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| = Inappropriate use of a constant covariate in repeated measures ANCOVA = | = Inappropriate use of a constant covariate in repeated measures ANCOVA = |
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| When a covariate which only varies between subjects (e.g. age) is in a repeated measures ANCOVA it has no effect on the ''main effect'' of any repeated measures factor e.g. time. It can, however, influence the factor by being present in a factor by covariate interaction e.g. age by time. An ANCOVA assumes there is ''no'' covariate by w subs factor interaction but some packages such as SPSS automaticallyfit such a term. If there is ''no'' covariate by time interaction then the term may be dropped from the model using, for example, the ''custom model'' option in the SPSS GLM procedure. This can also be achieved using ''SPSS MANOVA'' OR ''SPSS MIXED'' syntax although the latter requires a reformatting of the data. | When a covariate which only varies between subjects (e.g. age) is in a repeated measures ANCOVA it is termed a ''constant'' covariate. A constant covariate has no effect on the ''main effect'' of any repeated measures factor e.g. time. It can, however, influence the w subs factor by being present in a w subs factor by covariate interaction e.g. age by time. A repeated measures ANCOVA assumes there is ''no'' covariate by w subs factor interaction but some packages such as SPSS automatically fit such a term. If there is ''no'' covariate by time interaction then the interaction term may be dropped from the model using, for example, the ''custom model'' option in the SPSS GLM procedure. This can also be achieved using ''[:FAQ/manova:SPSS MANOVA]'' OR ''[:FAQ/wmixed:SPSS MIXED]'' syntax although the latter requires a reformatting of the data. |
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| [http://journals.cambridge.org/download.php?file=%2FINS%2FINS13_02%2FS1355617707070464a.pdf&code=5f2a2f071eb28ffc6ca4bcf617ba24df here).] This approach is supported by SPSS (A copy of this is reproduced [:FAQ/res22133:here.)] | [http://journals.cambridge.org/download.php?file=%2FINS%2FINS13_02%2FS1355617707070464a.pdf&code=5f2a2f071eb28ffc6ca4bcf617ba24df here).] This approach is supported by SPSS (See [:FAQ/res22133:here.)] |
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If the interaction term is not statistically significant it may be dropped from the model using procedures mentioned above. If the interaction term is not statistically significant then it would appear useful to interpret the covariate by factor interaction by, for example, splitting the covariate into two groups and analysing the within subjects factor in the two groups separately. If the interaction is not a crossed interaction and, therefore, the differences between the levels of a within subjects factor are ''statistically significant'' and in the ''same'' direction and differ ''only'' in the ''magnitude'' of these differences then one could also quote the main effect of the w subs factor (after dropping the interaction term from the model) which would represent w subs factor level differences averaged across the covariate values. |
Inappropriate use of a constant covariate in repeated measures ANCOVA
When a covariate which only varies between subjects (e.g. age) is in a repeated measures ANCOVA it is termed a constant covariate. A constant covariate has no effect on the main effect of any repeated measures factor e.g. time. It can, however, influence the w subs factor by being present in a w subs factor by covariate interaction e.g. age by time. A repeated measures ANCOVA assumes there is no covariate by w subs factor interaction but some packages such as SPSS automatically fit such a term. If there is no covariate by time interaction then the interaction term may be dropped from the model using, for example, the custom model option in the SPSS GLM procedure. This can also be achieved using [:FAQ/manova:SPSS MANOVA] OR [:FAQ/wmixed:SPSS MIXED] syntax although the latter requires a reformatting of the data.
There is some debate about what to do if there is such an interaction. Some authors advocate dropping the w subs factor by subject interaction and interpreting the main effect of the within subjects factor with no interaction present even if the interaction is statistically significant (see [http://journals.cambridge.org/download.php?file=%2FINS%2FINS13_02%2FS1355617707070464a.pdf&code=5f2a2f071eb28ffc6ca4bcf617ba24df here).] This approach is supported by SPSS (See [:FAQ/res22133:here.)] Others suggest ignoring the main within subjects effect altogether and explaining the interaction (see [http://journals.cambridge.org/download.php?file=%2FINS%2FINS13_02%2FS135561770707049Xa.pdf&code=f1fdb8258ee7f4da74f024857fd4885c here.)]
It is a good idea to centre the covariate (by subtracting the overall sample mean from each data point) before entering it into the repeated measures ANCOVA. This has the advantage over using raw covariate values of correctly leaving unaltered the within subjects factor sum of squares in the presence of the covariate. The error sum of squares for the within subjects factor (ignoring the covariate) is divided into a sums of squares for the factor by covariate interaction and a remainder term.
If the interaction term is not statistically significant it may be dropped from the model using procedures mentioned above. If the interaction term is not statistically significant then it would appear useful to interpret the covariate by factor interaction by, for example, splitting the covariate into two groups and analysing the within subjects factor in the two groups separately.
If the interaction is not a crossed interaction and, therefore, the differences between the levels of a within subjects factor are statistically significant and in the same direction and differ only in the magnitude of these differences then one could also quote the main effect of the w subs factor (after dropping the interaction term from the model) which would represent w subs factor level differences averaged across the covariate values.