I have a problem with a 3 way ANOVA with repeated measures. The design is the following: "localization" is the dependent variable, than I have the following within subjects factors "material" (4 levels), "diffusion technique" (6 levels) and "typology" (2 levels).
This is the formula I used:
aov_Material = aov(abs(Localization) ~ Diffusion_Type*Material*Typology + Error(Subject/(Diffusion_Type*Material*Typology)), data=scrd) summary(aov_Material)
And this is the output I get as result:
Warning message: In aov(abs(Localization) ~ Diffusion_Type * Material * Typology + : Error() model is singular > summary(aov_Material) Error: Subject Df Sum Sq Mean Sq F value Pr(>F) Residuals 11 2117 192.5 Error: Subject:Diffusion_Type Df Sum Sq Mean Sq F value Pr(>F) Diffusion_Type 5 20.2 4.032 0.423 0.83 Residuals 55 523.7 9.522 Error: Subject:Material Df Sum Sq Mean Sq F value Pr(>F) Material 3 1967 655.6 21.4 7.03e-08 *** Residuals 33 1011 30.6 --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 Error: Subject:Diffusion_Type:Material Df Sum Sq Mean Sq F value Pr(>F) Diffusion_Type:Material 15 170.1 11.338 1.308 0.202 Residuals 165 1430.3 8.668 Error: Within Df Sum Sq Mean Sq F value Pr(>F) Residuals 288 2888 10.03
My questions are:
- Why there is the warning (and, BTW, what does it means that the model is singular)?
- Why there is not the effect for typology listed in the results? How can I understand if there is a difference between the two levels of typology?