Trying to understand statistical methods through the lens of replication

It’s disappointing to see that you are still making the same mistake which we pointed out to you several months ago. In Appendix 1 on p23 (3rd line from below) you define the z-statistic of the replication study as

z_\text{repl} = b_\text{repl} / \sqrt{v_1+v_2}

where \sqrt{v_1} is the standard error from the first study and \sqrt{v_2} is the standard error from the replication study. This is a mistake because z_\text{repl} doesn’t have the standard normal distribution under the null hypothesis of no treatment effect. In other words, it’s not a proper z-statistic. The z-statistic of the replication study should simply be defined as the estimate divided by its standard error

z_\text{repl} = b_\text{repl} / \sqrt{v_2}.

If you do that, and assume the uniform prior for the true effect, then you should get the same result as Goodman (1992).

I will not get into another endless debate about this, so I won’t comment any further.