Robustness and power of thet-Test compared with some nonparametric alternatives when sampling from a poisson distribution#x2020;

摘要

Pseudo random numbers were drawn from a variety of Poisson distributions to see how several popular two-sample tests might be affected by the presence of ties in the data. Nearly all tests were conservative under the null hypothesis, with actual #x3B1; levels averaging about 1.5 less than the nominal #x3B1; levels. Under various alternative hypotheses, the Mann-Whitney test, the van der Waerden test, and a nonparametric test designed for power when sampling from a Poisson distribution, exhibited more power than did the Student'st-test; the median test showed less power. The power of the nonparametric tests was less when ties were broken by randomization than when either midranks or average scores were used. Using thetstatistic in the nonparametric tests, rather than in the usual large sample normal approximation, resulted in greater power when testing at the 0.05 alpha level, but less power at #x3B1; = 0.10