Which of the following statements is correct about the Mann-Whitney U-test?
1. It is a non-parametric test
2. It requires that samples are independent
3. It can be used when populations involved are normally distributed
4. It is used to test the null hypothesis that the two populations involved are identical
5. It is always a two-tailed test
Choose the correct answer from the options given below:

Correct option is A

The Mann-Whitney U-test, also called the Wilcoxon rank-sum test, is a non-parametric test used to compare two independent groups. It evaluates whether their population distributions are identical without assuming normality. Here’s a breakdown of the correct statements:

1. It is a non-parametric test (Statement 1):

   • This test does not rely on the assumption of normal distribution, making it suitable for data that do not meet parametric test assumptions.

2. It requires that samples are independent (Statement 2):

   • The test compares two independent groups, meaning observations in one sample must not influence the other.

3. It is used to test the null hypothesis that the two populations involved are identical (Statement 4):

   • The Mann-Whitney U-test assesses whether there is a significant difference between two populations' distributions under the null hypothesis of identical populations.

Information Booster:

Key Features of the Mann-Whitney U-test:

• Purpose: To determine if there is a significant difference in the distributions of two independent groups.
• Data Type: Works with ordinal, interval, or ratio data that may not be normally distributed.
• Assumptions:
  1. The samples are independent.
  2. The data are ordinal or continuous.
  3. The two groups have the same shape of distribution under the null hypothesis.

Applications:

• Comparing test scores of two independent groups.
• Analyzing non-normally distributed data in medical or social sciences.

Additional Knowledge:

1. Statement 3 (It can be used when populations involved are normally distributed):

   • This is incorrect because the Mann-Whitney U-test does not assume normality. It is specifically advantageous when the data do not follow a normal distribution.

2. Statement 5 (It is always a two-tailed test):

   • This is incorrect because the Mann-Whitney U-test can be one-tailed or two-tailed based on the hypothesis. For example:
     • One-tailed: Testing if one group tends to have higher ranks than the other.
     • Two-tailed: Testing for any difference in ranks between the two groups.