Topic: Non-Parametric Tests on Two Variables Using the Wilcoxon Signed Rank Test Name: Charles Thornton Institution: Course:Testing the Effectiveness of Prolonged Hours of Exercises on Treatment of ObesityA research was carried out to determine the effectiveness of the hours of exercises on the rate of patients’ weight loss. The medical practitioner decided to apply different lengths of physical exercises time on each of the five patients under her care. The patients were put under daily 2, 3, 4, 5, and 6 hours of practice for one month. The net weight loss for each patient was recorded before and at the end of the study period. She then took non-parametric tests on the data recorded to determine whether the length of time a patient exercises corresponds to their weight loss.Question: Does the length of time a patient exercises daily correspond to their resultant weight loss? To answer this question she came up with the null hypothesis:H0: The length of time a patient is subjected to daily physical exercises is independent of the corresponding weight loss.The variables for the study are:Independent variable: The length of time a patient takes to exercise daily.Dependent variable: The weight loss recorded for each patient after taking daily physical exercises for one month.Alternative hypothesis: The length of time a patient takes to exercise daily determines their corresponding weight loss at the end of the study period. To test the hypothesis, the Wilcoxon signed rank tests would be the fitting test. This test examines whether the data available supports the assertion that a prolonged daily exercise length implies a faster rate of weight loss. The test has been used previously in similarly befitting roles. (Han et al. 2011) notes: We used two-sided Wilcoxon rank sum tests for differences in location for these variables as well as for age and years of education. To carry out the test, the researcher needs to calculate the differences in recorded weights before and after the study period. All weight losses will be noted with a plus sign and all gains by a minus sign. Because the positive results (those with plus signs) are the center of our study, we assign them the title k-observed, denoted as kobs. Then using the value of the smallest integer kα we shall calculate the rejection region for kobs. We then observe whether our kobs is contained in R, that is without the boundaries of the rejection region. If kobsЄR, we fail to reject the null hypothesis. Let us put our R at 4, just for illustration. If kobs=3, then we fail to reject the H0 owing to the earlier explanation that kobsЄR.Reference ListHan, X., Rozen, S., Boyle, S. H., Hellegers, C., Cheng, H., Burke, J. R……, Kaddurah-Daouk, R. (2011). Metabolomics in Early Alzheimer’s Disease: Identification of Altered Plasma Sphingolipidome Using Shotgun Lipidomics. Lipidomics in Alzheimer’s Disease. Vol 6. Issue 7. p. 7. Nishiumi, S., Kobayashi, T., Ikenda, A., Yoshie, T., Kibi, M., Izumi, Y.,…..Yoshida, M. (2012). A Novel Serum Metabolomics-Based Diagnostic Approach for Colorectal Cancer. Metabolomics for Colorectal Cancer. Vol. 7, issue 7. p. 4. Plichta, S. B., Kelvin, E. Munros Statistical Methods for Health Care Research. Statistical Methods for Health Care Research. (6th edition). (2012). Smith, G. L., Xu, Y., Buchholz, T. A., Giordano, S. H., Jiang, J., Shih, Y. C. T., amp. Smith, B. D.(2012). Association Between Treatment With Brachytherapy vs Whole-Breast Irradiation and Subsequent Mastectomy, Complications, and Survival Among Older Women With Invasive Breast Cancer. The Journal of the American Medical Association. par 17.