Rank Procedures for the Two-Factor Mixed Model
针对两因素混合模型中固定处理效应的检验问题，提出了一种基于部分秩变换的检验统计量，该统计量在交互作用存在且单元格频数不等时仍适用，是Friedman检验的推广。
Abstract The test problem of fixed treatment effects is considered in the two-factor mixed model with interaction and unequal cell frequencies when the classical assumptions of normality do not hold. An explicit form of a test statistic is derived using a partial rank transform (ranking all observations within each block), and the asymptotic distribution of the statistic is determined under the assumption that the number of blocks tends to infinity and the cell frequencies are bounded. The statistic reduces to Friedman's statistic if no interactions are involved in the model and all cell frequencies are equal; hence the proposed test can be regarded as a generalization of Friedman's test for repeated observations when the cell frequencies are not equal. The test is compared to a corresponding test that can be used under the assumption of normality by the criterion of asymptotic relative efficiency. In the case of two treatments, the exact conditional distribution is determined and estimators and confidence intervals for the shift effect are proposed.