Control of spurious association and the reliability of the controlled variable.

The techniques of matched groups, analysis of covariance, and partial correlation represent various approaches to the prevention of a spurious association between Xi and X2 due to a confounding variable, Xa. In all these techniques the use of an unreliable measure for Xa leads to a systematic bias of undercorrection. Adequate corrections are possible for the case of known reliability of XB. Groups should be matched on true scores rather than observed scores, but no correction is possible for the factorial design in which groups are formed on the basis of unreliable correlated measures. Partial correlations should be corrected for the effects of unreliability of the controlled variable. Spuriously high partials are usually obtained when this correction is not applied.