What differentiates parametric and nonparametric tests?

• A. Nonparametric tests require distributional parameters.
• B. Parametric tests require distributional parameters; nonparametric tests do not rely on such assumptions.
• C. Parametric tests are always more robust to outliers.
• D. Nonparametric tests assume normal distribution.

Answer: (B)

The key idea is how tests handle distribution assumptions and what information about the distribution they use. Parametric tests rely on a specific distribution form (often normal) and depend on distributional parameters like the mean and standard deviation to compute their test statistics. Nonparametric tests, on the other hand, do not assume a particular distribution and do not depend on those parameters; many use the data’s ranks instead of raw values, making fewer assumptions about the distribution.

That’s why the statement that parametric tests require distributional parameters while nonparametric tests do not rely on such assumptions is the best answer. It captures the fundamental distinction between the two approaches.

Why the other ideas don’t fit: the notion that nonparametric tests require distributional parameters is incorrect because they are designed to avoid such requirements. The idea that parametric tests are always more robust to outliers isn’t reliable—outliers can heavily distort parametric tests, whereas nonparametric ones often cope better with them. And the claim that nonparametric tests assume normal distribution is false; their appeal is precisely that they do not rely on that assumption.