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Chapter 13

Nonparametric Statistics

非参数统计简介
非参数统计简介
Most inferential statistical methods are parametric, requiring normally distributed populations with specific parameters such as the mean, standard ...
行列
行列
Ranking is a nonparametric assessment method that organizes data according to specific criteria, for instance, from best to worst or heaviest to ...
Sign 测试简介
Sign 测试简介
The sign test is a nonparametric method for evaluating claims about simple random data from matched pairs, nominal data, or assertions regarding the ...
匹配对的符号测试
匹配对的符号测试
Consider the data on hamsters' speed before and after administering a stimulant, which constitutes a matched pair. How does one test the claim that ...
名义数据的符号检验
名义数据的符号检验
Nominal data, consisting of non-orderable names, labels, and categories, only allows for population proportions analysis. Given that the data is nominal, ...
单一总体中位数的符号检验
单一总体中位数的符号检验
In a class of 100 students, 60 scored a grade of less than 45 on a test, 15 scored 45, and 25 scored more than 45. This simple random data, drawn from a ...
匹配对的 Wilcoxon Signed-Ranks 检验
匹配对的 Wilcoxon Signed-Ranks 检验
Consider the dataset of fasting blood sugar levels of patients for two consecutive months. How does one test the claim that there is no difference between ...
单个总体中位数的 Wilcoxon 符号秩检验
单个总体中位数的 Wilcoxon 符号秩检验
Consider an example of a novel rice variety genetically modified to produce longer rice grains. To know if the grain length of the novel variety is ...
Wilcoxon 秩和检验
Wilcoxon 秩和检验
Wilcoxon rank-sum, or the Mann-Whitney U, is a nonparametric test used to determine the difference between two populations by comparing their medians. It ...
引导
引导
Bootstrapping is a resampling method that uses samples randomly drawn from the already collected sample with replacement. Imagine a paleontologist trying ...
安德森-达林测试
安德森-达林测试
In many cases, the distribution of the population from where the random samples are drawn is often unknown or difficult to determine. In these cases, the ...
Spearman 的等级相关性测试
Spearman 的等级相关性测试
Spearman's rank correlation is a nonparametric test used to find the association between two variables in paired data. Consider an example of finding ...
Kendall 的 Tau 测试
Kendall 的 Tau 测试
Consider an example where 35 pieces of vintage porcelain teacups are ranked independently by an artisan and an ordinary buyer. Kendall's tau test can ...
Kruskal-Wallis 试验
Kruskal-Wallis 试验
The Kruskal-Wallis, or H test, is a non-parametric alternative to one-way ANOVA. It effectively tests the null hypothesis that three or more populations ...
Wald-Wolfowitz 运行检验 I
Wald-Wolfowitz 运行检验 I
The Wald-Wolfowitz runs test examines the randomness in ordered or sequential data. It uses computed runs from the data, where the randomness is rejected ...
Wald-Wolfowitz 运行检验 II
Wald-Wolfowitz 运行检验 II
A scientist collected data on the body lengths of 30 baboons approaching a water source. So, the Wald-Wolfowitz test can determine if the sequence in ...
Behrens-Fisher 测试
Behrens-Fisher 测试
The Behrens-Fisher test assesses mean differences between two groups with disparate variances. It is especially effective for small samples, where ...
费舍尔精确检验
费舍尔精确检验
Fisher's exact test determines the significance of a nonrandom relationship between two categorical variables in a two-by-two contingency table. ...
按秩划分的 Friedman 双因子方差分析
按秩划分的 Friedman 双因子方差分析
Friedman's two-way Analysis of Variance by ranks evaluates differences among related groups. It is ideal for data that is ordinal or not normally ...
Cochran Q 检验
Cochran Q 检验
Cochran's Q test is used when the same individuals in the data are tested repeatedly for the presence or absence of an attribute. For example, 24 ...
McNemar 检验
McNemar 检验
McNemar's test applies to paired nominal data presented in two-by-two contingency tables. This is a special case of randomized block design, where ...
Kendall 的一致性系数
Kendall 的一致性系数
Kendall's coefficient of concordance is a nonparametric statistic test that measures the agreement among ranks of the variables. It assesses the ...
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