Vol. 38 No. 1, 1999
Permutation Tests for Difference between Two Multivariate Allometric Patterns
TzongDer Tzeng and SheanYa Yeh*
^{}
Institute of Oceanography, National Taiwan University, Taipei, Taiwan 106
TzongDer Tzeng and SheanYa Yeh (1999) Studies
that include comparisons of multivariate allometric patterns between
sexes, species, discrete growth stages, or geographic populations have
gradually increased. Some statistical methods assume that compared
groups share the same multivariate allometric pattern, so comparisons
of multivariate allometric patterns also have to be performed before
using these methods. Several methods have been used to detect the
difference between 2 multivariate allometric patterns, but these
methods lack an objective guide to test whether the 2 multivariate
allometric patterns are the same or not. In this study, a permutation
test was used to determine whether the difference of 2 patterns was
significant or not. Four examples were used to explain and verify this
test. The multivariate allometric pattern was estimated by the 1st
eigenvector of the sample covariance matrix of the logarithmic
measurement. The angle between the 2 first eigenvectors was taken as
the test statistic. For each example, 5000 permutations were performed
to assess the significance level. Finally, the effect of sample size
difference on the permutation test was also examined. We found that all
1st eigenvalues explained the largest part of total variance and all
1st eigenvectors can satisfactorily interpret the multivariate
allometric patterns. These tests can successfully detect the
relationship between 2 multivariate allometric patterns in each
example, so they can be a tool to test whether the difference of 2
multivariate allometric patterns is significant or not. Although this
method is not sensitive to sarnple size differences, we still suggest
that the sample size difference be as small as possible when using
permutation tests to address this question.
Key words: First eigenvector, Angle, Allometry, Reorder.
*Correspondence: Tel: 886223637753. Fax: 886223925294.
