Simple Robust Tests for Scale Differences in Paired Data
针对配对数据中两个尺度参数的差异检验，提出了Pitman检验的稳健替代方法，通过单样本t检验框架构造渐近分布自由的检验，并利用蒙特卡洛模拟评估小样本表现和功效，最后应用于癌变与非癌变肺部的比较。
The classical statistical test for assessing the difference between the two scale parameters in paired data due to Pitman (1939) and Morgan (1939) is not robust. This paper explores robust alternatives to Pitman's test, using the framework of the one-sample t-test. The asymptotic behaviour of the tests under the null hypothesis is examined. In general, it is easy to construct tests that are asymptotically distribution-free, provided the data come from a symmetric bivariate distribution. Versions of these tests that do not require symmetry are derived. Monte Carlo simulation experiments are done to assess small sample behaviour and power characteristics. The tests are applied to a small data set comparing cancerous and noncancerous lungs.