费里德曼双向方差分析

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--- 费里德曼双向方差分析 [2024/04/19 06:23] – [2.检测统计量 Test Statistic] hant_g._cavendish
+++ 费里德曼双向方差分析 [2024/04/19 10:17] (当前版本) – [3.假设检验 Hypothesis Test] hant_g._cavendish
@@ 行 6: / 行 6: @@
 {{ ::费里德曼双向方差分析的检测统计量.png?400 |}}\\
 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
+n is the sample size of each sample, k is the number of samples, R is the rank sum of each sample.
-===== 3.假设检验=====
+===== 3.假设检验 Hypothesis Test =====
-**第一步：给出虚无假设和备择假设**
+**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
+  * **H0**：无显著差异 No significant difference
-  * **H1**：有显著差异
+  * **H1**：有显著差异 Significant difference
-**第二步：将每个样本在不同条件下得到的结果进行排序**
+**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**
-**第三步：求出每种条件下各个样本的秩次和**
+**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**
-**第四步：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**
+**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✘<sup>2</sup><sub>r</sub>的观测值大于临界值时才能拒绝虚无假设H<sub>0</sub>。
+  * The null hypothesis H0 can be rejected only if the observed value of ✘2r is greater than the critical value.
 ===== 4.大样本情况下的费里德曼双向方差分析 The case of Large Samples =====
 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✘<sup>2</sup><sub>r</sub>的取样分布近似于自由度为k-1的✘<sup>2</sup>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.

费里德曼双向方差分析.1713507791.txt.gz · 最后更改: 2024/04/19 06:23 由 hant_g._cavendish