Chi-square vs Fisher exact test

pplogOR.jl

using Distributions
using Plots

function Chisqtest(tab, beta0)
  beta = log(tab[2,2]) - log(tab[2,1]) - (log(tab[1,2])-log(tab[1,1]))
  V = sum(inv.(tab))
  return ccdf(Chisq(1.0), (beta-beta0)^2/V)
end

function Fishertest(X, phi)
    cs = sum(X, dims=1)
    rs = sum(X, dims=2)
    f(x, phi) = pdf(FisherNoncentralHypergeometric(cs[1],cs[2],rs[1], exp(phi)), x)
    prob = f.(0:cs[1], phi)
    return sum(prob[prob .<= prob[X[1,1]+1]])
end 

X = [12 6; 5 12]

pf(phi) = Fishertest(X, phi)
pc(phi) = Chisqtest(X, phi)
plot(x->pf(x), label="Fisher", -5, 5)
plot!(x->pc(x), label="Chisq")

png("pplot.png")