Estimators for the difference in means/medians (2 independent samples)

Estimators for the difference in means/medians of independent samples and their properties and assumptions.

Estimator Purpose
Mean difference Estimate the difference between the means.
Standardized mean difference Estimate the standardized difference between the means.

Cohen's d is the most popular estimator using the difference between the means divided by the pooled sample standard deviation. Cohen's d is a biased estimator of the population standardized mean difference (although the bias is very small and disappears for moderate to large samples) whereas Hedge's g applies an unbiasing constant to correct for the bias.

Hodges-Lehmann location shift Estimate the shift in location.

A shift in location is equivalent to a difference between means/medians when the distributions are identically shaped.