Weighted comparison of means

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Abstract
In a recent Statistics Note1 we referred to a weighted two sample t test. Here we describe how it is done. The data were the percentage of requests from general practitioners for x ray examinations which were judged appropriate (table 1), where general practitioners had been randomised to intervention or control groups.2 View this table: Table 1 Number of requests conforming to guidelines for each practice in the intervention and control groups If we compare the two sets of percentages by the usual two sample t method, each observation (practice) has an equal impact on the result. As some practices contributed fewer requests than others, we wish these practices to have a lesser effect on the estimate of the difference. We can do this by weighting the practices by the …

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