Nonparametric Statistics

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

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

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

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

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 …

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 …

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 …

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

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

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

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 …

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 …

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 rank-sum, or the Mann-Whitney U, is a nonparametric test used to determine the difference between two populations by comparing their medians. It …

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 …

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

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

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'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'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's coefficient of concordance is a nonparametric statistic test that measures the agreement among ranks of the variables. It assesses the …