Question

What nonparametric test will I use and why? A researcher tests three groups of participants on a psychomotor test under three levels of illumination: dim, average and bright. Each group has seven participants. Which test will you use?

Answer 1

The Kruskal-Wallis H test is the correct nonparametric test for comparing three groups of participants in a psychomotor test under three different illumination conditions due to its suitability for non-normally distributed data and small sample sizes.

Step-by-step explanation:

For the given scenario where a researcher is testing three groups of participants on a psychomotor test under three levels of illumination (dim, average, and bright) with each group having seven participants, the appropriate nonparametric test to use is the Kruskal-Wallis H test. The Kruskal-Wallis H test is chosen because it is designed to compare the medians of three or more groups when the assumptions of normality and/or equal variances are not met, which is common in small samples like those with seven participants each.

The Kruskal-Wallis H test does not assume a normal distribution, making it suitable for these conditions. Additionally, since there is only one factor (level of illumination) with three levels being tested, the Kruskal-Wallis H test is the nonparametric equivalent to the one-way ANOVA.