Question

2. For the data below perform a Wilcoxon Rank-Sum Test by-hand showing all steps (you may verify your results using software if you want to but it's not required). Two treatments were developed for asthma patients. Twelve patients were randomly assigned to one of Treatment A or Treatment B (six patients on each treatment). The response variable is the number of days that the patients were symptom free after using their assigned treatments for a week. Test to see if Treatment A has a distribution that is shifted to the right (.e. tends to have larger values) than Treatment B. Show all steps of your test and use 5% level of significance. Trt A 4 Trt B 2 11. 193 ART 1516

Answer 1

First, we put both samples together and organize it in ascending order, which is shown in the table below:

Sample

Now, that the values that are in ascending order are assigned ranks to them, taking care of assigning the average rank to values with rank ties

Rank (Adjusted for Sample Value Rank ties)

The sum of ranks for sample 1 is: R1 = 3+5+6+8+10+11 = 43 and the sum of ranks of sample 2 is: R2 = 1+2+4+7+9+12 = 35 Hence, the test statistic is R = R1 = 43. (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: Median (Difference) = 0 He: Median (Difference) > 0

Conclusion: there is sufficient evidence to conclude that the Treatment A has a diatribution that is shifted to the right than the Treatment B.

(2) Rejection Region The critical value for the signficance level provided and the type of tail is Rc = 17, and the null hypothesis is rejected if R <17. (3) Decision about the null hypothesis Since in this case R= 43 > 17, there is not enough evidence to claim that the population median of differences is greater than 0, at the 0.05 significance level.