THE EFFECTIVENESS OF ADJUSTMENT BY SUBCLASSIFICATION IN REMOVING BIAS IN OBSERVATIONAL STUDIES.
HARVARD UNIV CAMBRIDGE MASS DEPT OF STATISTICS
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In some investigations, comparison of the means of a variate y in two study groups may be biased because y is related to a variable x whose distribution differs in the two groups. A frequently used device for trying to remove this bias is adjustment by subclassification. The range of x is divided into c subclasses. Weighted means of the subclass means of y are compared, using the same weights for each study group. The effectiveness of this procedure in removing bias depends on several factors, but for monotonic relations between y and x, an analytical approach suggests that for c 2, 3, 4, 5, and 6 the percentages of bias removed are roughly 64, 79, 86, 90, and 92, respectively. The extent to which adjustment reduces the sampling error of the estimated difference between the y means is examined. Under a simple mathematical model, errors of measurement in x reduce the amount of bias removed to a fraction 11h of its value, where h is the ratio of the variance of the errors of measurement to the variance of the correct measurements.