Hello Tuhinur,

The implied question in your query is, can a study be overpowered (by huge N) so as to flag as significant models which don't account for a meaningful amount of the observed differences (e.g., trivial effects)? The answer, of course, is "Yes."

It's always a judgment call, however, as to whether an effect is trivial.

Now, let me try to address your query. First, I would not rely on pseudo-R-square values as the measure of model adequacy for a logistic regression model. The reason is three-fold: (a) the value does not truly represent variance accounted for (as in OLS regression), so trying to adapt guidelines you may have seen for OLS models may not make sense; (b) context matters: the variables involved, the target population, the perspective of the decision-maker, and the intended use(s) of the model; and (c) many times people choose to focus on the exponentiated regression coefficients for IVs (the "OR" or odds ratio estimates) and/or the classification accuracy of the model and/or AIC/BIC indicators. For me, I'd stick with OR and classification accuracy, or information, and try to interpret those in context of my research aims.

Here's a link you may find handy that compares a number of the common pseudo R-square values: https://stats.oarc.ucla.edu/other/mult-pkg/faq/general/faq-what-are-pseudo-r-squareds/

Good luck with your work.

Hello Professor David Morse !

Thank you very much for your answer. I really appreciate your time and I found the attached reference very helpful.

I don't understand your question. Acceptance of a value of 0 (or below for adjusted R^2 values) is fine. If you are saying you should you only say a study is valid is the R^2 is above a certain value this leads to the file drawer problem. If it is as David Morse suggests that you just don't understand what p-values are, I recommend re-writing your question.

For More Information Following below link

https://statisticalhorizons.com/r2logistic/