d.f. in Hotelling's T^2

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d.f. in Hotelling's T^2

Christian Rau
Dear all,

I am writing to ask for your help in the following matter
which may be trivial, but nevertheless baffled me:
Consider the data below, consisting of n=20 three-dimensional vectors,
one per row. We want to estimate the hypothesis that the mean
vector is the zero vector, and use Hotelling's T^2 for this.

* In SPSS 13, I select Analyze, Scale, Reliability Analysis;
click Statistics; then I check Hotelling's T-square. *

This is the procedure I used. The output
in SPSS 11.0 shows 5.0749 as the value for
Hotelling's T-Squared. The degrees of freedom are
2 and 18, not 3 and 17 as I think they should be. Any suggestions
why this is so (and possibly, how to get SPSS to use what are the
"right" numbers of degrees of freedom) would be much appreciated.
Thanks and Regards
Christian


-0.3    -1.5    -0.7
1.7     15.1    -2
-0.2    -2.8    0.9
-0.8    3.2     2
-0.9    5.5     -0.3
0.6     -13.9   -2.1
-1.6    -25.2   4
3.2     -16.9   -2.4
2.7     -2.6    -1.5
1.4     4.1     1.3
-0.1    -13.1   2.7
0.5     8.8     2.3
-0.5    -22.2   -0.2
0.5     -9.8    -1.6
-2.5    -36.5   0.1
4.5     6.4     -2.9
0.5     21.6    -1.8
2.5     2.8     0.9
0.1     -5.9    1.2
1.5     -9.1    -0.6