Question

Non-parametric tests are
A. Wilcoxon signed-rank test
B. Kruskal - Wallis test
C. Spearman's rank correlation
D. One way ANOVA
E. Paired t-test
Choose the correct answer from the options given below

• A. A, B and C only
• B. B, C and D only
• C. D and E only
• D. All A, B, C, D and E

Hint:

Parametric vs Non-Parametric Equivalents:
Paired t-test $\leftrightarrow$ Wilcoxon Signed-Rank test.
Independent t-test $\leftrightarrow$ Mann-Whitney U test.
One-way ANOVA $\leftrightarrow$ Kruskal-Wallis test.
Pearson $r \leftrightarrow$ Spearman Rank $r_s$.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
Statistical inference: parametric tests assume underlying normal distribution parameters ($\mu, \sigma^2$), whereas non-parametric distribution-free tests operate on ranked or categorical data.

Step 2: Detailed Explanation:
Statistical test classification:
1. Non-Parametric (Distribution-Free) Tests:
- A. Wilcoxon Signed-Rank Test: Non-parametric equivalent of paired t-test.
- B. Kruskal-Wallis Test: Non-parametric equivalent of one-way ANOVA.
- C. Spearman's Rank Correlation ($r_s$): Non-parametric measure of monotonic rank association.
- Mann-Whitney U test, Chi-square test.
2. Parametric Tests (Assume Normal Distribution): D. One-way ANOVA and E. Paired t-test.
Thus, non-parametric tests are A, B, and C only.

Step 3: Final Answer:
Thus, the non-parametric tests are A, B and C only, matching option (A).