**Discussion Question 6 – CLOs 1, CLO 2, CLO 3, CLO 9, & CLO 11**

You have been learning about the nonparametric methods and models and now please answer the following questions in detail by applying the knowledge that you have gained from readings and lectures. It is important to include hypothetical examples whenever applicable.

1. Describe the objective of non-parametric Mann-Whitney-Wilcoxon (MWW) test in comparing the median of a population with the median of another population. State the underlying assumptions. Explain formulation of the hypothesis, the test statistic, the rationale for rejecting the null, the criterion for choosing the critical points, possible test outcomes, and the criterion for evaluating the p value. Include both non-directional and directional hypotheses. Provide a hypothetical example of formulating hypotheses in comparing medians based on MWW tests.

2. Explicate the covariance between two numeric (ratio or interval) variables and its significance and define correlation between these two variables, and its significance, and provide a hypothetical example of evaluating covariance and correlation along with interpretations. State and explain if the correlation between two variables and simple regression are of the same nature. Describe the rank correlation, its purpose, and significance. Discuss why the rank correlation is bound between -1 and 1.

**Activity 9 – CLO 1, CLO 2, CLO 3, CLO 9, CLO 11, CLO 12**

Populations A and B are both measured in the same ordinal scale. A sample from these populations is taken which contains two (2) elements from A and three (3) elements from B. State all possible rank ordering of the elements in the sample. Under validity of the null hypothesis that the medians of the two populations are identical, assign probabilities for all possible values for the statistic in the MWW test on equality of the medians. For each value of the test statistic, state if the null hypothesis is rejected, and also evaluate the associated p value. Use 0.05 once and then 0.1 for significance level.