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I'm using SPSS and this drop-down menu: Analyze -> General Linear Model -> Univariate.

DV:                 Number of times patient visited doctor over one year 
Factor 1: 2 levels: Two different drugs
Factor 2: 2 levels: Gender
Factor 3: 4 levels: Race
Factor 4: 3 levels: drug taken morning, afternoon, evening
Covariate:          Age (continuous) 

There are 500 subjects. Only 10 missing values, all in the factor with 4 levels.

The main effect I'm really interested in is for Factor 1. In a 1-way ANOVA it was highly significant. When I added the next 3 factors and the covariate in a full-factorial model it became not significant (none of the factors were, though when I had just 3 factors + the covariate 2 of the factors were significant).

  • Have I included too many factors (+ the covariate) to expect a significant main effect for any of the factors? Somehow "overloaded" the model?
  • When I tried a "custom" model, removing all the interactions from the model, 2 of the factors were now significant, which is what I expected. Is that legitimate?
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  • $\begingroup$ Your total 500 doesn't matter nearly as much as the size of each cell. Nevertheless, it's probably not causing the problem you have (see my answer) but it is more important than the total N to report. $\endgroup$ – John May 15 '13 at 11:18
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You have correlations among your covariate and predictor variable(s). Probably you have one between factor 1 and the covariate. This is a no no (see the assumptions). Given that it's probably important to be assessing age you need to look at regression techniques instead of ANCOVA and what to do when multi-collinearity is involved.

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  • $\begingroup$ The OP is interested in the effect of Factor 1 when adjusting for the covariate. What would this adjustment accomplish if the correlation between the covariate and Factor 1 were zero? $\endgroup$ – rolando2 May 15 '13 at 0:24
  • $\begingroup$ It might remove variability from the response variable and increase power. This is accomplished when the relationship between the covariate and the response variable is not 0. If they're interested also in the relationship between the covariate and factor 1 then they have to examine that. The effect of the covariate will then matter. At that point the technique you want is no longer ANCOVA but multiple regression. However, the question states only an interest in factor 1. $\endgroup$ – John May 15 '13 at 0:47
  • $\begingroup$ And BTW, what does "adjusting for" mean anyway? Age may be associated with the response variable. It's definitely associated with the drug. How can you tell from simple ANCOVA what exactly age is adjusting? The question becomes much more complex once the predictors are correlated. $\endgroup$ – John May 15 '13 at 1:42
  • $\begingroup$ Adjusting (partialling out, holding constant, removing the influence of, accounting for) would mean estimating the group difference in the DV by Factor 1 if each group had the same mean age. (There are causality issues to be addressed here, but statistically it's straightforward.) Whether one calls this ANCOVA or regression or a GLM is a matter of semantics and perhaps of the type of output one chooses to examine. Also, it's not clear to me from the OP that age and Factor 1 are correlated, though it seems a good guess. Cheers ~ $\endgroup$ – rolando2 May 15 '13 at 10:55
  • $\begingroup$ The primary linear model run is a matter of semantics, yes. The analysis technique and assumptions are not. In an ANCOVA the covariate is only assessed for assumptions and little else. In this case it's imperative that multiple models, or minimally the predictor correlations, be assessed in order to ascertain the effects of all of the predictors. And you're right, it's not clear it's the covariate that's correlated with factor 1. It could be one or more of the other factors as well. I misread the question as also assessing a simple model with just factor 1 and the covariate. $\endgroup$ – John May 15 '13 at 11:15

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