Essay on nonparametric analyses

There were five nonparametric methods used, namely: Chi-square, binominal test, rank test, Mann-Whitney test, and Wilcoxon test. The research question for each nonparametric test depends on its specificity. Chi-square test does not require calculation of mean or standard deviation (Conover, 1999). A significant advantage of Chi-square method is that it allows clarifying whether two variables correlate if the dependence between the results distribution is known. The research question for this nonparametric test will be: Is there a statistically significant difference between high school GPA and first-year college GPA of test subjects?
Binominal test is a method that allows checking whether one independent variable influenced task performance (Conover, 1999). The research question in this case can be framed as follows: Is there a statistically significant difference between the high school GPA, first-year college GPA of the test subjects, and random results?
Rank test is designed to check if an order of events random or it is connected with the influences of factors that were not taken into consideration (Conover, 1999). Thus, the research question using rank test can be framed as follows: Do high school GPA and first-year college GPA of each test subjects alternate when influenced by certain factors?
Nonparametric test of Mann-Whitney (u-test) is used for checking whether there is a statistically significant difference between two independent samples after grouping data of those samples were ranked (Conover, 1999). The research question can be formed as follows: Based on the system of ranks, is there a correlation between the first-year college GPA and high school GPA of test subjects?
Wilcoxon (t-test) is used for dependent samples. This method is based on both ranking and on the sign of difference between each data pair (Conover, 1999). The research question in this case will sound like this: Do differences in high school GPA and first-year college GPA of test subjects have individual or mass character?

References

Conover, W. J. (1999). Practical nonparametric statistics. 3d ed. Oxford: John Wiley & Sons.