Question

Analyze the similarities and differences between parametric and nonparametric tests, and justify when is it appropriate to run a nonparametric test and when it is not, while identifying three parametric tests and nonparametric equivalents in your analysis.

Answer 1

Similarities between parametric and nonparametric tests

1. Both of these tests have similar approaches i.e. the logic of building these tests is usually the same.

2. Both these tests have some common design based assumptions for e.g. independence of individual observations.

3. The following tests are generally equivalent:

PARAMETRIC TESTS	NONPARAMETRIC TESTS
1. ANOVA test 2. T-test (for independent sample) 3. ANOVA (one way repeated measure) test 4. T-test (paired)	1. Kruskal Wallis test 2. Mann- Whitney test 3. Friedman's ANOVA test 4. Wilcoxon signed rank test

Differences between parametric and nonparametric tests

PARAMETRIC TESTS

NONPARAMETRIC TESTS

1. Here we have knowledge of population parameters. 2. Parameters of the population are used to formulate the null hypothesis. 3. Here a statistical probabilistic distribution is used for the test statistics. 4. These tests generally use the mean as the measure of central tendency. 5. Here we require past information about the population. 6. Here assumptions are made about the population. 7. These tests are less robust. 8. These tests have greater statistical power than nonparametric tests. This means that the ability to reject the null hypothesis is more. 9. Here the measurements usually fall in interval or ratio level. 10. These tests can only be applied to variables.

1. We do not have knowledge of population parameters. 2. Parameters of the population are not used to formulate the null hypothesis. 3. Here any arbitrary distribution is used for the test statistics. 4. These tests generally use the median as the measure of central tendency. 5. Here we does not require past information about the population. 6. No need of making assumptions about the population. 7. These tests are more robust. 8. These tests have lesser statistical power than parametric tests. This means that the ability to reject the null hypothesis is less. 9. Here generally ordinal/ nominal measurements are used. 10. These tests can be applied to variables and attributes.

When is it appropriate to run a nonparametric test

A nonparametric test is conducted when we are asked to test the hypothesis on the population and we do not have any knowledge about the population parameters.

When is it not appropriate to run a nonparametric test

Because of the more statistical power of parametric tests, a parametric test is conducted when we are asked to test the hypothesis on the population and we have complete knowledge about the population parameters.

Examples of parametric tests

1. T-test (one sample)

2. Z-test (one sample)

3. Paired t-test (two paired samples)

4. F- test

Examples of nonparametric tests

1. Chi-squared test (one sample/ two independent samples)

2. Kolmogorov- Smirnov Test (one sample/ two independent samples)

3. Mann Whitney Test (two independent samples)

4. Kruskal- Wallis Test