Question

Parametric tests (such as t or ANOVA) differ from nonparametric tests (such as chi-square) primarily in terms of the assumptions they require and the data they use. Which of the following are true about nonparametric tests?

Check all that apply.
A. Nonparametric tests require data measured on an interval or ratio scale.
B. Nonparametric tests make few if any assumptions about the populations.
C. Nonparametric tests require the populations to satisfy numerous assumptions.
D. Nonparametric tests do not require the populations to have normal distributions.
E. Nonparametric tests can be performed on data measured on any scale.
F. Nonparametric tests require different populations to have equal variances.

Answer 1

Nonparametric tests such as chi-square make few if any assumptions about the populations from which data are drawn, do not require normal distributions, and can be performed on data measured on any scale.

Step-by-step explanation:

When considering whether nonparametric tests require data measured on an interval or ratio scale, it's actually the opposite; nonparametric tests do not typically require data measured on these scales. Nonparametric tests such as the chi-square are often used precisely because they make few if any assumptions about the populations from which data are drawn. This includes not assuming that the populations have normal distributions, which is a requirement of many parametric tests, such as the t-test or ANOVA. Nonparametric tests also do not generally require that the populations have equal variances, which is another assumption of tests like ANOVA.

So, for the statements provided:

• B. Nonparametric tests make few if any assumptions about the populations. (True)
• D. Nonparametric tests do not require the populations to have normal distributions. (True)
• E. Nonparametric tests can be performed on data measured on any scale. (True)