I was wondering what (if any) the benefit is of reporting effect sizes (e.g., eta-squared) after running a regression model in which the dependent variable is z-transformed.
In such a model, the beta estimates of your predictor variables indicate change in z-score per unit of the predictor. This is pretty intuitive in terms of understanding the magnitude of the effect.
Effect sizes are also helpful in determining the magnitude of the effect of a certain variable. For example in terms of explained variance in the model.
I am unsure if it is informative to report standardized effect sizes in addition to reporting z-scores (with standard error).