Question

Nonparametric Methods
In this assignment, we will use the following nonparametric methods:

• The Wilcoxon signed-rank test: The Wilcoxon signed-rank test is the nonparametric test analog of the paired t-test.
• The Wilcoxon rank-sum test or the Mann-Whitney U test: The Wilcoxon rank-sum test is an analog to the two-sample t-test for independent samples.

Part 1: Wilcoxon Signed-Rank Test

Let's take a hypothetical situation. The World Health Organization (WHO) wants to investigate whether building irrigation systems in an African region helped reduce the number of new cases of malaria and increased the public health level.

Data was collected for the following variables from ten different cities of Africa:

• The number of new cases of malaria before the irrigation systems were built
• The number of new cases of malaria after the irrigation systems were built

Table 1: Cases of Malaria

City	Before	After
1	110	55
2	240	75
3	68	15
4	100	10
5	120	21
6	110	11
7	141	41
8	113	5
9	112	13
10	110	8

Using the Minitab statistical analysis program to enter the data and perform the analysis, complete the following:

• Run a sample Wilcoxon signed-rank test to show whether there is a statistically significant difference between the number of cases before and after the irrigation systems were built.
• Obtain the rank-sum.
• Determine the significance of the difference between the groups.
• Determine whether building these systems helped reduce new cases of malaria.
• In a Microsoft Word document, provide a written interpretation of your results.

Answer 1

Wilcoxon signed rank test:

Step.1 First enter data in minitab.

Step.2 Find difference between number of cases before and after the irrigation systems were built.

Step.3 Go to 'Stat' ---> 'Nonparametric' ----> select '1-sample wilcoxon' . New window will pop-up on screen. Refer following screen shot and provide required information accordingly.

Minitab output:

MTB > Let 'Difference' = 'Before' - 'After'

MTB > WTest 0 'Difference';
SUBC> Alternative 0.

Wilcoxon Signed Rank Test: Difference

Test of median = 0.000000 versus median ≠ 0.000000

N for Wilcoxon Estimated
N Test Statistic P Median
Difference 10 10 55.0 0.006 99.00

Since p-value for Wilcoxon signed rank test is 0.006 which is less than 0.05, hence we reject null hypothesis and conclude that there is a statistically significant difference between the number of cases before and after the irrigation systems were built.

Wilcoxon Rank sum Test:

Step.3 Go to 'Stat' ---> 'Nonparametric' ----> select 'Mann Whitney' . New window will pop-up on screen. Refer following screen shot and provide required information accordingly.

Output:

MTB > Mann-Whitney 95.0 'Before' 'After';
SUBC> Alternative 0.

Mann-Whitney Test and CI: Before, After

N Median
Before 10 111.00
After 10 14.00

Point estimate for η1 - η2 is 97.00
95.5 Percent CI for η1 - η2 is (62.98,106.98)
W = 154.0
Test of η1 = η2 vs η1 ≠ η2 is significant at 0.0002
The test is significant at 0.0002 (adjusted for ties)

Since p-value for Mann whitney test is 0.0002 which is less than 0.05, hence we reject null hypothesis and conclude that there is significant difference between number of cases before and after the irrigation systems were built.

It means building this system significantly reduce malaria cases.