Which of the following BEST distinguishes parametric from non-parametric statistical 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.

• 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.

• 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.

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 $\boxed{\text{c. Parametric methods assume specific distributional properties (e.g., normality), while non-parametric methods do not.}}$.