pottwhitt: Potthoff-Whittinghill's Statistic for Overdispersion

In DCluster: Functions for the Detection of Spatial Clusters of Diseases

Potthoff-Whittinghill's Statistic for Overdispersion

Description

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
H_1	:	\theta_i \sim Ga(\lambda^2/\sigma^2, \lambda/\sigma^2)

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.

References

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.

See Also

DCluster, pottwhitt.stat, pottwhitt.boot, pottwhitt.pboot

DCluster documentation built on Sept. 3, 2023, 5:07 p.m.