Trying to understand statistical methods through the lens of replication

EvZ:

you define the z-statistic of the replication study as

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

I am not going to enter into a debate about formulae, but I would like to correct a misunderstanding in your comment about page 24 in Appendix 1 of my paper. The expression 𝑧_repl =𝑏_repl/√(𝑣1+𝑣2) was not described nor intended to be a classical z-statistic (I took on board your point about this potential source of confusion from our previous discussion). To be clear, 𝑧_repl =𝑏_repl/√(𝑣1+𝑣2) is a predictive standardisation reflecting uncertainty in both original and replicating studies conditional on the result of the original study. However, in Appendix 2 lower down on page 24 and onwards, a z-statistic and P value are used in their conventional sense to describe probabilities under a specified null hypothesis. This is distinct from the predictive framework used in the main text, where standardisation is based on the distribution of possible replication outcomes.