Which statement about non-parametric tests is true?

• A. They make inferences about population parameters
• B. They require a normal distribution
• C. They do not infer about population parameters
• D. They assume equal variances

Answer: (C)

Non-parametric tests are distribution-free and rely on ranks or signs rather than specific population parameters. Because of that, the inference they provide is about the distribution as a whole or about a central tendency like the median, not about a fixed parameter such as the mean or variance. In other words, these tests ask questions like whether two populations differ in location or whether one distribution tends to yield larger values, rather than estimating a population parameter.

That’s why the statement that they do not infer about population parameters is true: their goal is not to estimate or test a particular parametric value, but to compare distributions or medians without assuming a particular distributional form. It’s also why they don’t require normality and generally don’t assume equal variances. For example, the Mann-Whitney U test, Wilcoxon signed-rank test, and Kruskal-Wallis test compare distributions or medians rather than means under a parametric model.