c. What conditions need to be satisfied to validate the test in part (d)? Refer to the output to assess whether it’s reasonable to assume the conditions are satisfied. If the conditions are not met, is the above p-value still approximately correct? d. The comparison of medians yields a p-value of 3.56 × 10-6. This is a result from the Wilcoxon Rank Sum test. State the conclusion from this test in the context the problem. Use α = 0.05. What assumption is needed to validate this test? Comparison of MediansMedian of sample 1: 3254Median of sample 2: 2782Mann-Whitney (Wilcoxon) W-test to compare mediansNull hypothesis: median1 = median2Alt. hypothesis: median1 > median2Average rank of sample 1: 98.8138Average rank of sample 2: 64.9247W = 2038.5 P-value = 3.54263E-06Reject the null hypothesis for alpha = 0.05.The StatAdvisorThis option runs a Mann-Whitney W-test to compare the medians of the two samples. This test is constructed by combining thetwo samples, sorting the data from smallest to largest, and comparing the average ranks of the two samples in the combined data.Since the P-value is less than 0.05, the median of the first sample is significantly greater than the median of the second at the 95%confidence level.

Median of 1st sample =μ~1=3254 and for 2nd sample=μ~2=2782 To compare median, Mann-Whitney W-test is…

Answered: Comparison of Medians Median of sample…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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c. What conditions need to be satisfied to validate the test in part (d)? Refer to the output to assess whether it’s reasonable to assume the conditions are satisfied. If the conditions are not met, is the above p-value still approximately correct?
d. The comparison of medians yields a p-value of 3.56 × 10-6. This is a result from the Wilcoxon Rank Sum test. State the conclusion from this test in the context the problem. Use α = 0.05. What assumption is needed to validate this test?

Comparison of Medians
Median of sample 1: 3254
Median of sample 2: 2782
Mann-Whitney (Wilcoxon) W-test to compare medians
Null hypothesis: median1 = median2
Alt. hypothesis: median1 > median2
Average rank of sample 1: 98.8138
Average rank of sample 2: 64.9247
W = 2038.5 P-value = 3.54263E-06
Reject the null hypothesis for alpha = 0.05.
The StatAdvisor
This option runs a Mann-Whitney W-test to compare the medians of the two samples. This test is constructed by combining the
two samples, sorting the data from smallest to largest, and comparing the average ranks of the two samples in the combined data.
Since the P-value is less than 0.05, the median of the first sample is significantly greater than the median of the second at the 95%
confidence level.

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

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