Using the following dataset I compared the 2 groups with respect to x1 and x2 using Hotelling's T squared statistic.
group animal x1 x2 x3
|--------------------------------------
1. | 0 1 52.2 35.4 12.4
2. | 0 2 32.6 42.3 25.1
3. | 0 3 48.5 37.0 14.5
4. | 0 4 32.1 46.5 21.4
5. | 0 5 38.4 46.0 15.6
|--------------------------------------
6. | 1 6 19.2 50.1 30.7
7. | 1 7 11.7 55.0 33.3
8. | 1 8 7.0 64.5 28.5
9. | 1 9 6.4 50.2 43.4
10. | 1 10 6.2 50.0 43.8
+--------------------------------------
I got the following results:
2-group Hotelling's T-squared = 40.80087
F test statistic: ((10-2-1)/(10-2)(2)) x 40.80087 = 17.850381
H0: Vectors of means are equal for the two groups
F(2,7) = 17.8504
Prob > F(2,7) = 0.0018
I didn't include all 3 x variables because x1+x2+x3=100. Since I had given the investigator a long sermon about why I couldn't include x1 and x2 and x3, I decided to run Hotelling's T square with all 3 variables just to demonstrate that it would fail because of a singular matrix. Instead of failing, I got these results:
2-group Hotelling's T-squared = 40.80087
F test statistic: ((10-3-1)/(10-2)(3)) x 40.80087 = 10.200218
H0: Vectors of means are equal for the two groups
F(3,6) = 10.2002
Prob > F(3,6) = 0.0090
Shouldn't I have received an error message?
The regression command operated as expected. When I executed regress x1 x2 x3, x1 was dropped. The results of Manova were consistent with Hotelling's T-square.
Judith Abrams, PhD
Director, Integrated Biostatistics Unit
Phone 313 966 8657
Fax 313 966 8334
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