From: gregory@eos.arc.nasa.gov (Kevin Gregory)
Subject: BMDP and ANOVA Help Needed
Keywords: analysis of variance
Organization: NASA Ames Research Center
Distribution: usa
Date: Wed, 30 Sep 1992 00:06:41 GMT

I need some help in comparing results received from BMDP and the Gary Perlman
ANOVA program. I have run a simple one-way analysis of variance with both the
7D program in BMDP and ANOVA. I have one within factor with 4 levels. I have
always recognized that these program make their computations in different
manners, but it is only recently that we have paused to consider the
implications of these differences.

The results from ANOVA look as so:

SOURCE: grand mean
trip       N       MEAN         SD         SE
         124    14.4713     2.3808     0.2138

SOURCE: trip
trip       N       MEAN         SD         SE
1         31    14.6048     2.0009     0.3594
2         31    13.4282     1.5817     0.2841
3         31    14.9677     2.9719     0.5338
4         31    14.8844     2.5154     0.4518

FACTOR:         id       trip   tot_rate
LEVELS:         31          4        124
TYPE  :     RANDOM     WITHIN       DATA

SOURCE                SS     df             MS         F      p
===============================================================
mean          25967.9232      1     25967.9232  2767.426  0.000 ***
i/              281.5026     30         9.3834

trip             47.2105      3        15.7368     3.844  0.012 *
ti/             368.4486     90         4.0939


whereas, the result table from BMDP-7D (using the same data file), looks as
so:

MEAN      14.479              13.326                14.968                14.592

STD.DEV.   2.535               2.895                 2.972                 2.950

S. E. M.   0.301               0.173                 0.534                 0.350

MAXIMUM   20.000              20.000                20.000                20.000

MINIMUM    8.000               5.000                 6.000                 7.000

CASES INCL.   71                 279                    31                  71

----------------------------------------------------------------------------
        ALL GROUPS COMBINED
| ANALYSIS OF VARIANCE TABLE FOR MEANS                 TAIL     |
|SOURCE     SUM OF SQUARES  DF  MEAN SQUARE F VALUE PROBABILITY |VALUES FOR
|--------   -------------- ---- ----------- ------- ----------- |
|duty          181.9639     3      60.6546   7.44    0.0001    |
|ERROR        3653.1600   448       8.1544                     |
|--------------------------------------------------------------------------|
| EQUALITY OF MEANS TESTS; VARIANCES ARE NOT ASSUMED TO BE EQUAL           |
|   WELCH                          3, 101                7.36    0.0002    |
|   BROWN-FORSYTHE                 3, 168                7.52    0.0001    |
|--------------------------------------------------------------------------|
 | LEVENE'S TEST FOR VARIANCES      3, 448                1.04    0.3736    |
 ----------------------------------------------------------------------------


Would anyone care to comment on the differences I am encountering and of what
significance they are? Help with this example or general info on these programs
would be most appreciated.

thanks,

kevin