Introduction
The use of non-parametric statistical tests makes sense in practical situations when the distribution of the variables used does not correspond to the normal distribution, including for reasons of small sample sizes. Ignoring the assumption of normality of distribution can create distorted results and negatively affect the quality of the obtained conclusions.
Main Body
As an example, if statistics are used to test vaccine efficacy in before/after dependent samples, it is acceptable to use a paired t-test if the sample size is large enough (n ≥ 30) (McClenaghan, 2023). However, if the sample size is not large enough or the distribution does not obey normality requirements, the paired t-test is not applicable, and a non-parametric alternative may be used instead. The Wilcoxon Signed-Rank Test is a non-parametric substitute for the paired t-test, for which the normality of the distributions is not essential; moreover, instead of the values themselves, their corresponding ranks are used in the case of the analysis (LS, 2022). Otherwise, both tests have the same functional essence, so there are not many differences.
The proposed research scenario tests the effectiveness of the WHO irrigation construction program in reducing malaria infection in some African regions. Thus, two dependent samples were collected to represent the number of new malaria cases before and after the introduction of the irrigation intervention for ten cities. Since the sample is represented by a small number of values (n ≤ 30), the use of a paired t-test was not acceptable and instead required the use of the Wilcoxon Signed-Rank Test to find numerical differences between the two dependent samples.
Table 1 shows the descriptive statistics results for each of the two samples: the mean number of new malaria cases was higher before the irrigation intervention was introduced (M = 122.4, SD = 45.1) and decreased by a factor of about five when it was introduced (M = 25.4, SD = 23.6). The sizes of both samples are identical and equal to ten records (ten observation cities).
Table 2 presents the results of the main test, namely the Wilcoxon Signed-Rank Test. Turning to the top half of Table 2 allows us to draw two interesting conclusions. First, the average number of new cases of malaria was higher before the irrigation intervention was implemented than it was after, according to all observations. Second, none of the observations had an increase in the number of new malaria cases after the introduction of the WHO intervention. Turning to the bottom of Table 2, which contains vital information for identifying the significance of differences, suggests that the introduction of the WHO irrigation intervention in the African region resulted in a statistically significant decrease in the number of new malaria cases in the local population (Z = -2.810, p =.005).
The present work focused on conducting statistical analysis to find the statistical significance of differences between two dependent samples that do not obey the conditions of normal distributions. The use of the classical parametric paired t-test was not acceptable, as it would lead to skewed results, so it was decided to use a non-parametric alternative, the Wilcoxon Signed-Rank Test.
Conclusion
When compared to the pre-intervention condition, the test results generated by IBM SPSS demonstrated a statistically significant decrease in the number of new malaria cases in the local community. In other words, WHO’s malaria containment strategy has proven clinically effective.
References
LS. (2022). Wilcoxon signed-rank test using SPSS statistics. Statistics Laerd. Web.
McClenaghan, E. (2023). The Wilcoxon signed-rank test. TN Informatics. Web.