Response

Discussion 5: Nonparametric Tests 
The key difference between parametric and nonparametric statistical tests is that the parametric test relies on statistical distributions in data whereas nonparametric do not depend on any distribution. Non-parametric statistical test does not make any assumptions and measures the central tendency with the median value. In essence, nonparametric statistics refers to a statistical method in which the data are not assumed to come from prescribed models that are determined by a small number of parameters. Such models include the normal distribution model and the linear regression model. It is important to know whether to use parametric or nonparametric data. If the mean more accurately represents the center of the distribution of your data, and your sample size is large enough, use a parametric test. If the median more accurately represents the center of the distribution of your data, use a nonparametric test (even if you have a large sample size).
In terms of data, parametric test data indicates that each comparison group show a normal (or Gaussian) distribution. Parametric tests make assumptions about the parameters of the population distribution from which the sample is drawn. Data in each comparison group also exhibit similar degrees of homogeneity of variance. In contrast, the common assumptions in nonparametric tests are randomness and independence. The chi-square is one of the nonparametric tests for testing three types of statistical tests: the goodness of fit, independence, and homogeneity. Non-parametric tests are “distribution-free”, and as such, can be used for non-normal variables.
Hypothetical Scenario: The researcher conducted a quantitative, quasi-experimental study using a nonequivalent pretest-posttest design to determine the effectiveness of virtual manipulatives for teaching fractions and mathematics performance. The convenience sample consisted of two groups of third graders (n=94) attending an urban public elementary school in Mississippi. Each group of students received math instruction from the same teacher, but instruction in one group included virtual manipulatives (vm). The state math test, MAAP, was used as the pretest and posttest. A Kruskal-Wallis and a Mann-Whitney U (non-parametric tests) were used to test the hypotheses related to mathematics performance and the use of virtual manipulatives. Results indicated that there was no statistical significant difference in gain scores between the intervention and comparison groups, with neither group scoring higher than the other. The utilization of virtual math manipulatives has been used for the benefit of mathematics instruction, although no statistically significant difference was found between pretest and posttest scores of the two groups in the study. The non-parametric test is the most appropriate test to use in this study. This is due to the small sample size in the study, which permits the researcher to validate the distribution of data. Additionally, non-parametric tests are feasible for data types such as nominal and ordinal. As a result of such and for future related research studies, the researcher recommends the use of virtual manipulatives should include longer periods of time for their use to maximize the possibility of effects.
                                                                           References
Huck, S. W. (2012). Reading statistics and research. Pearson.
Morgan, S. E., Reichert, T., & Harrison, T. R. (2017). From numbers to words. Routledge.