Development of a Distribution Free Multivariate Canonical Analysis (Published)
This study illustrates the use of Median Polish analysis (MP) as a distribution free procedure that can be used to identify multivariate canonical data structures. The MP may be especially useful in situations where the sample sizes are small, or where the distributions do not meet the assumptions of conventional Canonical Correlation analysis (CC). We begin by comparing the CC and MP analyses with a sample multivariate data set. We go on to compare Type 1 error rates for each of these analyses using Monte Carlo procedures in which we manipulated sample size and skewness of the data distributions. Results indicated that Type 1 error was significantly higher for the CC relative to the MP when the distributions were skewed and/or when the sample sizes were n=20 or 30.
Keywords: Monte-Carlo Simulation, Multivariate, canonical correlation analysis, distribution free, exploratory research, hypothesis testing, median polish analysis, non-parametric