Assertion (A) Analysis: Applicability of Parametric Methods

The assertion states that parametric methods are not applicable when the sample size is small or the data are badly skewed, making the normality assumption doubtful.

• Parametric methods rely on specific assumptions about the population distribution, most commonly normality.
• Violating these assumptions, especially with small sample sizes or significant skewness, can compromise the validity and reliability of the results obtained from parametric tests.
• Therefore, the statement that parametric methods are not applicable under these conditions is generally considered correct in the context of ensuring valid statistical inference.

Reason (R) Analysis: Normality Assumption in Parametric Tests

The reason explains that parametric tests assume scores are normally distributed in the population.

• This is the fundamental definition of parametric statistical tests. They are designed based on the assumption that the data are drawn from a population with a specific probability distribution, typically the normal distribution.
• This statement accurately describes a core requirement for the application of parametric methods.

Linking Assertion (A) and Reason (R)

The reason (R) provides the underlying justification for the assertion (A).

• Since parametric tests inherently assume population normality (Reason R), their applicability (Assertion A) is directly challenged when this normality assumption is in doubt due to factors like small sample size or skewed data.
• The violation of the normality assumption, as highlighted in (A), is precisely why the statistical properties assumed in (R) no longer hold, making the application of parametric methods questionable.
• Thus, Reason (R) is a correct explanation for Assertion (A).

Conclusion

Both Assertion (A) and Reason (R) are correct statements, and Reason (R) correctly explains why Assertion (A) is true.