Correspondence Between Confidence Intervals and Hypothesis Tests

Although for quantitative data and means there is a direct correspondence between the confidence interval approach and a t test ofthe null hypothesis at the associated level of statistical significance, this is not exactly so for qualitative data and proportions. The reason is related to the use of different estimates of the standard error for the usual tests of the null hypothesis from those given here for constructing confidence intervals. The lack of direct correspondence is small and should not result in changes of interpretation. In addition, more accurate confidence intervals can sometimes be obtained by using estimates of the standard error of the sample statistic at the confidence limits themselves-such as derived by Cornfield for relative risks.

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