Question

Choose the non-parametric tests among the following :
(A) Mann-Whitney test
(B) Pearson correlation
(C) Spearman's rank correlation
(D) t-test
(E) The Wilcoxon signed-rank test
Choose the correct answer from the options given below :

• A. (A), (C) and (D) only.
• B. (A), (C) and (E) only.
• C. (B), (D) and (E) only.
• D. (B), (C) and (E) only.

Hint:

Remember these common parametric/non-parametric pairs:
- Independent t-test \(\leftrightarrow\) Mann-Whitney U test
- Paired t-test \(\leftrightarrow\) Wilcoxon signed-rank test
- Pearson correlation \(\leftrightarrow\) Spearman's rank correlation

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Statistical hypothesis tests are divided into parametric and non-parametric tests.
Parametric tests assume that the underlying data follow a specific probability distribution (typically a normal distribution) and require interval or ratio-level data.
Non-parametric tests do not assume a specific distribution, making them useful for analyzing ordinal or ranked data, or data with non-normal distributions.

Step 2: Detailed Explanation:
Let us evaluate each of the given statistical tests:
- (A) Mann-Whitney test: This is a non-parametric test used to compare differences between two independent groups when the data are not normally distributed. It is the non-parametric equivalent of the independent t-test.
- (B) Pearson correlation: This is a parametric test used to measure the strength and direction of a linear relationship between two continuous variables, assuming both variables are normally distributed.
- (C) Spearman's rank correlation: This is a non-parametric test used to measure the monotonic relationship between two ranked variables, and does not require normally distributed data.
- (D) t-test: This is a classic parametric test used to compare the means of two groups, assuming the data are normally distributed.
- (E) The Wilcoxon signed-rank test: This is a non-parametric test used to compare paired or repeated measurements. It is the non-parametric equivalent of the paired t-test.
Therefore, the non-parametric tests among the options are (A), (C), and (E).

Step 4: Final Answer:
The non-parametric tests are (A), (C), and (E), which corresponds to Option (B).