We often want to compare two estimates of the same quantity derived from separate analyses. Thus we might want to compare the treatment effect in subgroups in a randomised trial, such as two age groups. The term for such a comparison is a test of interaction. In earlier Statistics Notes we discussed interaction in terms of heterogeneity of treatment effect.1^–3 Here we revisit interaction and consider the concept more generally.

The comparison of two estimated quantities, such as means or proportions, each with its standard error, is a general method that can be applied widely. The two estimates should be independent, not obtained from the same individuals—examples are the results from subgroups in a randomised trial or from two independent studies. The samples should be large. If the estimates are E₁ and E₂ with standard errors SE(E₁) and SE(E₂), then the difference d=E₁-E₂ has standard error SE(d)=√[SE(E …