应用统计学_非参数剖析.ppt

Non-parametric tests for paired samples Wilcoxon signed rank sum test This is used when The objective is to compare 2 populations The data are numerical but not normally distributed The samples are matched pairs We begin as in the t test for paired samples. We calculate Di = X1i - X2i. Null hypothesis The null hypothesis is that the differences are symmetric around zero. Under the null hypothesis, the distribution of negative differences is the same as the distribution of positive differences. SPSS两配对样本非参数检验 正负符号检验(sign) 将样本2的各样本值减去样本1的各样本值.如果差值为正,则记为正号;如果差值为负,则记为负号 如果正号的个数与负号的个数相当,则认为无显著变化.否则,认为有显著变化 例如:采用新训练方法前后的最好成绩比较 两配对样本Wilcoxon符号秩检验 首先，按照符号检验的方法，用正负号分别表示两组对应样本数据差值情况。 然后，将差值变量进行升序排序，并求出差值变量的秩。分别计算正号秩及统计量W+ 和负号秩及统计量W- 基本思想 Wilcoxon signed rank test cont… Procedure Consider the differences Di = X1i - X2i. Look at the differences and ignore the negative signs. Delete any zero differences from the sample. Rank the differences (ignoring the signs) 1 = lowest to n = highest. Attach signs to the ranks. Add the positive ranks to get T+ and the negative ranks to get T-. Rationale: If HO is true, T+ ? T- The test statistic: T = min{T+, T-}. For n 50, T has a normal distribution so proceed as for a t test. Example 2 The following table shows exports figures of a product to Country X before and after a bi-lateral trade agreement is signed. Estimate the difference b/w sales figures assign ranks ignoring the + or - sign Now estimate the total of positive negative ranks (T) Decision criteria Obtain critical values from Table E9, Berenson et al (2013) Appendices (p 756) On a 2-sided test with ? = 0.05 and n = 10, critical values are 8 47 Rule is that reject HO if T 8 Result Since T = 17, we cannot reject the null hypothesis Conclusion At 5% significance level, we are unable to conclude that there is any difference in exports of the product to Country X in the population distribution of before and after the trade agreement. Table E9 Berenson et al (2013)