# address the content of each colleague’s analysis and evaluation of the topic and of the integration of the relevant resources.

**Respond to two or more** of your colleagues’ postings in one or more of the following ways:

- Address the content of each colleague’s analysis and evaluation of the topic and of the integration of the relevant resources.
- Link each colleague’s posting to other colleagues’ postings or to other course materials and concepts, where appropriate and relevant.
- Extend or constructively challenge your colleagues’ work.
- Answer question(s) posed by your colleague(s) for further discussion.

Please note that for each response you must include **a minimum of one** appropriately cited scholarly reference.

**Original question **

**Post **an analysis of the relationship between data assumption violations and nonparametric analyses. In your analysis, do the following:

· Compare the similarities and differences of parametric and nonparametric analyses in the context of data assumptions.

· Provide at least one example of a parametric statistical test and its nonparametric equivalent, and explain how these examples illustrate the comparison of the two types of analysis.

· Explain conditions under which you would use a nonparametric test (e.g., Mann-Whitney U-test over the independent samples t-test), including supportive examples from the course Resources for your explanation.

Mythily

Data Assumptions and Nonparametric Analyses

Parametric statistical analysis methods are based on the numerical value of the mean while analysis by nonparametric methods is based onrank order (Morris, 2000). Parametric statistics require data to be normally distributed, represent sample size, and generally numeric in nature (Morris, 2000; Saunders, Lewis, & Thornhill, 2015). Nonparamteric methods do not concern with the variability of the data samples, which can be ordinal in nature. Nonparametric methods are not frequently used, however, there are equivalents for every parametric test (Morris, 2000).

Analysis of Variance test (ANOVA) is parametric and Kruskal-Wallis test is its nonparametric equivalent (Green & Salkind, 2017; Morris, 2000). When the dependent variable in the study is on an interval or ratio scale, ANOVA, Kruskal-Wallis, or median tests can be used. If the dependent variable is ordinal, then the Kruskal-Wallis test is preferred because the medians are more meaningful measure of central tendency for ordinal data (Green & Salkind, 2017).

Independent samples *t*-test is a parametric test and its nonparametric equivalent is the Mann-Whitney *U* test (Green & Salkind, 2017; Morris, 2000). If the normality assumption for the independent samples t-test is not met, the nonparametric tests can be more powerful (Green & Salkind, 2017).

References

Green, S. B., & Salkind, N. J. (2017). *Using SPSS for Windows and Macintosh: Analyzing and understanding data* (8th ed.). Upper Saddle River, NJ: Pearson.

Morris, R. E. (2000). The use of nonparametric statistics in quantitative electron microscopy. *Journal of Electron Microscopy*, *49*(4), 545. Retrieved from https://search-ebscohost-com.ezp.waldenulibrary.org/login.aspx?direct=true&db=edb&AN=101215914&site=eds-live&scope=site

Saunders, M. N. K., Lewis, P., & Thornhill, A. (2015). *Research methods for business students* (7th ed.). Essex, England: Pearson Education Unlimited.

Juan,

**Compare the similarities and differences of parametric and nonparametric analyses in the context of data assumptions.**

** **Saunders**, **Lewis, and Thornhill (2015) noted that both parametric and nonparametric tests are used to compare relationships between variables, and to evaluate the statistical significance of the data gathered. According to Green, and Salkind (2017), unlike parametric tests, nonparametric tests do no assume underlying statistical distributions in data. Additionally, nonparametric tests are less statistical powerful than parametric tests, require fewer validity conditions, and unlike parametric test nonparametric test mainly uses the central tendency of the median instead of the mean (Weinberg, & Schumaker, 1962). Wienclaw (2019) noted that parametric tests provide robust results when variability differ, while nonparametric tests are well suited to analyze data not randomly sampled.

** **

**Provide at least one example of a parametric statistical test and its nonparametric equivalent, and explain how these examples illustrate the comparison of the two types of analysis.**

Fay and Proschan (2010) discussed the use of the Wilcoxon-Mann-Whitney in situations where the researcher wants to compare two sample means from the same population. Additionally, the researchers highlighted that the choice of a nonparametric test is based on circumstances when the data does not meet the assumptions of the t-test. As the authors described, the decision to utilize the Wilcoxon-Mann-Whitney test as an alternative to the t-test increases opportunities for researchers to evaluate hypothesis when the variable is not normally distributed or when the dependent variable is measured as ordinal or categorical.

** **

**Explain conditions under which you would use a nonparametric test (e.g., Mann-Whitney U-test over the independent samples t-test), including supportive examples from the course Resources for your explanation.**

** **According to Green, and Salkind (2017) the usefulness of nonparametric test provides researchers with additional statistical analysis for situations were variables are nominal or ordinal and very little is known about the population parameters. As an example, Salahuddin, Khan, Ullah, and Jahan (2015) relied on the chi-square test to evaluate the relationship job satisfaction of respondents.

** **

References

Fay, M. P., & Proschan, M. A. (2010). Wilcoxon-Mann-Whitney or t-test? On assumptions for hypothesis tests and multiple interpretations of decision rules. *Statistics Surveys*, *4*, 1–39. Retrieved from https://search-ebscohost-com.ezp.waldenulibrary.org/login.aspx?direct=true&db=mnh&AN=20414472&site=eds-live&scope=site

Green, S. B., & Salkind, N. J. (2017). *Using SPSS for Windows and Macintosh: Analyzing and understanding data* (8th ed.). Upper Saddle River, NJ: Pearson.

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. Retrieved from http://www.jaqm.ro/

Saunders, M. N. K., Lewis, P., & Thornhill, A. (2015). *Research methods for business students* (7th ed.). Essex, England: Pearson Education Unlimited

Weinberg, G. H., & Schumaker, J. A. (1962). Nonparametric statistical tests. *Statistics: An intuitive approach.* (pp. 291–305). Belmont, CA: Wadsworth Publishing Company.

Wienclaw, R. A. (2019). Introduction to nonparametric methods. *Salem Press Encyclopedia*. Retrieved from https://search-ebscohost-com.ezp.waldenulibrary.org/login.aspx?direct=true&db=ers&AN=89163799&site=eds-live&scope=site