Nonparametric and Parametric Tests

PARAMETRIC AND NONPARAMETRIC TESTS

Methodology: Research Proposal

From the onset, it would be prudent to note that there are a number of differences that exist between parametric and nonparametric tests. To begin with, one key deference between these two statistical procedure classifications relates to the making of assumptions. A number of assumptions are made when it comes to parametric tests (i.e. in relation to underlying statistical distributions) (Weaver, Morales, and Dunn, 2017). However, according to the authors, assumptions are not made in nonparametric tests. Thus, it should be noted that the latter - unlike the former - is not hinged upon any distribution. It should also be noted that unlike nonparametric tests, parametric tests have a number of conditions for validity. This is instrumental in efforts to ensure that parametric test results are reliable. According to Scott and Mazhindu (2005), the meeting of certain conditions of validity is, however, not necessary in the case of nonparametric tests. This is more so the case given that as has been indicated above, they do not rely on any distribution. According to Sheskin (2010), parametric tests also happen to be less robust than nonparametric tests. This essentially means that unlike is case with parametric tests, there are minimal validity conditions when it comes to nonparametric tests – effectively meaning that the validity of nonparametric tests is broader.

Some of the examples of parametric tests are inclusive of z-test and t-test (Taylor and Cihon, 2004). Z-tests are instrumental in hypothesis testing – specifically in those instances where the population variance is known. When the population variance is unknown, the z-test can still be used if there is a large sample size (i.e. more than 30). On the other hand, in those instances whereby the population variance is not known and the sample size happens to be small (i.e. < 30), then a t-test should be used. On the other hand, as Taylor and Cihon (2004) further indicate, some of the examples of nonparametric tests are inclusive of Kruskal-Wallis and Mann-Whitney. In relation to the utilization of the two statistical procedure classifications highlighted above, it is important to note that whereas nonparametric tests (such as z-test and t-test) come in handy in efforts to find nominal data, parametric tests (such as Kruskal-Wallis and Mann-Whitney) are essential in finding interval data.

As has been indicated elsewhere in this discussion, there are a number of assumptions that have to be met in relation to parametric tests. The said assumptions, in the words of Myers, Well, and Lorch (2010), are; normality, equal variance, independence, and no outliers” (187). When it comes to ‘normality’, this relates to the normal distribution of each group’s data. Secondly, in relation to ‘equal variance’, the authors indicate that this relates to the assumption that there should be equal variance (in approximate terms) in each group’s data. Third, ‘independence’ has got to do with the assumption that each group’s observations is not dependent on another group’s observations. Lastly, the ‘no outliers’ assumption, as Myers, Well, and Lorch (2010) point out, relates to the assumption that the group outliers are not extreme, i.e. to the extent of having an adverse impact of the test results.