pottwhitt: Potthoff-Whittinghill's Statistic for Overdispersion

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

Description

This statistic can be used to test for homogeinity among all the relative risks. The test statistic is:

E_+ * sum_i [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 = ... = theta_n)=lambda
H_1	:	theta_i ~ 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 May 2, 2019, 6:10 p.m.