I would be very grateful about an explanation:
I calculated an ANOVA without covariates. Due to the study design I added co-variates and and the ANOVA results (p and F values) for the main effects changed. Can someone explain we why the results are changing for the dependent variables. For my understanding, the main effects should remain unaffected by adding co-vaiates.
Kind regards,
Ramona
Why not? You don't have the same model when you included covariates. They should have some effects, shouldn't they?
What you do in the second model is an adjustment. You controlled for the effects of your covariates on your DV. Hence you got different significance. The main effects can retain their significances but this is not necessary.
Ramona,
"Covariates are usually used in ANOVA and DOE. In these models, a covariate is any continuous variable, which is usually not controlled during data collection. Including covariates the model allows you to include and adjust for input variables that were measured but not randomized or controlled in the experiment."
Link: https://support.minitab.com/en-us/minitab/18/help-and-how-to/modeling-statistics/anova/supporting-topics/anova-models/understanding-covariates/
Hope this helps.
If you are using software to produce an anova table for the model terms, you might look into the concepts of Type I, Type II, and Type III sums of squares.
You want to know which your software is using.
Type I sums of squares are sequential, so the first term entered into the model will be apportioned the maximum sums of squares possible. In this case, the sum of squares for terms shouldn't change for terms entered later in model.
However, with Type III, a term is awarded sum of squares only to the extent that it explains variation in the dependent variable given the other terms in the model. That is, the unique sum of squares. So if two terms are highly correlated, neither is likely to be awarded many sums of squares, because neither adds much unique to the explanatory power of the model.
Also, consider that the F-test is based on both the sum of squares for the terms and the residual degrees of freedom. So even with Type I sum of squares, as you add more terms, you "use up" degrees of freedom, and the p-value for a given term increases.
These explanations are a little off-the-cuff, so hopefully they make sense and won't cause any statisticians' heads to explode.
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