Data Assumptions and Nonparametric Analysis

Unlike parametric procedures, nonparametric tests do not rely on assumptions about the data's distribution. They are often chosen when standard assumptions are violated, when sample sizes are too small, or when the measurement scale renders parametric methods inappropriate. Common nonparametric techniques include the chi-square test, two-way contingency analysis (a variant of the chi-square test), and the Mann-Whitney U test.

Parametric methodssuch as the t-test, ANOVA, and multiple regressionassume specific properties of the population from which the sample is drawn. While these tests are powerful and useful, their assumptions are not always satisfied. In such cases, researchers can turn to nonparametric alternatives that do not require the same conditions. Although nonparametric tests typically have somewhat less statistical power, they are suitable when parametric tests cannot be applied, a situation that frequently arises with small samples.

Question:

1)). Considering the impact of data analysis when the data distribution does not meet expected assumptions. Also, considering conditions in which a nonparametric test is the most appropriate test,

a)). Provide a comparison of the similarities and differences of parametric and nonparametric analyses in the context of data assumptions.

b)). Provide at least one (1) example of a parametric statistical test and its nonparametric equivalent, and explain how these examples demonstrate the comparison of the two types of analysis.

c)). Provide an explanation of the conditions under which an independent researcher/scholar would use a nonparametric test (e.g.,Mann-WhitneyU-testover the independent samplest-test),including supportive examples from the suggested references.

Suggested References

Salahuddin, A. F., Khan, M. M. A., Ullah, M. O., & Jahan, N. (2015).Job satisfaction and university administrative staffs: An exploratory study.Journal of Applied Quantitative Methods, 10(4), 27-39.

Yu, W., Azizi, L., & Ormerod, J. T. (2020). Variational nonparametric discriminant analysis.Computational Statistics and Data Analysis,142. https://doi.org/10.1016/j.csda.2019.106817

Treister, R., Nielsen, C. S., Stubhaug, A., Farrar, J. T., Pud, D., Sawilowsky, S., & Oaklander, A. L. (2015). Experimental Comparison of Parametric Versus Nonparametric Analyses of Data From the Cold Pressor Test.Journal of Pain,16(6), 537-548. https://doi.org/10.1016/j.jpain.2015.03.001

Wu, J. C., & Wilson, C. L. (2007). Nonparametric analysis of fingerprint data on large data sets.Pattern Recognition,40(9), 2574-2584. https://doi.org/10.1016/j.patcog.2006.11.021

Green, S. B., & Salkind, N. J. (2016).Using SPSS for Windows and Macintosh(8th ed.). Pearson Education (US).https://mbsdirect.vitalsource.com/books/9780134416441