Let's say I have a quantitative variable Y that ranges between 0 and 1. I have a categorical variable X that has 3 levels, A, B, C. Since Y ranges between 0 and 1, I transform all of Y using the logit transformation so that logit(Y) = ln(Y / (1 - Y))
I build the model logit(Y) = A + B + C, with no intercept, and thus the coefficients basically tell me mean logit(Y) given A.
However, I don't want mean logit(Y) given A, I want mean Y given A. Should I do my ANOVA without transforming my Y. Note that my final model will have both categorical and continuous predictors. That is, lets say Z is a continuous variable. Should I do:
- logit(Y) = A + B + C + Z
- Y = A + B + C + Z