Nonparametric methods of statistical hypothesis testing

In some cases, the fact that we use less reliable methods adds to the probability of errors with statistical inferences. It does not sound nice, but such is reality.
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Dembitskyi S. Nonparametric methods of statistical hypothesis testing [Electronic resource]. - Access mode:
A part of statistical inferences dealing with the contrast of parameter intensity is divided into parametric (contrast of means) and nonparametric tests (comparison of value ranks measured with ordinal scales).
The application of parametric comparison tests is based on a set of assumptions which must be met by the research data (e.g., the form of the sample statistics distribution, equal variances, the metric scale of a dependent variable) in order to use the relevant test.
However, the property to be compared is often measured on an ordinal scale. This fact makes the validation of parametric tests meaningless, because the majority of mathematical operations cannot be applied for ordinal scales.
For such cases there exist nonparametric counterparts of parametric tests and they do not need to meet any assumptions:
Number of Samples
Two Samples
More Than Two Samples
Sample Dependence
Measurement Scale
Parametric Comparison Tests
Student’s t-test for independent samples
Student’s t-test for dependent samples
ANOVA (analysis of variances)
rANOVA (repeated measures analysis of variances)
Nonparametric Comparison Tests
Mann-Whitney U test, run test
Wilcoxon test, sign test
Kruskal-Wallis H test
Friedman test
It is worth noting that in real research practice, if we speak about social and behavioural sciences, ordinal variables are treated as if they were metric. In this case, it means that though it is impossible to verify the assumptions correctly, parametric tests for contrast of means are often applied.
  • default_titleХили Дж. Статистика. Социологические и маркетинговые исследования. - К.: ООО "ДиаСофтЮП"; СПб.: Питер, 2005. - 638 с.
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