The Higgs Boson and the relationship between P values and the probability of replication

[R_cubed]

I posted a thread that relates p-values, s–values (Shannon Information), and the Bayes Factor Bound in this thread:

Relating S-values to other measures of statistical information

After reading this paper again: I wanted to share some R code I wrote to improve my intuition on how information measures relate to other common statistical quantities (ie Z-scores). # Converting among various measures of information and evidence # Shannons, p values, Z_scores, Bayes Factor Bounds. bayes_factor <- function(p) { e <- 2.71828 if (p >= 1/e) { bayes_factor <- 1.00 } else { bayes_factor <- 1/(-e*p*log(p)) } } shannon_table <- function(lower, upper) { bits …

I know of 2 recent papers on study design and replication conditional on a “significant” p-value:

van Zwet, EW, Goodman, SN (2022). How large should the next study be? Predictive power and sample size requirements for replication studies. Statistics in Medicine. 41( 16): 3090– 3101. link

van Zwet, E, Schwab, S, Senn, S (2021). The statistical properties of RCTs and a proposal for shrinkage. Statistics in Medicine. 2021; 40( 27): 6107– 6117. link