Created March 2020, By Jackpeter Nduati. (firstname.lastname@example.org)
A Mann-Whitney test also referred to as a U-test is a non-parametric tests alternative of an independent t-test that examines the difference between two unrelated/ independent groups where the dependent variable being tested, either continuous or ordinal, is not normally distributed. For instance, A Mann-Whitney U test can be used to understand whether the salary of employees measured on a continuous scale differed based on their gender. In this case salary, not normally distributed, would be the dependent variable while gender would be the independent variable.
Wilcoxon signed-rank Tests
A Wilcoxon signed-rank test is a non-parametric test equivalent of a dependent t-test that is used to examine a statistical hypothesis on whether two related samples or repeated measures were drawn from a population having the same distribution. The test is often used when the assumption of normality is violated. Wilcoxon signed-rank test can be used in a research project scenario where the researcher wishes to understand whether there was a difference in individuals daily alcohol consumption before and after a two-month intervention rehabilitation program. In this case, the dependent variable would be daily alcohol consumption while the two related observation group will be alcohol consumption values before and after the intervention rehabilitation program
Analysis: Emotional Well-Being Data Set
I conducted a Mann-Whitney U test to examine whether there was a difference in BMI index between male and female participants in the emotional-wellbeing study. The dependent variable was BMI index while the independent variable was gender. I tested the null hypothesis that there is no significant difference in BMI index between male and female participants. Before performing the Mann-Whitney U test I checked whether the method was fir for this analysis by conducting a normality test on the dependent variable. Shapiro-Wilk (W) statistic was utilized for the test. The results of the normality test perfumed are presented in table 1 and figure 1 below.
Based on the results in table 1, the Shapiro-Wilk statistic was significant, W = .936, p < .05. Therefore, we conclude that the data on BMI was not normally distributed as Shapiro-Wilk statistic would need to be insignificant for the data to have a normal distribution (Das & Imon, 2016). The graphical representation as presented by the histogram in figure 1 above also shows that the distribution of BMI was not normally distributed. Since the assumption of normality is not satisfied we can go ahead and use the Mann-Whitney U test instead of independent paired t-test to test the formulated hypothesis. The results obtained from the Mann-Whitney U test conducted are presented in table 2 and table 3 below.
|Ranks Summary Results (N = 72)|
|gender||N||Mean Rank||Sum of Ranks|
|Test Statistics Summary (N = 72)|
|Asymp. Sig. (2-tailed)||.553|
The rank results presented in table 2 below indicate the female participants, who have the highest mean rank of 37.92, can be considered to have a higher BMI than their male counterparts. The results presented on table 3 are statistically insignificant, U = 595, P > 0.5. Therefore, we have enough evidence not to reject the null hypothesis and conclude that there is no significant difference in BMI index between male and female participants. The results presented mean that in the population where the participants in the study were drawn, men have basically the same BMI as females.
Wilcoxon signed-rank Tests
I conducted a Wilcoxon signed-rank test to examine there is a difference in well-being scores of female participants at baseline and after dietary treatment. I tested the null hypothesis that there was no significant difference in female participants’ well-being scores at the baseline and after treatment. The results from the Wilcoxon signed-rank test conducted are presented in table 4 and table 5 below.
|Ranks Summary Results (N = 37)|
|N||Mean Rank||Sum of Ranks|
|Post-Tx Well-Being – Basline SF-36 Well-Being Score||Negative Ranks||9a||10.28||92.50|
|a. Post-Tx Well-Being < Basline SF-36 Well-Being Score|
|b. Post-Tx Well-Being > Basline SF-36 Well-Being Score|
|c. Post-Tx Well-Being = Basline SF-36 Well-Being Score|
|Test Statistics Summary (N = 37)|
|Post-Tx Well-Being – Basline SF-36 Well-Being Score|
|Asymp. Sig. (2-tailed)||.000|
|a. Based on negative ranks.|
The rank results presented in table 4 help us compare the female participants before and after dietary treatment well-being scores. Based on the results presented, nine female participants had a higher well-being score before the dietary treatment than after the dietary treatment. Moreover, the results indicate that 27 female participants had a higher well-being score after the dietary treatment than before the dietary treatment. However, one female participant had no change in her well-being score, before and after the dietary treatment. The results of the Wilcoxon signed-rank test as presented in table 5 were significant, Z = -3.799, p < .05. Therefore, we have enough evidence to reject the null hypothesis and conclude that there was a significant difference in female participants’ well-being scores at the baseline and after treatment. These results indicate that dietary treatment did elicit a statistically significant change in well-being in female participants. The results further suggest that in a population where the female participants were drawn from, if the dietary treatment can be used as an intervention strategy it will improve the wellbeing of the females in that population.
Das, K. R., & Imon, A. H. M. R. (2016). A brief review of tests for normality. American Journal of Theoretical and Applied Statistics, 5(1), 5-12.