Chapter 11, Problem 2UA

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.

To determine

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