text: user12360: Considering that the p-value of a chi statistic(df=1) is uniform, the expected genomic inflation factor is λ=1. I show its calculation in R with the next chunk of code:
  chi = qchisq(df$pval,df=1,lower.tail=FALSE)
  factor = median(chi)/qchisq(p=0.5,df=1)
  
  My question comes here. Imagine that I compute λ on several (e.g. >30 independent GWAS) studies. My null hypothesis is that all of them lack true-polygenic signals (i.e. uniform p-value distribution). What test can I do to reject H0? What is the distribution that I can assume for the inflation factors?
  
  user12360: The distribution as I suspected seems very much like a normal distribution. However if someone knows to explain the reason (limit central theorem?) I will give select their answer.
      # Do simulation    
      factor_calc = function(pvals){
        chi = qchisq(pvals,df=1,lower.tail=FALSE)
        return(median(chi)/qchisq(p=0.5,df=1))}
      pvals_studies = sapply(1:10000, function(i){runif(10000)})
      factor_distribution = apply(pvals_studies, 2, function(pvals){factor_calc(pvals)})
  
      # Plot resulting distribution
      hist(factor_distribution)
  
  
  
original_text: 12360: <p>Considering that the p-value of a chi statistic(df=1) is uniform, the expected genomic inflation factor is λ=1. I show its calculation in R with the next chunk of code:</p>
  <pre><code>chi = qchisq(df$pval,df=1,lower.tail=FALSE)
  factor = median(chi)/qchisq(p=0.5,df=1)
  </code></pre>
  <p>My question comes here. Imagine that I compute λ on several (e.g. &gt;30 independent GWAS) studies. My null hypothesis is that all of them lack true-polygenic signals (i.e. uniform p-value distribution). What test can I do to reject H0? What is the distribution that I can assume for the inflation factors?</p>
   12360: <p>The distribution as I suspected seems very much like a normal distribution. However if someone knows to explain the reason (limit central theorem?) I will give select their answer.</p>
  <pre><code>    # Do simulation    
      factor_calc = function(pvals){
        chi = qchisq(pvals,df=1,lower.tail=FALSE)
        return(median(chi)/qchisq(p=0.5,df=1))}
      pvals_studies = sapply(1:10000, function(i){runif(10000)})
      factor_distribution = apply(pvals_studies, 2, function(pvals){factor_calc(pvals)})
  
      # Plot resulting distribution
      hist(factor_distribution)
  </code></pre>
  <p><a href="https://i.stack.imgur.com/5PmPD.png" rel="nofollow noreferrer"><img src="https://i.stack.imgur.com/5PmPD.png" alt="enter image description here" /></a></p>
  