This statistic can be used to test for homogeinity among all the relative risks. The test statistic is:
$$E_+ \sum_{i=1}^n \frac{O_i(O_i-1)}{E_i}$$
If we supposse that the data are generated from a multinomial model, this is the locally U.M.P. when considering the next hypotheses:
| \(H_0\) | : | \(\theta_1 = \ldots = \theta_n=\lambda\) |
Notice that in this case, \(\lambda\) is supposed to be unknown. The alternative hypotheses means that relative risks come all from a Gamma distribution with mean \(\lambda\) and variance \(\sigma^2\).
pottwhitt.stat is the function to calculates the value of the statistic for the data.
pottwhitt.boot is used when performing a non-parametric bootstrap.
pottwhitt.pboot is used when performing a parametric bootstrap.
Potthoff, R. F. and Whittinghill, M.(1966). Testing for Homogeneity: I. The Binomial and Multinomial Distributions. Biometrika 53, 167-182.
Potthoff, R. F. and Whittinghill, M.(1966). Testing for Homogeneity: The Poisson Distribution. Biometrika 53, 183-190.
DCluster, pottwhitt.stat, pottwhitt.boot, pottwhitt.pboot