Approximate Confidence Intervals for Estimates of Redundancy Between Sets of Variables

Use of redundancy analysis would be enhanced by having available a procedure that (a) evaluates the statistical significance of the estimated proportion of variance in the criterion variable set extracted by a given predictor variate, Ry i (2), as well as by all predictor variates combined, R(y 2), and (b) is lenient with respect to assumptions about the distributions of redundancy estimates. A previous testing method leaves in doubt the assessment of redundancy attributed individually to each predictor variate, and it requires parametric assumptions about the distributions of the estimators. This paper describes and demonstrates the bootstrap methodology which yields approximations of the sampling variation of redundancy estimates while assuming little a priori knowledge about the distributions of these statistics. The procedure is applicable for evaluating the estimated proportions of criterion set variance explained solely by a given predictor variate and cumulatively by all predictor variates.