I have used two-way ANOVA (repeated measures) in my study to investigate the intervention effect on the quality of interaction with three measurements of time. The within-subjects variable is the quality of interaction, between-subjects factors are intervention/control group and professionals education with three subgroups, and the covariate is professionals age. According to results, I have a statistically significant interaction between the quality of interaction, study group and professionals education. To find out more I would need a post hoc test for education variable with three subgroups. The problem is that SPSS prevents me to use this function, if there is an age covariate included in the model. So, should I remove the age covariate from the model for post hoc testing, or what would be the most reliable way to do this?
Intuitively, one would think an ANOVA on the residuals (followed by Post Hoc tests) could be used. Yet, as pointed out on (on the misuse of residuals):
Article On the misuse of residuals in ecology: testing regression re...
This is not the correct method.
The most primitive solution to remove the size effect is to compute a ratio by dividing the response variable (Y) by the concomitant variable (X) or some power of it (see comprehensive review in Albrecht, Gelvin & Hartman 1993). Among the simplest forms are a ‘simple ratio’ (Y/X) (Albrecht et al. 1993) or Fulton’s condition factor (Y/X3) in the fish literature (García‐Berthou & Moreno‐Amich 1993). These ratios are then analysed with general linear models, e.g. comparing different groups with a t‐test or anova. Although this procedure has been criticized unanimously (see e.g. Atchley, Gaskins & Anderson 1976; Packard & Boardman 1988; Jackson, Harvey & Somers 1990; Albrecht et al. 1993), it is still sometimes used in ecology (Table 1).
This paper should be helpful:
Article Simultaneous Inference in General Parametric Models
It is implemented in R (package "multcomp", function glht(). Here is the vignette:
https://cran.r-project.org/web/packages/multcomp/vignettes/generalsiminf.pdf
Thank you both Jos Feys and Jochen Wilhelm for the information. I think these will help me to solve the problem with Two-way ANOVA.
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