My first thought is to use a random permutation test.
In this setting the main question you need to ask is
what distance measure do you want to use between
variance matrices -- there are lots of choices. One
that I've found useful is the absolute value of the
maximum eigenvalue of the difference of the matrices.
If you have a hypothesis about how the variances may
differ, then you should be able to come up with a more
powerful statistic.
Patrick Burns
patrick at burns-stat.com
+44 (0)20 8525 0696
http://www.burns-stat.com
(home of S Poetry and "A Guide for the Unwilling S User")
Aldi Kraja wrote:
>Hi,
>Using package gclus in R, I have created some graphs that show the
>trends within subgroups of data and correlations among 9 variables (v1-v9).
>Being interested for more details on these data I have produced also the
>var-covar matrices.
>Question: From a pair of two subsets of data (with 9 variables each, I
>have two var-covar matrices for each subgroup, that differ for a
>treatment on one group (treatment A) vs (non-Treatment A).
>
>Is there a software that can compare if two var-covar matrices are
>statistically the same?
>
>Below are a pair of two matrices, from several others.
>Thank you in advance for any input.
>Aldi
>
> First group var-covar matrix (the data were under treatment a)
>
>v1 v2 v3 v4 v5
>v6 v7 v8 v9
>
>
>
>v1 730.87 3.406 -283.41 -74.68
>107.57 -1355.13 -112.46 14.000 5.776
>
>v2 3.41 24.950 105.45 -121.31
>-307.68 -285.40 29.65 -2.500 -7.796
>
>v3 -283.41 105.451 6292.19 -2676.46
>-970.80 29296.23 10715.29 3.156 -66.313
>
>v4 -74.68 -121.307 -2676.46 124492.30
>-2289.47 -20377.34 -409.71 183.500 563.102
>
>v5 107.57 -307.681 -970.80 -2289.47
>7045.62 12118.09 954.51 38.258 96.355
>
>v6 -1355.13 -285.404 29296.23 -20377.34
>12118.09 218555.93 70126.71 137.000 -130.667
>
>v7 -112.46 29.645 10715.29 -409.71
>954.51 70126.71 28239.57 67.989 -26.370
>
>v8 14.00 -2.500 3.16 183.50
>38.26 137.00 67.99 24.500 9.000
>
>v9 5.78 -7.796 -66.31 563.10
>96.35 -130.67 -26.37 9.000 22.776
>
>
>
>
>
> Second group var-covar matrix (the data were NOT under treatment a)
>
>v1 v2 v3 v4 v5
>v6 v7 v8 v9
>
>
>
>v1 2696.25 27.05 201.06 2745.54
>-344.39 540.48 654.20 34.363 7.623
>
>v2 27.05 86.37 -96.89 -497.28
>-1185.10 -3108.71 -910.38 -4.254 -9.115
>
>v3 201.06 -96.89 10647.26 8378.07
> 595.81 66122.43 26237.21 -65.093 -51.998
>
>v4 2745.54 -497.28 8378.07 408391.25
>-3887.28 40477.40 30652.01 450.539 50.311
>
>v5 -344.39 -1185.10 595.81 -3887.28
>29204.00 65320.00 15238.41 -98.237 102.975
>
>v6 540.48 -3108.71 66122.43 40477.40
>65320.00 549955.14 194691.90 -555.552 -95.210
>
>v7 654.20 -910.38 26237.21 30652.01
>15238.41 194691.90 82698.88 -70.417 -75.585
>
>v8 34.36 -4.25 -65.09 450.54
>-98.24 -555.55 -70.42 79.689 8.164
>
>v9 7.62 -9.11 -52.00 50.31
>102.97 -95.21 -75.58 8.164 30.492
>
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