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Concept explainers
Using an Inappropriate Test Discuss the nonparametric tests described in this chapter and match each test with its parametric counterpart, which you studied in earlier chapters.
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To discuss: The nonparametric tests and match each test with its parametric counterpart.
Answer to Problem 2UA
Nonparametric tests:
Sign test: It is used for testing population median.
Wilcoxon signed rank test: It is used for testing two samples of the dependent groups come from the population having same distribution or not.
Wilcoxon rank sum test: It is used for testing two samples of the independent groups come from the population having same distribution or not.
Spearman rank correlation coefficient test: It is used for testing whether there is relation between two variables or not.
Run test: It is used for testing whether the sample is drawn randomly or not.
Kruskal-Wallis test: It is used for testing three or more samples come from the population having same distribution or not.
Match the nonparametric test with its parametric counterpart:
Nonparametric test | Parametric test |
Wilcoxon signed-rank test | t test for two dependent samples |
Wilcoxon rank sum test | z and t test for two independent samples |
Kruskal-Wallis test | One-way ANOVA |
Spearman rank correlation | Pearson correlation |
Explanation of Solution
Non-parametric tests:
When the distribution of the population is not known or when the population distribution does not follow normality, then the non-parametric statistical tests are used to test the population parameters.
The non-parametric tests are listed below:
- Sign test
- Wilcoxon signed-rank test
- Wilcoxon rank sum test
- Kruskal-Wallis test
- Spearman rank correlation
- Run test
Sign test: It is used for testing population median.
Wilcoxon signed rank test: It is used to compare ranks the population of the paired samples or the matched samples. This implies that the Wilcoxon sign rank test is used to compare the matched pair groups. Moreover, it is used for testing two samples of the dependent groups come from the population having same distribution or not.
Wilcoxon rank sum test: It is used to compare the population ranks of the two different or independent samples. Moreover, it is used for testing two samples of the independent groups come from the population having same distribution or not.
Spearman rank correlation coefficient test: It is used for testing whether there is relation between two variables or not.
Run test: It is used for testing whether the sample is drawn randomly or not.
Kruskal-Wallis test: It is used for testing three or more samples come from the population having same distribution or not.
Parametric tests:
When the distribution of the population is known or when the population distribution follows normality, then the parametric statistical tests are used to test the population parameters.
Match the nonparametric test with its parametric counterpart:
Nonparametric test | Parametric test |
Wilcoxon signed-rank test | t test for two dependent samples |
Wilcoxon rank sum test | z and t test for two independent samples |
Kruskal-Wallis test | One-way ANOVA |
Spearman rank correlation | Pearson correlation |
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Chapter 11 Solutions
Elementary Statistics: Picturing the World (7th Edition)
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