How we calculate the p-values?

Hello, dears! I’m fitting the loess regression (M = f(E)) . After, I go through it, I want to calculate the p-values from the variable M. My thinking was, if M follows an normal distribution, I will convert the M value to the Z and calculate the p-values from Z-scores using the standard normal distribution. But as we see in the histogram and QQ plot, it fails to satisfy the assumption. Even I have tried the assumption over the different intervals of variable E. But the results are the same. Therefore, could you please recommend something for this issue?

Thanks for your help!

I don’t calculate p-values for Bayesian analysis. Do you mean p-values as in a frequentist inference? What questions are you trying to answer with the data and model?

Yes! I want to calculate the p-values in frequentist approach.

I am not sure this forum is the best place for that. Are you using rstanarm, rstan, pystan, brms, or some Stan based model? If not would be a better place.


In the book Bayesian Data Analysis (Gelman et al), there is an alternative notion of frequentist p value, which is called the posterior predictive p value. Using the generated quantities block in Stan file, we can code it.