# st: RE: ANOVA Multiple Comparison Questions

 From "FEIVESON, ALAN H. (AL) (JSC-SK) (NASA)" To "'statalist@hsphsun2.harvard.edu'" Subject st: RE: ANOVA Multiple Comparison Questions Date Fri, 5 Mar 2004 12:41:24 -0600

```There is a method of doing multiple comparisons aftter a KW test. I don't
have the original source, but there is a website from P. Cabillo and J.
Masaro that describes the procedure. See

p. 27

Al Feiveson

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu]On Behalf Of
gte573q@mail.gatech.edu
Sent: Friday, March 05, 2004 12:20 PM
To: statalist@hsphsun2.harvard.edu
Subject: st: ANOVA Multiple Comparison Questions

Hi! I have a question about ANOVA.
I'd like to see the differences of per capita income(index) for four
different areas. I chose oneway ANOVA and multiple comparison command.
But the problem is the violation of equal variances (please refer to
Bartlett's
test for equal variances below).
My questions are:
1) Can I say that my analysis is valid under the violation of equal
variances?
2) If the violation of equal variances is a problem, is there any way to
get over it?
3) As an alternative, I tried to nonparametic test using Kruskal-Wallis
test.
But "Kwallis" command does not produce multiple comparison for each
group.
Is there any nonparametric ANOVA techniques with multiple comparison?
4) I think this data is unbalanced in terms of # of observation. Is this
problem?

Thanks.
sugie

--------------------------------------------------------------
.oneway pci_index group [aweight=population], tabulate scheffe

|                Summary of pcir0
group |        Mean   Std. Dev.       Freq.        Obs.
------------+------------------------------------------------
A   |   1.2176654   .73457797      127574          47
B   |   .76321118   .43276015     2778506         845
C   |   1.0260904   .48150203     2989897         767
D   |   1.0885976   .37953544     6232038        1160
------------+------------------------------------------------
Total |   1.0000001   .44391706    12128015        2819

Analysis of Variance
Source              SS         df      MS            F     Prob > F
------------------------------------------------------------------------
Between groups      49.4593539      3   16.4864513     91.74     0.0000
Within groups      505.862359   2815   .179702437
------------------------------------------------------------------------
Total           555.321713   2818   .197062354

Bartlett's test for equal variances:  chi2(3) =  41.7568  Prob>chi2 = 0.000

Comparison of pcir0 by class
(Scheffe)
Row Mean-|
Col Mean |      A           B         C
---------+---------------------------------
B  |   -.454454
|      0.000
|
C  |   -.191575    .262879
|      0.029      0.000
|
D  |   -.129068    .325386    .062507
|      0.242      0.000      0.018

.kwallis pci_index, by(group)

Test: Equality of populations (Kruskal-Wallis test)

+--------------------------+
| group |  Obs |  Rank Sum |
|-------+------+-----------|
|   A   |   47 |  64350.00 |
|   B   |  845 | 801156.00 |
|   C   |  767 |  1.14e+06 |
|   D   | 1160 |  1.97e+06 |
+--------------------------+

chi-squared =   423.506 with 3 d.f.
probability =     0.0001

chi-squared with ties =   423.506 with 3 d.f.
probability =     0.0001
.

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```