-- VIVIAND Xavier <[email protected]> wrote,
> Before applying a repeated ANCOVA on my own data, I tried to run the example
> proposed by Tabachnick and Fidell (Computer-assisted research design and
> analysis, 2001) on page 417 (Table 8.13). The data set is a mixed ANCOVA
> with a single covariate (Easy) measured once for each case. The
> randomized-groups IV i type of music (labeled Music, 2 levels) and the
> repeated-measures IV is time of day (4 levels, labeled T1 through T4).
> The data are below :
>
> <data>
>
> I entered the following command :
> anova y easy music/id|music time time*music time*easy, rep(time) cont(easy)
> I got the same same results than reported by Tabachnick and Fidell (using
> SYSTAT GLM) except for the covariate :
> SS df MS F P
> Stata .125 1 .125 0.18 0.6921
> Tabachnick 11.327 1 11.327 15.96 0.01
> and Fidell
> How can this difference be explained ?
I don't have access to SYSTAT, so am not sure how it handles the sum of
squares for continuous covariates. In Stata, Tabachnick and Fidell's results
can be reproduced by using -sequential- option and changing the order of
covariates:
. anova y music easy id|music time time*music time*easy, cont(easy) seq
Number of obs = 32 R-squared = 0.9486
Root MSE = .870978 Adj R-squared = 0.8938
Source | Seq. SS df MS F Prob > F
-----------+----------------------------------------------------
Model | 210.120968 16 13.1325605 17.31 0.0000
|
music | 10.125 1 10.125 13.35 0.0024
easy | 11.3266129 1 11.3266129 14.93 0.0015
id|music | 3.5483871 5 .709677419 0.94 0.4859
time | 1.25 3 .416666667 0.55 0.6563
time*music | 179.625 3 59.875 78.93 0.0000
time*easy | 4.24596774 3 1.41532258 1.87 0.1788
|
Residual | 11.3790323 15 .758602151
-----------+----------------------------------------------------
Total | 221.50 31 7.14516129
The F-statisitic is computed as the ratio of mean sum of squares:
. di 11.3266129/.709677419
15.960227
> Secondly, I tried to test the homogeneity of regression slopes, i.e. the
> interaction between the covariate Easy and the factor Music by
> anova y easy easy*music music/id|music time time*music time*easy, rep(time)
> cont(easy)
> I got :
> SS df MS F P
> easy | .125 1 .125 0.18 0.6921
> easy*music | 0.00 0
> music | .491276672 1 .491276672 0.69 0.4433
> id|music | 3.5483871 5 .709677419
> Why the df of easy*music is 0 ?
The 0 degree of freedom for the interaction easy*music is due to collinearity
among the covariates. Let's consider a simpler model:
. anova y id easy*music,
Number of obs = 32 R-squared = 0.1129
Root MSE = 2.86138 Adj R-squared = -0.1459
Source | Partial SS df MS F Prob > F
-----------+----------------------------------------------------
Model | 25.00 7 3.57142857 0.44 0.8696
|
id | 25.00 7 3.57142857 0.44 0.8696
easy*music | 0.00 0
|
Residual | 196.50 24 8.1875
-----------+----------------------------------------------------
Total | 221.50 31 7.14516129
We can further tabulate the two factors:
. gen em = easy*music
. table id em, col
-----------------------------------------------------------
| em
id | 3 4 6 10 12 14 Total
----------+------------------------------------------------
1 | 4 4
2 | 4 4
3 | 4 4
4 | 4 4
5 | 4 4
6 | 4 4
7 | 4 4
8 | 4 4
-----------------------------------------------------------
There are only 8 non-empty cells in the table, corresponding to the 8
categories of "id". So in the ANOVA model, all the degrees of freedom are
taken by "id" first and nothing is left for the interaction "easy*music".
Hope this can clarify your questions.
Weihua Guan <[email protected]>
Stata Corp.
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