Parametric and Non-Parametric Tests

Selecting between parametric and non-parametric tests can be a confusing task.  There are many tests which are applicable to certain types of data and situations.  This post discusses parametric and non-parametric analysis and offers advice in the selection of the appropriate test.

Parametric Analysis

Parametric tests assume a normal distribution of data (Field, 2013).  The data must also be equally dispersed, also termed homogeneity of variance.  The data must be interval or ratio data. Lastly, the observations must be independent.  If data satisfies the requirements for parametric analysis, then a parametric test should be utilized.

Non-parametric Analysis

Non-parametric tests make fewer assumptions about data than do parametric tests (Field, 2013).  For example, non-parametric analysis is well suited to ordinal data which does not satisfy the requirements of parametric tests.  Another reason to utilize a non-parametric test is if the median better represents the central tendency of the data than does the mean (Frost, 2015).  This is an indication that the data is skewed and may contain outliers.  Non-parametric tests are also applicable when the sample size is smaller than that necessary for parametric approaches.

Comparison of Tests

Table 1 contains the various types of analysis and the corresponding parametric and non-parametric tests.  It was constructed by combining materials from Dr. Miller’s lecture with other sources (Frost, 2015; Hoskin, 2014; Miller, 2017).  The table breaks down the types of test that are appropriate for a kind of analysis.  If the data is parametric in nature, then a test in the corresponding parametric column should be utilized.

Table 1: Parametric and Non-Parametric Tests

Type of Analysis	Parametric	Non-Parametric
Is a sample similar to a known population	T-Test or Z-Test	Sign Test
Comparing means of independent groups	Two-sample T-Test	Mann-Whitney U Test
Comparing two quantitative measurements from the same individual	Paired T-Test	Wilcoxon Signed-Rank
Comparing means between three or more independent groups	1-way Analysis of Variance (ANOVA)	Kruskal-Wallis
Multiple comparisons of means	2-way Analysis of variance (ANOVA)	Friedman
Estimating the degree of association between two quantitative variables	Pearson Correlation Coefficient	Spearman’s Rank Correlation Coefficient and Kendall’ Tau Coefficient

 

Conclusion

The selection of a test is guided by understanding the type of analysis to be performed and the nature of the associated data.  Enumerating and discussing each scenario and test is beyond the scope of this assignment.  This, and Dr. Miller’s, table does provide a starting point for selecting the appropriate test.

References

Field, A. (2013). Discovering statistics using IBM SPSS statistics: Sage.

Frost, J. (2015). Choosing Between a Nonparametric Test and a Parametric Test.  Retrieved from http://blog.minitab.com/blog/adventures-in-statistics-2/choosing-between-a-nonparametric-test-and-a-parametric-test

Hoskin, T. (2014). Parametric and nonparametric: Demystifying the terms. Mayo Clinic CTSA BERD Resource Retrieved from http://www mayo edu/mayo-edudocs/center-fortranslational-science-activities-documents/berd-5-6.pdf.

Miller, R. (Producer). (2017, 2/11/2017). Re-record of chat on non-parametrics. Retrieved from http://ctuadobeconnect.careeredonline.com/p29vwep0e20/?launcher=false&fcsContent=true&pbMode=normal