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From |
Weihua Guan <wguan@stata.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
st: Re: Repeated ANCOVA |

Date |
Wed, 04 Dec 2002 12:33:12 -0600 |

-- VIVIAND Xavier <Xavier.Viviand@mail.ap-hm.fr> 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 <wguan@stata.com> Stata Corp. * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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