「処置前—処置後」データの解析と平均への回帰

Abstract

In various research fields, a pretest-posttest experiment is an important and frequently employed method to evaluate treatment effects. In a pretest-posttest experiment, the measurements are made both at baseline and at follow-up in order to eliminate individual variability. There exist several methods that have been proposed to estimate the treatment effect and/or to test that there is no effects at all.In pretest-posttest designs, screening is often made upon the baseline measurements: that is only the individuals who meet some pre-specified requirement are allowed to enter the experiment. In such cases, we have to take into account the effect of the regression to the mean in the analysis to obtain proper conclusions.In this review article, various topics are discussed which are related to pretest-posttest designs and to the regression to the mean as well. We give mathematical results concerning moments of truncated normal distributions, which are useful to understand the underlying theory of the pretest-posttest data. Extensive references are also given.