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December 2022


Journal/Book: Psychological Bulletin 1969 Vol. 72 No. S 336-337. 1969;

Abstract: 1 Requests for reprints should be addressed to Frederic M. Lord Division of Psychological Studies Educational Testing Service Princeton New Jersey 08540. Educational Testing Service Princeton New Jersey An illustration is given showing why the analysis of covariance usually does not provide the appropriate adjustment to compensate for preexisting differences between nonexperimental groups. Suppose two groups are to be compared an some criterion measurement y. However the investigator wishes to make an "adjustment" to cancel out the effect of preexisting differences between the two groups an some other variable x. For example a group of underprivileged students is to be compared with a control group an freshman grade-point average (y). The underprivileged group has a considerably lower mean grade-point average than the control group. However the underprivileged group started college with a considerably lower mean aptitude score (x) than did the control group. Is the observed difference between the groups an y attributable to initial differences an x? Or shall we conclude that the two groups achieve differently even after allowing for initial differences in measured aptitude? It is usual to attempt to answer such questions by analysis of covariance. An earlier note (Lord 1967) pointed out by an illustrative example how such an analysis can lead to absurd conclusions. (Some readers were inclined to shrug off the paradox by saying that they would never think of using covariance analysis in the illustrative situation-that a simple analysis of the gains y - x would be the obvious procedure to use. This escape is illusory however. The simplest rebuttal is that the difference y - x is a quantity of no interest except when y and x both measure the same dimension. The illustrative example is thus easily modified to make an analysis of gains meaningless-by substituting initial girth for initial weight for example.) ... ___MH

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