费里德曼双向方差分析 Freedman's two-way ANOVA

费里德曼双向方差分析用于分析多个顺序型相关样本(Multiple sequential correlation samples)。

其中，n为各样本的样本容量，k为样本个数，R为各个样本的秩次和。
n is the sample size of each sample, k is the number of samples, R is the rank sum of each sample.

Step 1: 给出虚无假设和备择假设 Give null hypotheses and alternative hypotheses

• H0：无显著差异 No significant difference
• H1：有显著差异 Significant difference

Step 2: 将每个样本在不同条件下得到的结果进行排序 Sort the results obtained for each sample under different conditions

Step 3: 求出每种条件下各个样本的秩次和 Find the rank sum of each sample in each condition

Step 4: 代入检测统计量公式求出统计量观测值，根据题目比较观测值与临界值 Substitute the formula for the test statistic to find the observed value of the statistic, and compare the observed value with the critical value according to the topic

• 只有当✘²_r的观测值大于临界值时才能拒绝虚无假设H₀。
• The null hypothesis H0 can be rejected only if the observed value of ✘2r is greater than the critical value.

与克-瓦氏单向方差分析一样，当样本数和样本容量较大时费里德曼双向方差分析的✘²_r的取样分布近似于自由度为k-1的✘²分布。

• As with the Kerr-Watt one-way ANOVA, the sampling distribution of the Freedman two-way ANOVA approximates the chi-square distribution with k-1 degrees of freedom when the number of samples and the sample size are large.