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st: Hotelling's T Squared


From   "Abrams, Judith" <abramsj@karmanos.org>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: Hotelling's T Squared
Date   Mon, 24 Nov 2003 17:46:27 -0500

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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