Question

Select the correct statement(s) from the followings:
A. Parametric test is known as distribution-free test
B. Parametric test is useful when the sample size is large and it comes from the population having normal distribution
C. Examples of non-parametric tests are t-test, z-test, ANOVA
D. Correlation coefficient (rho) is a non-parametric test
Choose the correct answer from the options given below:

• A. B and C only
• B. A and B only
• C. A and C only
• D. B and D only

Hint:

Always use parametric tests (t-test, ANOVA) for normally distributed interval/ratio data, and non-parametric tests (Mann-Whitney, Kruskal-Wallis, Spearman's rho) for ordinal, ranked, or skewed data.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Statistical hypothesis testing is classified into parametric and non-parametric tests based on assumptions made about the underlying population parameters and distribution.

Step 2: Detailed Explanation:
Let us analyze each statement individually:
- Statement A is incorrect: Parametric tests make strict assumptions about the population parameters and distribution.
It is non-parametric tests that are known as distribution-free tests because they do not require the population to follow a specific probability distribution.
- Statement B is correct: Parametric tests assume that the sample is drawn from a normally distributed population and work best when sample sizes are sufficiently large to satisfy the Central Limit Theorem.
- Statement C is incorrect: The t-test, z-test, and Analysis of Variance (ANOVA) are classic examples of parametric tests because they require continuous data, interval/ratio scales, and normal distributions.
- Statement D is correct: Spearman's rank correlation coefficient (rho, \(\rho\)) is a non-parametric measure of statistical dependence between two variables.
It assesses how well the relationship between two variables can be described using a monotonic function, making no assumptions about the normality of the underlying distributions.
Therefore, statements B and D are correct, while statements A and C are incorrect.

Step 3: Final Answer:
The correct option is (D).