Most medical researches are concerned with rare events such asdeaths or accidents, which are Poisson distributed. When these data, fromtheir Poisson distributions, are analyzed the likelihood ratio using achi-square approximation is usually applied to compare the means of morethan two populations where the sample size is large and- tends towardsinfinity. However, in the case of small and medium sample sizes thereappears to be no appropriate test. The objective of this study was to investigate the use of ANOVA(Analysis of Variance) for the comparison of the means of more than twoPoisson populations. The following equation for the transformation tonormality with homogeneous variances is proposed: (Formular)Where X(,ij) is a random variable in the j('th) trial from the i('th)Poisson population with a mean, ((+,l)(,i)), Y(,ij) the transformed variablein the j('th) trial from the i('th) group and (+,g) is an unknownconstant to be estimated. The half-reduction method was then applied toobtain the estimated value of (+,g) for a particular set of observed data. As the transformed data follows the two required assumptions forANOVA, that the data in normally distributed and there is equal variance inthe different data sets, this method can be applied to test for equalityamong the means of more than two Poisson populations. The powers of theANOVA F- test, the approximate likelihood ratio test and the Kruskal-Wallistest were then compared. It was found that for small sample sizes of 5 to10, the Kruskal-Wallis test had the highest power

ANOVA and theapproximate likelihood ratio tests have a higher power than theKruskal-Wallis test for samples sizes of 15 to 20. For samples sizes of 30to 50, the approximate likelihood ratio test has the highest power,followed by the ANOVA and the Kruskal-Wallis tests in that order. The samepattern of the powers resulting from the tests were obtained for the casesof three, five and ten Poisson populations with equal or unequal samplesizes in each group, (+,g)(,i) from 0.1 to 20, and alternative hypotheseswhere one parameter is different from the others or where all are different.