Parametric and non-parametric tests are used in the statistical analysis of data from research studies. The selection of parametric versus non-parametric tests is based on whether or not data fits into pre-determined parameters. Parametric statistics are always correlated with a certain set of expectations that the data must meet because formulas of parametric statistics yield valid results only when the properties of the data are within the confines of these assumptions. It is assumed that the research study data are normally distributed for all parametric tests. If the data does not fit into parametric assumptions, it can be more appropriately categorized into nonparametric alternatives because nonparametric statistical procedures can convert original data to rank-ordered data (Gray et al, 2016).
An example of parametric analyses used to test for significant differences between group means of two independent samples is the independent samples t-test. The independent samples t-test examines differences between two independent groups. The samples are independent if the study participants in one group are unrelated to or different from the participants in the second group. Use of the independent samples t-test involves the assumptions that sample means from the population are normally distributed, the dependent or outcome variable is measured at the interval/ratio level, the two samples have equal variance, and all observations within each sample are independent (Gray et al, 2016). The non-parametric alternative to the independent samples t-test is the Mann-Whitney U test. The Mann-Whitney U test should be used if the data do not meet the assumptions involving normality or equal variances for an independent samples t-test. Mann-Whitney U calculations translate the data to ranks while eliminating any inconsistency or normalcy problems associated with the original values (Gray et al, 2016).
Gray, J., Grove, S. & Sutherland, S. (2016). Burns and Grove’s The Practice of Nursing Research: Appraisal, Synthesis, and Generation of Evidence. (8th ed.). Elsevier – Health Sciences Division. ISBN: 9780323377584
There are numerous differences between non-parametric and parametric tests which manifest in the form of the applicability of each of the test and the assumption that underlie them. The major difference between the two tests, however, is that the parametric test is the hypothesis test which provides generalizations for making statements about the mean of the parent population (Murray, 2013). In the contrast, the non parametric test is a hypothesis test which is not based on underlying assumptions (Varabyova & Schreyögg, 2013). In other words, the non parametric test does not require populations distribution to be denoted by specific parameters. Also in the parametric test, the information regarding the population is known while in a non-parametric test, such information is totally unavailable.
Next, the two tests differ in terms of the level of measurement that may be used for each test. For the parametric test, the level of measurement is either is internal or ratio (John et al. 2013). For the non-parametric test, on the other hand, the level of measurement is either nominal or ordinal. The other difference between the two tests manifests in the form of the measure of central tendency. For the parametric test, the primary measure of central tendency is the mean (Hoskin, 2012). In contrast, the measure of central tendency for the non parametric test is the median. Lastly, the correlation applied for the parametric and the non-parametric tests differ whereby the Pearson test is used for the parametric test while the spearman one is used for the non-parametric test.
An example of when the non-parametric test could be used in research is when the available data is not normal. For example, a researcher can consider the distribution of the available data and determine where a parametric or a non parametric approach should be used. If the researcher finds out that the available data is approximately normal, then it would be advisable to use parametric statistical tests (Murray, 2013). If the data is normal, on the other hand, then the non parametric test would be used. The non-parametric tests should only be specifically used when (John et al. 2013):
Distinctly non-normal and cannot be transformed
From a sample that is too small for the central limit theorem to lead to normality of averages
From a distribution not covered by parametric methods
From an unknown distribution
Nominal or ordinal
A parametric approach, on the other hand, should be used if (Murray, 2013):
The assumptions for the population probability distribution hold true
The sample size is large enough for the central limit theorem to lead to normality of averages
The data is non-normal but can be transformed.
Murray, J. (2013). Likert data: what to use, parametric or non-parametric?. International Journal of Business and Social Science, 4(11).
Varabyova, Y., & Schreyögg, J. (2013). International comparisons of the technical efficiency of the hospital sector: panel data analysis of OECD countries using parametric and non-parametric approaches. Health policy, 112(1-2), 70-79.
Hoskin, T. (2012). Parametric and nonparametric: Demystifying the terms. In Mayo Clinic (pp. 1-5).
John, J. M. M., Van Lishout, F., Gusareva, E. S., & Van Steen, K. (2013). A robustness study of parametric and non-parametric tests in model-based multifactor dimensionality reduction for epistasis detection. BioData mining, 6(1), 9