| pottwhitt {DCluster} | R Documentation |
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