PERFORMANCE OF A PRELIMINARY TEST OF COMPARABILITY IN OBSERVATIONAL STUDIES.
HARVARD UNIV CAMBRIDGE MASS DEPT OF STATISTICS
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The note studies the performance of a preliminary test of significance sometimes used in observational studies. The means y1, y2 of a response variable are being compared in two independent samples of size n. It is feared that the comparison may be biased because a confounding variable x may have different levels means in the two populations. A t-test of x1-x2 is made. If t is not significant, y1-y2 is used as an estimate of the population difference delta y if t is significant, y1-y2 is adjusted by an analysis of covariance. This procedure is found to reduce the remaining bias in the estimate of delta y to a value that does not seriously disturb tests of significance or confidence probabilities based on this estimate. If the estimation of small values of delta y is important, however, the remaining bias may still be a sizeable percentage of delta y, except with large samples. Author
- Statistics and Probability