曾看到一个思路：
sigmastat 软件的帮助里介绍说
1) 关于RM ANOVA
the treatment effects are not normally distributed，Use a Repeated Measures ANOVA (analysis of variance) on Ranks when you want to see
当处理效应不是正态分布时，用基于秩次的重复测量方差分析可以比较
if a single group of individuals was affected by a series of three or more different experimental treatments, where each individual received treatment
单个样本组的个体是否受3个或3个以上不同条件处理的影响。
2) About the Repeated Measures ANOVA on Ranks
The Friedman Repeated Measures Analysis of Variance on Ranks compares effects of a series of different experimental treatments on a single group. Each subject's responses are ranked from smallest to largest without regard to other subjects, then the rank sums for the treatments are compared.
The Friedman Repeated Measures ANOVA on Ranks is a nonparametric test that does not require assuming all the differences in treatments are from a normally distributed source with equal variance.
这段提到这种分析方法属于非参数检验，跟Friedman秩和法是有联系的。详细翻译略。
所以要做这种分析，首先要将原始变量转换为秩，再对秩作重复测量方差分析。