For the one-way layout for Poisson counts, derive a test of H0: ????1 = ⋯ = ????c by applying a Pearson chi-squared goodness-of-fit test (with df = c − 1) for a multinomial distribution that compares sample proportions in c categories against H0 values of multinomial probabilities,

(a) when n1 = ⋯ = nc,

(b) for arbitrary {ni}, with n = ∑

i ni.