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Education And Debate Statistics Notes

# Interaction revisited: the difference between two estimates

BMJ 2003; 326 (Published 25 January 2003) Cite this as: BMJ 2003;326:219
1. Douglas G Altman (doug.altman@cancer.org.uk), professor of statistics in medicinea,
2. J Martin Bland, professor of medical statisticsb
1. a Cancer Research UK Medical Statistics Group, Centre for Statistics in Medicine, Institute for Health Sciences, Oxford OX3 7LF
2. b Department of Public Health Sciences, St George's Hospital Medical School, London SW17 0RE
1. Correspondence to: D G Altman

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.13 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 …

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