# Detecting overdispersion in Poisson data

 X2.overdisp.Poisson<-function(yy)  {
 # yy = vector of observed counts

   css <- var(yy)*(length(yy)-1)
   ybar<- mean(yy)
   X2 <- css/ybar
   Pvalue <- 1-pchisq(X2,length(yy)-1)
   list(X2=X2,Pvalue=Pvalue)
 }

 offsprg.0  <-c(27,32,34,33,36,34,33,30,24,31)
 offsprg.80 <-c(33,33,35,33,36,26,27,31,32,29)
 offsprg.160<-c(29,29,23,27,30,31,30,26,29,29)
 offsprg.235<-c(23,21, 7,12,27,16,13,15,21,17)
 offsprg.310<-c( 6, 6, 7, 0,15, 5, 6, 4, 6, 5)

 nitro.conc<-rep(c(0,80,160,235,310),c(10,10,10,10,10))

 offsprg<-c(offsprg.0,offsprg.80,offsprg.160,
            offsprg.235,offsprg.310)

 nitro.df<-data.frame(conc=nitro.conc,offspring=offsprg)

 nitro.ngrp<-length(unique(nitro.df$conc))

 nitro.lst<-split(nitro.df$offspring,nitro.df$conc)

 for (iii in 1:nitro.ngrp) {
   cat("Concentration = ",signif(unique(nitro.df$conc)[iii]),"\n")
   junk<-unlist(X2.overdisp.Poisson(nitro.lst[[iii]]))
   cat("\t","X2 = ",signif(junk[1]),
     "; P-value = ",signif(junk[2]),"\n")
 }

# output follows ...

 Concentration =  0
  X2 =  3.70701 ; P-value =  0.929617 
 Concentration =  80
  X2 =  3.06349 ; P-value =  0.961724 
 Concentration =  160 
  X2 =  1.77032 ; P-value =  0.994601 
 Concentration =  235 
  X2 =  18.2326 ; P-value =  0.0325693 
 Concentration =  310 
  X2 =  20.6667 ; P-value =  0.0142156