Type M error for effect size (cohen's W) in contingency tables

type.m.contingency.R

#proof of concept for calculating a type M error (exaggeration ratio) for effect size in contingency tables
# type M error is defined as "The expectation of the absolute value of the estimate divided by the effect size, 
# if statistically significantly different from zero."  
# http://www.stat.columbia.edu/~gelman/research/published/retropower_final.pdf

type.m.error = function(samp.size, dof, real.w, alpha=0.05, power=0.8, n.sim=10000, seed=0) {
  set.seed(seed)
  chis = rchisq(n=n.sim, df=dof, ncp =samp.size*real.w^2  )
  crit.value = qchisq(p=alpha, df=dof, lower.tail=T)  
  chis = chis[chis >= crit.value]  
  all.omegas = sqrt(chis/samp.size)
  exaggeration.ratio = mean(all.omegas) / real.w
  res = c( real.w, mean(all.omegas), exaggeration.ratio, real.w-mean(all.omegas))
  names(res) = c("real effect size", "mean observed effect size", "Type M error (exaggeration ratio)", "absolute difference")
                 
  return( res)
}

#type.m.error(samp.size=n, dof=dof, real.w=es, n.sim = 1000000, seed=NULL)