Analysis of one-way layout of count data with negative binomial variation

Two C(α) statistics (Neyman, 1959) for testing the equality of the means of several groups of count data in the presence of a common dispersion parameter are derived. The performance of the two C(α) statistics, the likelihood ratio statistic and two more statistics based on transformed data (Anscombe, 1948) is then compared in terms of size and power by using Monte Carlo simulations. The C(α) statistics are recommended. The C(α) statistics for testing the equality of the dispersion parameters of several groups of count data are also derived. Two applications are given.