Reasons for Selecting a Non-parametric Test
The nature of data determines the preference for non-parametric tests over parametric tests. The non-normal distribution of data is a major reason for choosing a non-parametric test. In essence, non-parametric tests apply when the distribution of data does not meet the assumption of normality required by parametric tests (Rana, Singhal, & Dua, 2016). The presence of outliers requiring consideration during analysis is another reason that allows the use of a non-parametric test. Small sample sizes, which do not permit the application of the central limit theorem, are robust for non-parametric tests (Rana et al., 2016).
When the median is an appropriate measure of central tendency in distribution, a non-parametric test is suitable. Unlike parametric tests that require data to be on a continuous scale, non-parametric tests work well with data on nominal and ordinal scales.
Statistical power is an integral aspect of statistical analysis because it determines the ability of a test to discriminate between significant and insignificant results. A comparison of the statistical power shows that parametric tests are more powerful than non-parametric tests when the assumption of normality holds (Rana et al., 2016). The normality of data and the use of continuous scales increase the statistical power of parametric tests because they provide accurate data about a given population. Non-parametric tests are prone to type II errors because they fail to reject null hypotheses when false. However, the statistical power of parametric tests varies according to the degree of violation of key assumptions relating to a specific test.
The Appropriate Non-parametric Counterparts
|Parametric Test||Non-Parametric Counterpart|
|Dependent t-test||Wilcoxon signed-rank test|
|Independent samples t-test||Mann‑Whitney U‑test|
|Repeated measures ANOVA (one-variable)||Friedman’s Test|
|One-way ANOVA (independent)||Kruskal‑Wallis|
|Pearson Correlation||Spearman’s rho|
Activity 8A: The Wilcoxon Signed-Rank Test
Descriptive statistics (Table 1) depict that the creativity of participants (N = 40) increased from the pre-test score (M = 40.15, SD = 8.304) to the post-test score (M = 43.35, SD = 9.598).
|Table 1. Descriptive Statistics.|
Table 2 indicates that 9 participants had higher creativity scores before the test than after the test, while 28 participants had greater creativity scores after the test when compared to before the test. However, 3 participants did not show variation in creativity scores before and after tests.
|Table 2. Ranks|
|N||Mean Rank||Sum of Ranks|
|Creativity post-test – Creativity pre-test||Negative Ranks||9a||15.67||141.00|
|a. Creativity post-test < Creativity pre-test|
|b. Creativity post-test > Creativity pre-test|
|c. Creativity post-test = Creativity pre-test|
The Wilcoxon signed-rank test (Table 3) indicates that creativity scores improved statistically significantly among participants from the pre-test to the post-test (Z = -3.179, p = 0.001).
|Table 3. Test Statistics.|
|Creativity post-test – Creativity pre-test|
|Asymp. Sig. (2-tailed)||.001|
|a. Wilcoxon Signed Ranks Test|
|b. Based on negative ranks.|
Activity 8B: The Mann-Whitney U test
Descriptive statistics (Table 4) show that the mean of creativity scores is 41.75 (SD = 9.062) with maximum and minimum values of 59 and 20, respectively.
|Table 4. Descriptive Statistics.|
According to Table 5, the pretest score had a lower mean rank of 36.23 than that of the post-test of 44.78. Hence, the results of the ranks table depict the existence of an apparent increase in creativity scores among participants.
|Table 5. Ranks.|
|Test||N||Mean Rank||Sum of Ranks|
The Mann-Whitney U test (Table 6) points out that the mean rank of creativity scores in the post-test was not statistically significantly higher than in the pre-test (U = 629, p = 0.100).
|Table 6. Test Statistics.|
|Asymp. Sig. (2-tailed)||.100|
Activity 8C: The Kruskal-Wallis H Test
Table 7 displays that systolic blood pressure has a mean of 124.77 (SD = 9.031), while diastolic blood has a mean of 82.90 (SD = 2.833).
|Table 7. Descriptive Statistics.|
|Systolic Blood Pressure||30||124.77||9.031||110||145||118.00||123.50||130.00|
|Diastolic Blood Pressure||30||82.90||2.833||78||90||81.00||82.00||85.00|
In the ranks table (Table 8), the doctor’s office has the highest mean rank followed by home and classroom settings in both systolic and diastolic blood pressure. In systolic blood pressure, the doctor’s office, home, and classroom settings have the mean ranks of 22.80, 14.25, and 9.45, correspondingly. Comparatively, doctor’s office, home, and classroom settings have the mean ranks of 16.30, 15.75, and 14.45 in diastolic blood pressure, respectively.
|Table 8. Ranks.|
|Systolic Blood Pressure||Home (control)||10||14.25|
|Diastolic Blood Pressure||Home (control)||10||15.75|
The Kruskal-Wallis H Test (Table 9) settings have a statistically significant influence on systolic blood pressure, χ(30) = 10.40, p = 0.006. Nevertheless, settings have no statistically significant effect on diastolic blood pressure, χ(30) = 0.268, p = 0.875.
|Table 9. Test Statistics.|
|Systolic Blood Pressure||Diastolic Blood Pressure|
Rana, R. K., Singhal, R., & Dua, P. (2016). Deciphering the dilemma of parametric and nonparametric tests. Journal of Practical of Cardiovascular Sciences, 2(2), 95-98. Web.