Is it possible to get low R2 and high f2?

[tinker18]

Hello everyone,
I am conducting a research in social science field. My model has higher order component Type 2 (reflective-formative). I have two questions. Hope to get some clarifications from this site.

1) Is it possible to get weak R2 values (0.05) but medium effect size (f2) (0.31)?
2) Is there any maximum value for effect size (f2)? Can it be higher than 1?

Thank you.

[jmbecker]

1) It is unlikely to get large effect sizes if you have low R² but possible. The f² effect size is the relative contribution (change in R² due to inclusion of the predictor, i.e., R² included - R² excluded), divided by the unexplained variance (1-R² included). Because of the devision the R² contribution gets slightly larger depending on the amount of explained variance (the larger the explained variance the larger the inflation).
However, the f² is naturally limited by the R² included in that the contribution cannot be larger than this. If you have R² included of 0.05 the f² should not be larger than (0.05-0)/(1-0.05)=0.053, because the maximum difference in R² is 0.05 (i.e., nothing is explained if the predictor is excluded).

2) Yes, it can be larger than 1, if your R² is very large und hence the unexplained variance (1-R² included) is very small.
For example, R² included=0.8, R² excluded=0.5 --> f²=1.5

[tinker18]

Hi Dr Becker,

I agree that the effect size f2 can be more than 1. Just that it is tricky to find journal articles that showed f2 > 1 for me to cite.

Thank you very much for the clarification. Have a great day!