When is a nonparametric test preferred over a parametric test?

When is a nonparametric test preferred over a parametric test?

• A. When the data are normally distributed and assumptions are satisfied
• B. When the data are normally distributed with large samples
• C. When the sample size is large and the population variance is known
• D. When normality or other assumptions are violated or sample size is very small

Answer: (D)

Nonparametric tests are used when the assumptions behind parametric tests don’t hold or when the sample size is very small. These methods don’t rely on a specific population distribution; they use the data’s ranks or order rather than the actual values, which makes them robust to outliers and skewed data. Because they make fewer assumptions, they’re appropriate when normality or equal-variance assumptions are questionable, or when you don’t have enough data to trust the parametric theory. If the data are truly normal and the assumptions are satisfied, parametric tests generally offer more statistical power, so they’re preferred in that scenario. With large samples and known population variance, parametric approaches remain the standard because of their efficiency. In short, nonparametric methods shine when distributions are uncertain or sample sizes are too small to rely on parametric results.

Nonparametric tests are used when the assumptions behind parametric tests don’t hold or when the sample size is very small. These methods don’t rely on a specific population distribution; they use the data’s ranks or order rather than the actual values, which makes them robust to outliers and skewed data. Because they make fewer assumptions, they’re appropriate when normality or equal-variance assumptions are questionable, or when you don’t have enough data to trust the parametric theory. If the data are truly normal and the assumptions are satisfied, parametric tests generally offer more statistical power, so they’re preferred in that scenario. With large samples and known population variance, parametric approaches remain the standard because of their efficiency. In short, nonparametric methods shine when distributions are uncertain or sample sizes are too small to rely on parametric results.