Standardised mean difference

A standardised mean difference expresses the gap between two group means in units of standard deviation instead of the original measurement units. It exists for one practical reason: meta-analyses often pool trials that measured the same construct with different instruments, and raw means from different scales cannot be averaged. The calculation divides the difference in means by a pooled standard deviation. Cohen's d uses the pooled standard deviation directly. Hedges' g adds a small sample correction that matters below roughly 20 participants per arm. A value of 0.45 means the groups differ by 0.45 standard deviations, whatever the instrument was. Cohen offered 0.2, 0.5 and 0.8 as small, medium and large. He described these as arbitrary conventions for fields with nothing better available, and they are routinely quoted as if they were empirical thresholds. For a cheap and safe intervention, 0.15 can be worth having. For an invasive one, 0.8 may not be. The main failure mode is that the denominator drives the result. A narrowly selected sample has a small standard deviation, which inflates the standardised effect without any larger underlying change. When every pooled trial used the same instrument, such as grip strength in kilograms, report the raw mean difference instead.

Last reviewed: August 25, 2026

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