 
Summary: A Multivariate Randomization Test of Association
Applied to Cognitive Test Results
Albert Ahumada and Bettina Beard
NASA Ames Research Center
Abstract
Randomization tests provide a conceptually simple, distributionfree way to implement significance
testing. We have applied this method to the problem of evaluating the significance of the association
among a number (k) of variables. The randomization method was the random reordering of k1 of the
variables. The criterion variable was the value of the largest eigenvalue of the correlation matrix.
Introduction
The experimental data for which the randomization test was devised were collected to measure possible
changes in cognitive abilities and in ratings of cognitive test difficulty following a simulated space
ascent in a vibrationaugmented centrifuge (Adelstein, et al., 2009). The simulated space ascent study
was done to evaluate the effects of Gload and vibration on display legibility (Beard, et al., 2009). The
cognitive study was "piggybacked" onto the legibility study. Each of 11 participants was given a 5 test
battery before and after the "ride" were also asked to rate the difficulty/unpleasantness of each test on 5
dimensions. The problem was then to assess the statistical significance of the correlations among the
ratings and the tests.
Multiple Correlation Correction
One approach would be to look at the largest absolute correlation and correct for the number of
