Which of the following BEST distinguishes parametric from non-parametric statistical methods?

The question asks to identify the statement that best distinguishes parametric from non-parametric statistical methods. Step 1: Understand Parametric Methods. Parametric statistical methods make specific assumptions about the distribution of the population data from which the sample is drawn. Common assumptions include normality (data follows a normal distribution), homogeneity of variances, and that the data is measured on an interval or ratio scale. These methods are generally more powerful when their assumptions are met. Step 2: Understand Non-Parametric Methods. Non-parametric statistical methods do not* make specific assumptions about the distribution of the population data. They are often called "distribution-free" methods. They can be used with data that is nominal or ordinal, or with interval/ratio data that violates the assumptions of parametric tests (e.g., highly skewed data, small sample sizes). They are generally less powerful than parametric tests when parametric assumptions are met. Step 3: Evaluate the given options. a. Parametric methods are always more accurate than non-parametric methods. This is incorrect. If the assumptions for a parametric test are violated, a non-parametric test can be more appropriate and lead to more accurate conclusions. b. Parametric methods are used only for qualitative data, while non-parametric methods are used for quantitative data. This is incorrect. Parametric methods are used for quantitative* data (interval/ratio scales). Non-parametric methods can be used for both qualitative (nominal/ordinal) and quantitative data. c. Parametric methods assume specific distributional properties (e.g., normality), while non-parametric methods do not. This statement accurately captures the fundamental difference. Parametric tests rely on assumptions about the population distribution (like normality), whereas non-parametric tests are free from such assumptions. d. Non-parametric methods require larger sample sizes than parametric methods. This is often true in practice to achieve comparable statistical power, especially when parametric assumptions are met. However, it is a consequence of their relative power, not the defining distinction* between the two types of methods. The core distinction lies in the distributional assumptions. Step 4: Conclude the best distinguishing factor. The most fundamental difference between parametric and non-parametric methods is the assumption (or lack thereof) regarding the underlying distribution of the data. The final answer is c. Parametric methods assume specific distributional properties (e.g., normality), while non-parametric methods do not.. Last free one today — make it count tomorrow, or type /upgrade for unlimited.