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等级资料，即有序分类数据，是在统计学中常见的一种数据类型。
这种数据的特点是各类别之间存在一定的顺序关系，但不具备等距性。
针对等级资料的统计学方法主要有以下几种：
一、秩和检验：秩和检验是一种非参数统计方法，其应用范围广，对于不满足正态分布的数据也可适用。
主要包括Wilcoxon秩和检验和Kruskal-Wallis H检验。
前者适用于两独立样本的比较，后者则适用于多个独立样本的比较。
二、Ridit分析：Ridit分析是一种用于处理等级资料的统计方法，其基本思想是将原始数据转换为Ridit值，这样就可以将等级资料转换为计量资料进行处理。
这种方法既保留了等级资料的顺序信息，又充分利用了数据的全部信息，因此具有较高的效率。
三、有序多分类Logistic回归：有序多分类Logistic回归适用于因变量为有序多分类的情况。
它通过分析自变量对因变量各类别发生概率的影响，来揭示自变量对因变量的作用。
四、累积比数Logit模型：累积比数Logit模型是一种处理等级资料的回归分析方法。
它假设因变量的各类别之间存在一种“累积”的关系，并通过构建Logit模型来估计这种关系。
这种方法可以有效地处理等级资料，并且能够处理存在缺失值的情况。
以上就是针对等级资料的几种主要统计学方法。
在实际应用中，应根据数据的具体特点和研究目的选择合适的方法进行统计分析。
多组等级资料比较的秩和检验及组间两两比较的SAS实现郭志武【摘要】目的探讨多组等级资料的秩和检验及组间两两比较的SAS实现.方法结合实例介绍多组等级资料Kruskal-Wallis H检验和两两比较Nemenyi检验的计算方法和步骤,通过编制SAS程序一次性完成Kruskal-Wallis H检验和Nemenyi 检验.结果运行SAS程序得到可靠结果.结论编制SAS程序可以有效实现多组等级资料的秩和检验及组间两两比较.【期刊名称】《中国医院统计》【年(卷),期】2018(025)003【总页数】2页(P233-234)【关键词】等级资料;秩和检验;两两比较;SAS【作者】郭志武【作者单位】518033 深圳市中医院【正文语种】中文多组独立样本等级资料是临床常见的资料类型。
针对多组独立样本等级资料比较的假设检验通常采用Kruskal-Wallis H检验，若检验结果具有统计学意义，则可以进一步采用Nemenyi检验进行组间两两比较[1]。
Kruskal-Wallis H检验利用通用的统计软件可以完成，但Nemenyi检验却不能直接从统计软件包的集成功能或模块中完成，需要另外编写自定义程序。
刘伟等采用SPSS菜单操作结合编程实现了Nemenyi检验[2]，本文通过编制SAS程序一次性完成Kruskal-Wallis H检验和Nemenyi检验。
1 方法与步骤参考文献[1]已详细介绍了Kruskal-Wallis H检验和Nemenyi检验的原理、方法和步骤。
本文只针对多组独立样本的等级资料结合实例介绍计算方法和步骤。
文献[1]第131页实例如下：4种疾病患者痰液内嗜酸性粒细胞的检查结果见表1。
问4种疾病患者痰液内嗜酸性粒细胞有无差别？表1 4种疾病患者痰液内嗜酸性粒细胞比较嗜酸性粒细胞(1)支气管扩张(2)肺水肿(3)肺癌(4)病毒性呼吸道感染(5)合计(6)秩范围(7)平均秩(8)-0353111～116+25751912～3021 ++95332031～5040.5+++62201051～6055.5Ri739.5 436.5 409.5 244.5 ni17 15 17 11 60Ri 43.5029.1024.0922.23(1)首先进行Kruskal-Wallis H检验检验统计量H按以下公式计算：(1)式中,ni为各样本例数，N为样本总例数(N=∑ni)，Ri为各样本秩和。
等级资料的秩和检验步骤The rank sum test, also known as the Mann-Whitney U test, is a non-parametric statistical test used to compare the means of two independent groups. It is commonly used when the data does not meet the assumptions of a parametric test, such as the t-test. The rank sum test is particularly useful when the data is ordinal or when the sample size is small. In this test, the data is ranked, and the sum of the ranks in each group is compared to determine if there is a significant difference between the groups.The first step in conducting a rank sum test is tostate the null and alternative hypotheses. The null hypothesis typically states that there is no difference between the two groups, while the alternative hypothesis states that there is a difference. For example, if we were comparing the test scores of two different teaching methods, the null hypothesis would be that there is no difference in the mean test scores between the two methods, while the alternative hypothesis would be that there is a difference.The next step is to rank the data. This involves combining the data from both groups and ranking it from lowest to highest. Ties are handled by assigning the average rank to the tied values. Once the data is ranked, the sum of the ranks for each group is calculated. The group with the lower sum of ranks is designated as Group 1, and the group with the higher sum of ranks is designated as Group 2.After the data has been ranked and the sum of ranks for each group has been calculated, the next step is to calculate the test statistic. The test statistic for the rank sum test is the smaller of the two sums of ranks, U. The value of U is compared to a critical value from a table of critical values for the Mann-Whitney U test to determine if the difference between the two groups is statistically significant. If the calculated value of U is less than the critical value, the null hypothesis is rejected, and it is concluded that there is a significant difference between the two groups.It is important to note that the rank sum test does not provide a measure of effect size. Therefore, if a significant difference is found, additional analyses may be needed to determine the magnitude of the difference between the groups. Additionally, the rank sum test assumes that the data is independent and that the groups are randomly sampled from the population. Violation of these assumptions can lead to inaccurate results.In conclusion, the rank sum test is a valuable tool for comparing the means of two independent groups when the data does not meet the assumptions of parametric tests. By ranking the data and comparing the sum of ranks for each group, the rank sum test provides a non-parametric alternative to traditional t-tests. However, it is important to carefully consider the assumptions of the test and to interpret the results in the context of the specific research question.。
