Comments on Huberty’s Test of the Squared Multiple Correlation Coefficient

Abstract

It is argued that Huberty’s (1994) test for inferring a better-than-“chance” performance of the observed R² value is inconsistent. Because there is a hidden change of the null distribution of R², the “chance” value and the observed R² value are not comparable in Huberty’s test. A new test is proposed for resolving these difficulties. It is shown that the new test is equivalent to an adjustment of the α-level of the classical test of the squared multiple correlation coefficient.