Find r given inferential stat and descriptives for a within-subject design

findr.R

library(faux)
library(afex)

f <- function(r, reported) {
  # simulate data for 3-level within design (change for your design)
  dat <- faux::sim_design(
    # you can add these parameters to f() arguments 
    # if you need to check varying analyses
    n = 100, within = 3,
    mu = c(100, 105, 110),
    sd = c(10, 11, 12),
    r = r, # assume all r are the same
    empirical = TRUE, # paramaters describe sample, not population
    long = TRUE, # table format for analysis
    plot = FALSE
  )
  
  # analyse data (change for your design/analysis)
  a <- afex::aov_ez(
    # generic column names from faux; 
    # change if you customise the simulation code
    id = "id",
    dv = "y",
    within = "W1",
    data = dat)
  
  # get the relevant statistic
  stat <- a$anova_table$F
  
  # compare it to the reported stat
  abs(reported - stat)
}

# search over a plausible range for the reported stat
op <- optimise(f, 
               interval = c(-.99, .99), 
               reported = 30.6)

r <- op$minimum