Performing multiple comparison tests in a multivariate analysis using PROC GLM


You can use the CONTRAST and MANOVA statements in PROC GLM to produce univariate and multivariate tests of a contrast. Note that the univariate tests are not adjusted for the multiple-testing problem.

In the following example, univariate and multivariate tests are requested to compare groups in a model with four response variables. Multivariate tests are requested by the MANOVA statement.

    data test;
       input group y1 y2 y3 y4;
       datalines;
        1      1.49028    1.74482      6.6918     6.9418
        1      1.59312    0.46965     -0.3768     9.5659
        1      2.20582    2.61775      3.7670     3.1233
        1      0.20009    1.76070      6.1829    14.2999
        1      1.19367    2.75009      3.1195     6.7870
        1      0.93351    1.91407      3.5872    10.2909
        1      2.67154    1.74562      5.8346     8.7408
        1      0.97910    2.14110      3.1196     4.1408
        1      1.80299    1.98272      3.6646     6.6423
        1      1.17798    1.64433      6.5740     2.0980
        2      1.82876    4.47122      8.2432     9.9703
        2      1.88284    4.18212      3.5319    10.5563
        2      3.93070    6.46548      9.1625     7.0587
        2      2.85041    4.83959      2.8077     9.1256
        2      5.04796    5.03031      4.4951     5.8871
        2      0.61298    4.57152      6.3513     4.7764
        2      1.82900    2.20315      5.5412     8.3127
        2      0.96052    6.19894      2.9801     9.9560
        2      1.66684    3.50519      5.1759    14.5258
        2      1.47132    5.54549      3.6985     6.9873
        3      4.75103    5.22271      8.8442    14.0241
        3      3.11277    7.12780      4.5145    19.0085
        3      3.76051    4.71655     10.8912    11.6810
        3      2.03498    4.48660     15.1921    11.7244
        3      2.56441    7.38403      7.0141    15.5431
        3      4.23825    4.69444      8.8626    14.8105
        3      3.96363    4.97571      9.1333    18.8830
        3      2.91472    5.27935     10.9329    16.7116
        3      3.92796    6.78625      5.0111    11.4309
        3      3.72776    7.33981     10.0552    14.1118
       ;
     proc glm data=test;
        class group;
        model y1-y4 = group;
        contrast 'group 1 vs 2' group 1 -1;
        contrast 'group 1 vs 3' group 1 0 -1;
        manova;
        run;
        quit;

Separate univariate analyses for the responses appear first in the results. This includes the univariate tests comparing groups in each dependent variable. Following the univariate analyses, the multivariate tests for the comparisons are given. The partial output below shows the results for response y1. The univariate tests comparing the groups are followed by the multivariate tests.

The multivariate tests provide comparisons across all four responses. They show that both pairs of groups differ significantly (p<.0001). The univariate test for y1 finds a significant difference between groups 1 and 3 (p<.0001) but at best marginal significance between groups 1 and 2 (p=0.0930).