Bradley J S, McKay R J
School of Biological and Environmental Sciences, Murdoch University, Western Australia.
Math Biosci. 1990 Jun;100(1):69-85. doi: 10.1016/0025-5564(90)90048-4.
Computer simulations are used to examine the significance levels and powers of several tests which have been employed to compare the means of Poisson distributions. In particular, attention is focused on the behaviour of the tests when the means are small, as is often the case in ecological studies when populations of organisms are sampled using quadrats. Two approaches to testing are considered. The first assumes a log linear model for the Poisson data and leads to tests based on the deviance. The second employs standard analysis of variance tests following data transformations, including the often used logarithmic and square root transformations. For very small means it is found that a deviance-based test has the most favourable characteristics, generally outperforming analysis of variance tests on transformed data; none of the latter appears consistently better than any other. For larger means the standard analysis of variance on untransformed data performs well.
计算机模拟用于检验几种已被用于比较泊松分布均值的检验的显著性水平和功效。特别地，当均值较小时，关注这些检验的行为，就像在生态学研究中使用样方对生物种群进行采样时经常出现的情况那样。考虑了两种检验方法。第一种方法对泊松数据假设一个对数线性模型，并导致基于偏差的检验。第二种方法在数据变换之后采用标准方差分析检验，包括常用的对数变换和平方根变换。对于非常小的均值，发现基于偏差的检验具有最有利的特性，通常优于对变换后的数据进行的方差分析检验；后者中没有一种始终比其他任何一种表现更好。对于较大的均值，对未变换数据进行的标准方差分析表现良好。
