Core - Statistics

Chapter 13

Nonparametric Statistics

13.1 : Introduction to Nonparametric Statistics

13.1 : Introduction to Nonparametric Statistics

Most inferential statistical methods are parametric, requiring normally distributed populations with specific parameters such as the mean, standard ...

13.2 : Ranks

Ranking is a nonparametric assessment method that organizes data according to specific criteria, for instance, from best to worst or heaviest to ...

13.3 : Introduction to the Sign Test

13.3 : Introduction to the Sign Test

The sign test is a nonparametric method for evaluating claims about simple random data from matched pairs, nominal data, or assertions regarding the ...

13.4 : Sign Test for Matched Pairs

13.4 : Sign Test for Matched Pairs

Consider the data on hamsters' speed before and after administering a stimulant, which constitutes a matched pair. How does one test the claim that ...

13.5 : Sign Test for Nominal Data

13.5 : Sign Test for Nominal Data

Nominal data, consisting of non-orderable names, labels, and categories, only allows for population proportions analysis. Given that the data is nominal, ...

13.6 : Sign Test for Median of Single Population

13.6 : Sign Test for Median of Single Population

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 ...

13.7 : Wilcoxon Signed-Ranks Test for Matched Pairs

13.7 : Wilcoxon Signed-Ranks Test for Matched Pairs

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 ...

13.8 : Wilcoxon Signed-Ranks Test for Median of Single Population

13.8 : Wilcoxon Signed-Ranks Test for Median of Single Population

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 ...

13.9 : Wilcoxon Rank-Sum Test

13.9 : Wilcoxon Rank-Sum Test

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 ...

13.10 : Bootstrapping

13.10 : Bootstrapping

Bootstrapping is a resampling method that uses samples randomly drawn from the already collected sample with replacement. Imagine a paleontologist trying ...

13.11 : The Anderson-Darling Test

13.11 : The Anderson-Darling Test

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 ...

13.12 : Spearman's Rank Correlation Test

13.12 : Spearman's Rank Correlation Test

Spearman's rank correlation is a nonparametric test used to find the association between two variables in paired data. Consider an example of finding ...

13.13 : Kendall's Tau Test

13.13 : Kendall's Tau Test

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 ...

13.14 : Kruskal-Wallis Test

13.14 : Kruskal-Wallis Test

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 ...

13.15 : Wald-Wolfowitz Runs Test I

13.15 : Wald-Wolfowitz Runs Test 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 ...

13.16 : Wald-Wolfowitz Runs Test II

13.16 : Wald-Wolfowitz Runs Test 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 ...

13.17 : Behrens–Fisher Test

13.17 : Behrens–Fisher Test

The Behrens-Fisher test assesses mean differences between two groups with disparate variances. It is especially effective for small samples, where ...

13.18 : Fisher's Exact Test

13.18 : Fisher's Exact Test

Fisher's exact test determines the significance of a nonrandom relationship between two categorical variables in a two-by-two contingency table. ...

13.19 : Friedman Two-way Analysis of Variance by Ranks

13.19 : Friedman Two-way Analysis of Variance by Ranks

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 ...

13.20 : Cochran's Q Test

13.20 : Cochran's Q Test

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 ...

13.21 : McNemar's Test

13.21 : McNemar's Test

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 ...

13.22 : Kendall's Coefficient of Concordance

13.22 : Kendall's Coefficient of Concordance

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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