# QL Trend test for count data

 Z.QL.Poisson<-function(conc,yy) {
 # formula (6.17)
 # conc = vector of concentrations
 # yy = vector of observed counts

      nreps <- unlist(lapply(split(yy,conc),length))
      means <- unlist(lapply(split(yy,conc),mean))
       vars <- unlist(lapply(split(yy,conc),var))
       xbar <- sum(conc)/length(conc)
      uconc <- unique(conc)
    top <- sum( nreps*(uconc-xbar)*means )
    bot <- sum( nreps*(uconc-xbar)^2*(nreps-1)*vars)
    cat("xbar = ",signif(xbar),"\n")
    cat("Z.QL= ",signif(top/sqrt(bot)),"\n")
    top/sqrt(bot)
 }

 Z.QL<-Z.QL.Poisson(nitro.df$conc,nitro.df$offspring)

# output follows ...

 xbar =  157 
 Z.QL=  -5.51591 

 pnorm(Z.QL)
 [1] 1.734933e-08