Questions about Non-Parametric Procedures
Non-parametric tests are choice tests if the dataset does not assume normality in its distribution (for skewed data) (Field, 2009). In addition, data that does not heed to the assumption of homogeneity of variances calls for the use of non-parametric rather than parametric tests. The preference for non-parametric tests in place of parametric tests would also be based on the fact that non-parametric tests can give exact probabilities despite how the population from which the sample was taken is distributed. In addition, a non-parametric test is valuable for analyzing data with small samples sizes. When working with data that is classificatory, non-parametric tests become vary indispensable just as they are when working with data that is collected from a number of different populations. Data that is essentially arranged in ranks or data which gets more strength by arranging its numerical scores in ranks is suitably handled by non-parametric tests (Hebel, 2002).
Non-parametric tests are less powerful compared to their parametric counterparts, unless when testing significance when power is almost equal. The low power of non-parametric tests is attributed to the fact that the data is usually not normally distributed but instead, the data is skewed towards one direction. Parametric tests calculate their statistical power by use of formulas as well as dependence on tables as well as graphs and hence they have more power. On the other hand, non-parametric tests register a lower statistical power since power calculation is done in less straightforward approaches (Hebel, 2002).
Non-Parametric Tests for Parametric Versions
Wilcoxon’s Test
Table 1 indicates that there were 9 cases where creativity pre-test scores were greater than creativity post-test scores. In 28 cases, the creativity test scores were greater than creativity pre-test scores, and only in 3 cases were creativity pre-test scores equal to the creativity post-test scores. The Wilcoxon’s test was conducted to establish whether 40 students registered higher post-test scores than pre-test scores. It was identified that the difference between pre-test and post-test creativity scores were significantly different, Wilcoxon’s Z = -3.179, p =.001 (2-tailed significance) (Table 2). It was clear that post-test scores were significantly higher than creativity pre-test scores.
Mann Whitney U test
A new dataset (activity 5b.sav) was created from activity 5a.sav for use in between-subjects design. The new data set contained two variables only (creativity test scores while pre-test and post-test scores became the grouping variable). This new dataset was used to conduct a Mann-Whitney U test. A Mann Whitney U test was conducted on creativity test scores and it was identified that the average rank (pretest) scores were 36.22 whereas the mean rank scores for post-test scores were 44.78 (Table 3). This implies that creativity test scores conducted after the test tend to be higher than creativity test scores registered before the creativity test was conducted. Table 4 displays the Mann Whitney U which was conducted at a 2-tailed level of significance. The Mann Whitney U when applied to creativity test scores found that there existed no significant differences between the pre-test creativity scores and the post-test creativity scores, Mann Whitney U (N = 80) = 929.00, p =.10 which is greater than the significance level of.05.
Friedman’s test
On conducting a Friedman test to find out differences in systolic and diastolic blood pressures based on the setting, the mean rank for systolic blood pressure was 3.00 while the mean rank for diastolic blood pressure was 2.00 (Table 5). The Friedman test was significant, Chi-Square (N = 30) = 60.00 p =.001 (Table 6). As a result, a Wilcoxon test was conducted as a follow-up test to enable pairwise comparisons and the Z score was significant, Wilcoxon Z = -4.784, p =.001 (Table 8). It was established that the median for systolic blood pressure was significantly greater than diastolic pressure, p <.05. In fact, in all the 30 cases (Table 7), the systolic blood pressure was higher than the diastolic blood pressure.
Kruskal-Wallis test
A Kruskal-Wallis test was performed to find out if there existed any differences between the three classroom sizes for math performance. The mean ranks for a classroom of 10 or fewer students were 43.02, 27.80 for 11 to 19 students, and 20.68 for a classroom of 20 or more students (Table 9). The Kruskal-Wallis test indicated that there were significant differences between the classroom sizes in math performance (Chi-Square (N = 60) = 17.197, p =.001) (Table 10).
Contingency Tables
A 2×2 cross-tabulation was conducted to determine the relationship between education (degree) and life. The actual count of ‘less than high school’ respondents who viewed life as exciting was 52 whereas the expected count for the same was 77.0; high school respondents who viewed life as exciting were an actual count of 221 and an expected count of 226.7. On the other hand, the actual count of ‘junior college or more’ respondents who viewed life as exciting was 162 whereas the expected count was 131.4. There was an actual count of 95 for respondents who had ‘less than a high school education and viewed life as a routine with an expected count of 79.1. For ‘high school students’, there was an actual count of 242 who viewed life as a routine with an expected count of 232.9. There was an actual count of 110 for respondents who viewed life as a routine and had a junior college education or more whereas the expected count for the same was 135.0. Finally, the actual count of high school respondents who viewed life as dull was 17 while the expected count was 8.0. For high school students, the actual count of those who viewed life as dull was 20 with an expected count of 23.4. The actual count of respondents with at least a junior college education and who viewed life as dull were 8 and the expected count was 13.6 (Table 11).
The Pearson Chi-Square value for this analysis was 36.630, 2-tailed significance p =.001 at 4 degrees of freedom (Table 12). This value was significant and it was large enough to indicate that the null hypothesis is rejected as there are large differences between actual and expected counts for a degree (education) and perception of life. In other words, the two variables (education and perception of life) are not independent. The largest number of respondents who viewed life as exciting had at least a junior college education while a majority of those who viewed life as dull had a high school education (Figure 1).
References
Field, A. (2009). Discovering statistics using SPSS, Third edition. San Diego, CA: Sage Publications Ltd.
Hebel, A. (2002). Statistics-when to use them and which is more powerful? Lecture Notes. Department of Natural Sciences, University of Maryland Eastern Shore.
Appendix
Table 1: Ranks for Creativity Pre- and Post-test Scores.
Table 2: Wilcoxon’s Test for Creativity Pre- and Post-test Scores.
Table 3: Ranks for Pre- and Post-Test Score.
Table 4: Mann Whitney U Test for Creativity Test Scores.
Table 5: Ranks for Systolic and Diastolic Blood Pressures.
Table 6: Friedman Test for Systolic and Diastolic Blood Pressures.
Table 7: Follow up Wilcoxon Signed Ranks Test for Blood Pressures.
Table 8: Follow up Wilcoxon’s test for Blood Pressures.
Table 9: Mean Ranks and Number of Students.
Table 10: Kruskal-Willis Test with Chi-Square Value.
Table 11: A Cross-Tabulation (2×2 Contingency Table) of Degree and Life Expectations.
Table 12: Chi-Square Test for Degree and Life.
