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?