Criteria for non-parametric analysis
Non-parametric analysis draws upon a combination of statistical models and tests. The most frequently used nonparametric tests are McNemar-test, Kruskal-Wallis –test, Wilcoxon signed-rank test, and Mann-Whitney U test. MacNemar is used upon paired nominal datasets such as 2x2 contingency tables or dichotomies. Kruskal-Wallis is a one-way analysis of variance calculated on rank-transformed data, it is utilised for testing if samples originate from a similar distribution. It can be used to determine the comparisons between various different sample sizes and structures. Wilcoxon signed-rank –test is used when there are two sets of data drawn from a non-normal distribution and produces an equivalent result to that of a t-test. However, the results have greater statistical power than that of a t-test and it is more likely to produce statistically significant results. Mann-Whitney u –test is to test if random values from A or B are different from each other.
The term "non-parametric" is not meant to imply that the tests (or the model behind them) are without parameter assumptions, it is that the requirements placed upon them are more relaxed. Consequently, the parameters are not fixed, because they provide explanatory logic to the test. Researcher(s) using a non-parametric test can make the assumptions of an identically shaped and scaled distribution which does not require normal distribution. This differs from other statistical methods such as ANOVA, Pearson's correlation, t-test and others which do not make assumptions and which utilise samples from a normal distribution. Participant’s preferences and similar behaviours are considered to culminate in the development of a normal distributed dataset, but rarely do, as the data generation process relies on self-construction.
Interpretation of the results
As non-parametric statistics result in less assumptions being drawn from the data sample, this results in greater application than parametric statistics. However, in certain cases, parametric testing are more appropriate, while non-parametric methods will be less efficient. This is because non-parametric statistics do not utilise certain information within the dataset. Non-parametric statistics correspond better to natural phenomenon allowing for easier to use and validation. Thus, the removal or relaxation of parameters thresholds, result in more data becoming available for testing and applicable to a larger variety of tests.
Parametric and non-parametric methods are often used on different types of data. Parametric statistics generally require interval or ratio data. An example of this type of data is age, income, height, and weight in which the values are continuous and the intervals between values have meaning. Also the interval between the values are proportional, not only qualitative. Non-parametric statistics are typically used on data that nominal or ordinal. Nominal variables are variables for which the values have not quantitative value. Common nominal variables in social science research, for example, include sex, whose possible values are discrete categories, "boy" and "girl."' Ordinal variables are those in which the value suggests some order. An example of an ordinal variable would be if a survey respondent asked a question and the answer is given on 5-point Likert scale from agree to disagree.
Altman, D. G., & Bland, J. M. (2009). Parametric v non-parametric methods for data analysis. Bmj, 338.
Brodsky, E., & Darkhovsky, B. S. (2000). Non-parametric statistical diagnosis: problems and methods (Vol. 509). Springer Science & Business Media.
Härdle, W., & Linton, O. (1994). Applied nonparametric methods. Handbook of econometrics, 4, 2295-2339.
Kraska-Miller, M. (2013). Nonparametric statistics for social and behavioral sciences. CRC Press.
Pesaran, M. H., & Timmermann, A. (1992). A simple nonparametric test of predictive performance. Journal of Business & Economic Statistics, 10(4), 461-465.