Bias and precision of eight multivariate measures of association for a fixed-effects analysis of variance model

A number of multivariate effect-size measures for MANOVA contexts have been proposed in the statistics literature. These measures however overestimate the strength of relationship between independent variable and dependent variable. A procedure by Tatsuoka (1973) and a procedure by Serlin (1982) have been suggested to adjust for the bias. The purposes of proposed study are to investigate the sampling distribution of selected eight measures of strength of association and to evaluate the two adjustment procedures using a computer simulation method. The results, when there are no true effects, indicate that eight effect- size measures are highly biased with small sample size and large number of variables. When two groups are compared, Serlin adjustment provides a better adjustment than Tatsuoka adjustment. When three or more groups are compared, Serlin adjustment for SGI, SEI, and CNI can provide an appropriate adjustment.