Some thoughts on uniform prior probabilities when estimating P values and confidence intervals

[R_cubed]

@HuwLlewelyn

Please understand that although I have a 'b' for z1, I don’t have a b_{repl} for z2 (only the SE for the distribution of z2).

Given that, how do you distinguish between 2 cases:

1. Estimate b2 comes from the same normal distribution as b1 and
2. Estimate b2 comes from a different normal distribution as b1?

Remember, the normal distribution is entirely described by 2 parameters \beta, \sigma^2