Cohen's D

A standardised measure of effect size expressing the difference between two group means in units of their pooled standard deviation.

Source: Cohen 1988

Cohen's d expresses the difference between two group means in units of their pooled standard deviation, turning a raw gap into a standardised effect size. Dividing by the spread of the data makes the difference comparable across studies and outcomes measured on different scales, so a d of one means the groups differ by one standard deviation. This helps convey how large an effect is, independent of the original units, and supports comparison across research. Standardising a mean difference is what it does. Cohen (1988) describes this measure.

Source: Cohen 1988

Cohen's d is calculated by dividing the difference between the two group means by the pooled standard deviation of the groups, so it expresses the mean difference in standard deviation units. The pooled standard deviation combines the variability of both groups. So Cohen's d is calculated as the mean difference divided by the pooled standard deviation, which standardises the effect by the data's spread, giving a unit-free measure that indicates how many standard deviations separate the group means, and this standardisation is what allows effects measured on different scales to be compared on a common footing.

Source: Cohen 1988

Cohen's d is interpreted as the number of standard deviations between the group means, with larger absolute values indicating larger effects. Cohen suggested rough benchmarks of around 0.2 for a small effect, 0.5 for medium, and 0.8 for large, though these are conventions to be applied with judgement rather than fixed rules. So Cohen's d is interpreted by its magnitude on the standardised scale, with the conventional small, medium, and large labels offering a rough guide, though the practical importance of a given d depends on the context, so the benchmarks are used cautiously alongside consideration of what the effect means in the specific field.

Source: Cohen 1988

Cohen's d is useful because it expresses effect size in a standardised, unit-free way, allowing effects from different studies, outcomes, or scales to be compared and combined, as in meta-analysis, and providing a sense of magnitude beyond statistical significance. So Cohen's d is useful for quantifying and comparing the size of effects independently of the measurement units and the sample size, which is valuable for interpreting the importance of findings, for synthesising evidence across studies, and for planning studies, since it separates the magnitude of an effect from whether it is statistically significant, complementing p-values with information about how large an effect is.

Source: Cohen 1988

The limitations of Cohen's d include that its benchmarks for small, medium, and large are arbitrary conventions that may not suit every field, so a given value's importance depends on context; that it assumes a meaningful common standard deviation, which may not hold if group variances differ; and that it can be biased in small samples. So Cohen's d is interpreted with attention to context and to its assumptions, since the conventional labels do not capture practical significance in every setting and the measure depends on the variability being comparable, which is why it is used as a guide to effect magnitude rather than an absolute judgement of importance.

Source: Cohen 1988