terms get used loosely and interchangeably in a way that can genuinely confuse a careful reader trying to reproduce your analysis.

Extracting the right numbers from primary studies

Calculating either effect size requires each study's group means, standard deviations, and sample sizes. When a study reports a p-value or confidence interval instead of a standard deviation directly, standard conversion formulas exist to back-calculate an approximate standard deviation, though this introduces some additional uncertainty worth acknowledging rather than presenting the back-calculated value with the same confidence as a directly reported one.

When standardized mean difference is the wrong tool

If all your included studies happen to use the exact same measurement instrument, a raw mean difference, not standardized, is actually the more interpretable and preferable choice, since it preserves the original, clinically meaningful units rather than converting to an abstract standard-deviation scale that's harder for a non-statistician reader to interpret directly. Reserve standardization specifically for the situation it solves: genuinely different instruments measuring the same underlying construct.

Interpreting a standardized result for a non-statistical audience

Because a standardized mean difference is inherently more abstract than a raw difference on a familiar scale, translating your pooled Hedges' g back into a concrete, interpretable statement -- what this magnitude of difference would mean using one commonly understood version of the outcome scale, if one exists -- helps readers who aren't fluent in standard-deviation units actually use your finding. This translation step is often skipped under space pressure, but it's frequently the single most useful sentence in your entire results section for a reader trying to decide whether your finding matters practically.

Reporting your effect size choice transparently

Whichever measure you use, state it explicitly in your methods section, along with your rationale if you departed from Hedges' g as the more commonly recommended default. This transparency, combined with providing your underlying extracted means, standard deviations, and sample sizes in a supplementary table, lets any reader independently verify or recalculate your effect sizes rather than simply trusting a reported number they cannot check themselves.

A note on software defaults

Most meta-analysis software packages, including R's metafor and Stata's meta suite, default to calculating Hedges' g rather than uncorrected Cohen's d when a standardized mean difference is requested, though the specific default and the exact terminology used can vary between packages and versions. Checking your software's documentation directly, rather than assuming a specific default, avoids an easily made and easily overlooked reporting error in your final manuscript. Given how mechanical this check is relative to the confusion it can cause a careful reader, verifying it directly against your software's own documentation before finalizing your statistics section is a small, worthwhile habit to build into your standard pre-submission review process. A short, dated note in your project records confirming which formula and software version you used costs almost nothing to maintain and can resolve a reviewer's question about your methodology within minutes rather than requiring you to reconstruct the reasoning from memory months after the analysis was originally run.