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--- 曼-惠特尼u检验 [2023/04/14 10:59] – yunyuqu
+++ 曼-惠特尼u检验 [2024/04/24 05:08] (当前版本) – zwz
@@ 行 1: / 行 1: @@
 ====曼-惠特尼U检验（Mann-Whitney U Test）====
-.使用场景
+**1. 使用场景（Usage Scenarios）**
   * 用于两个独立样本的检验；
   * 顺序性数据
+  * For tests of two independent samples；
+  * For sequential data.
 ----
-.步骤
+**2. 步骤（Steps）**
   * 对每种处理条件各得到一个独立的样本，以nA表示样本A中的被试数目，以nB表示样本B中的被试数目；
   * 将两个样本合并，将所有被试（nA +nB）排序；
@@ 行 11: / 行 14: @@
   * 如图：从下到上，对每个字母，分别计算下面有多少个另外的字母（如：等级6的B下面有多少个A），计算结果作为点数U
   * {{:mann-witney.png?400 |}}
+  * An independent sample was obtained for each treatment condition, with nA denoting the number of subjects in Sample A and nB denoting the number of subjects in Sample B.
+  * Combine the two samples and rank all subjects (nA + nB).
+  * Determine whether scores from two samples are systematically clustered at opposite ends of the metric in mixed ordering.
+  * As shown: from bottom to top, for each letter, count how many other letters are below it (e.g., how many A's are below B on a scale of 6), and use the result as the number of points U.
 ----
-.公式
+**3. 公式（Formulas）**
   * UA+UB = nA*nB
   * UA= nA*nB+[nA（nA+1）/2]-∑RA
   * UB= nA*nB+[nB（nB+1）/2]-∑RB
-  * 选择UA、UB中较小点数作为U
 ----
-.假设检验
+**4. 假设检验（Hypothesis Testing）**
-  * H0：两处理之间无系统差异
-  * H1：两处理之间有系统差异
+**第一步：给出虚无假设和备择假设**
+  * **H0**：两处理之间无系统差异
+  * **H1**：两处理之间有系统差异
+**第二步：得到分界点Ucrit**
   * 根据nA,nB,查表得到Ucrit
-  * Mann-Whitney U的结果分析：
+**第三步：计算U**
-  - 若U=0，其中一个样本不得分，两个样本无重叠，有最大的差异
+  * 选择UA、UB中较小点数作为U
-  - U越大，两个样本越接近
+**第四步：Mann-Whitney U的结果分析**
-  - ∴当Uobs ≤ Ucrit时,才能拒绝H0 （与参数检验正好相反）
+  * 若U=0，其中一个样本不得分，两个样本无重叠，有最大的差异
+  * U越大，两个样本越接近
+  * ∴当Uobs ≤ Ucrit时,才能拒绝H0 （与参数检验正好相反）
+**Step 1: Give null hypotheses and alternative hypotheses**
+  * **H0**：Without systematic differences between the two treatments.
+  * **H1**：With systematic differences between the two treatments.
+**Step2：obtain Ucrit of boundary point**
+  * According to nA,nB, look up the table to get Ucrit.
+**Step 3: Calculate U**
+  * Select the smaller of UA and UB as U.
+**Step 4: Analysis of results for Mann-Whitney U**
+  * If U = 0, one of the samples is not scored . There is no overlap between the two samples and the difference is the largest.
+  * The larger U is, the closer the two samples are.
+  * ∴Only when Uobs ≤ Ucrit can H0 be rejected (the opposite of a parametric test).
+----
+**5. 大样本情况下的正态近似（Normal approximation in the case of large samples）**
+  * 当n>20, Mann-Whitney U统计量接近正态分布
+  *  When n>20, Mann-Whitney U statistic is close to normal distribution.
+  * μ= nAnB/2
+  * σ= sqrt（nAnB （nA+nB+1）/12）
+  * {{:u正态近似.png?200 |}}
+----
+**6. 统计前提（Statistical Prerequisites）**
+  * 要求观察独立
+  * 要求变量是连续的，即较少相同的等级
+  * 不要求正态分布
+  * 不要求方差同质
+  * Requiring independent observation.
+  * Requiring variables to be continuous, i.e., less equal in rank.
+  * Not requiring normal distribution.
+  * Not requiring variance to be homogeneous.