Here is my problem. Abridged and annotated output from my function applied
to some of my own test data is below:
$"Group Sizes":
1 2 3
75 66 59 <===== IDENTICAL in SAS, SPSS, NCSS
$"Num Cases":
[1] 200 <====== IDENTICAL in SAS, SPSS, NCSS
$"Num Groups":
[1] 3 <======= IDENTICAL in SAS, SPSS, NCSS
$"Box's M":
[1] 22.7283 <===== ???? answer from SPSS and NCSS 25.681 (not reported
in SAS)
$"Chi Square Probability":
[1] 0.3372944 <===== ???? answer from SAS 0.2043 & NCSS, not reported in
SPSS
$"Log Determinants":
[1] 27.67216 27.59350 27.35155 <======IDENTICAL to SPSS, SAS, NCSS
$"Pooled Within Groups Determinant":
[1] 27.66719 <======== IDENTICAL to SPSS, SAS, NCSS
$"Chi Square Statistic":
[1] 22.05943 <====== ?????? 24.924802 in SAS and NCSS, not reported in SPSS
$DF1:
[1] 20 <=======IDENTICAL in SAS, SPSS, NCSS
$DF2:
[1] 129299.2 <=======IDENTICAL in SAS, SPSS, and NCSS
$"F Statistic":
[1] 1.102796 <=====????? 1.246 in SPSS and NCSS, not reported in SAS
$"F Probability":
[1] 0.3375029 <=====????? 0.204 in SPSS and NCSS, not reported in SAS
I've manually calculated the M statistic using the determinantal
information provided by all of the programs. My hand calculations give me
the same answers as I report above (for the SPlus function), suggesting
that SAS, SPSS, and NCSS are all wrong, something I find impossible to
believe.
The wrong answers are all interrelated. The figure that is incorrect is
the Box's M value itself. All other incorrect values depend on it.
For those unfamiliar with Box's M, it is calculated as:
Let ni=n-1 for the i th population
S = pooled within groups covariance matrix
Si = covariance matrix for ith group
M = (Sum(ni) * ln|S|) - Sum(ni * ln|Si|)
So, for the example above
M = (197 * 27.66719) - [(74*27.67216) + (65*27.59350) + (58*27.35155)]
M = 22.7292
Sorry to be such a nuisance, but I'm completely stumped here.
Dr. Marc R. Feldesman
Professor and Chairman
Anthropology Department
Portland State University
P.O. Box 751
Portland, Oregon 97207
email: feldesmanm@pdx.edu
phone: 503-725-3081
fax: 503-725-3905
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