How big is the difference, in units that travel?
A 9-mark gap means one thing on a test scored in hundreds and another on a quiz marked out of 20. Effect sizes standardise the gap by the data's own spread, so results can be compared across studies, measures and fields. This calculator produces the two-group family: Cohen's d (pooled SD), Hedges' g (the same, with the small-sample bias corrected) and Glass's Δ (standardised by the second group's SD, for when group 2 is a control whose spread is the natural yardstick).
The two quiz classes (means 84.625 and 75.75; SDs 4.8385 and 2.8158; n = 8 each): pooled SD = 3.9585, so d = 2.24 and g = 2.12. By the conventional labels (0.2 small, 0.5 medium, 0.8 large) this is far past "large". Concretely, a random student from class 1 outscores a random student from class 2 about 94% of the time.
Labels are training wheels
Cohen offered 0.2/0.5/0.8 as rough landmarks for behavioural research, and said so. A d of 0.1 on a mortality outcome matters more than a d of 1.0 on a preference survey. Report the number, translate it into the units your reader lives in (the probability-of-superiority line on the results card does this), and let importance be argued on substance.
Computing d with one group's SD while calling it Cohen's d: that is Glass's Δ, a different statistic with a defensible purpose (a control group's natural spread) but a different name. The calculator keeps them labelled and separate.
Frequently asked questions
d or g: which should I report?
Hedges' g whenever samples are small (the correction bites below n ≈ 20 per group) or when a meta-analysis may consume your number. For large samples they agree to two decimals.
Can an effect size be negative?
Yes. The sign follows the subtraction order (group 1 minus group 2). Report the sign and say which group leads.