# Re: st: Hotelling's T Squared

 From khigbee@stata.com To statalist@hsphsun2.harvard.edu Subject Re: st: Hotelling's T Squared Date Tue, 25 Nov 2003 08:17:45 -0600

```Judith Abrams <abramsj@karmanos.org> asks:

> 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 b
> ecause 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.

Notice that the T-squared value is the same and the difference in
the F test and p-value are due to the number of degrees of
freedom.

It is as if -hotelling- drops one of the collinear variables, but
forgets to adjust the degrees of freedom downward accordingly.

I will look into fixing -hotelling- so that it displays a message
saying that a particular variable (or variables) are dropped due
to collinearity and then have it adjust the d.f.s.

This fix will probably be available in time for an ado-file
udpate we are planning for next week.

Ken Higbee    khigbee@stata.com
StataCorp     1-800-STATAPC

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