Generally speaking, parametric tests work well with skewed and non-normal distributions where the spread of each group is different and non-parametric tests work well when the area is better represented by the medium, and there is a very small sample size. The decision on which test to use has to do on evaluating the mean or medium and how accurately it represents the center of the dataset’s distribution. Assuming an accurate sample size, if the mean does seem to represent the center of the dataset’s distribution, the parametric test may be a good choice. However, if the medium more accurately represents the center of the distribution, then a nonparametric test may want to be considered.
Some common parametric and non-parametric tests that can be useful in statistical analysis include:
- If comparing means between two groups, the parametric procedure could be the two-samples t-Test and the nonparametric procedure could include a Wilcoxon Rank-Sum test.
- If comparing two quantitative measurements from the same individual, the parametric procedure could be the Paired t-Test and the nonparametric procedure could be the Wilcoxon Signed-Rank test.
- If comparing means between three or more independent group, the parametric procedure could be the Analysis of Variance (or ANOVA) and the nonparametric procedure could be the Kruskal-Wallis test.
- If estimating the degree of association between two quantitative variables, the parametric procedures could include the Pearson coefficient of correlation and the non-parametric procedure could include the Spearman’s Rank Correlation.
Regarding which test to use in the list, it is best to first consider what you are trying to compare or estimate. In terms of scientific research, a useful process includes thinking through the potential the null and alternative hypotheses. The null hypothesis can include ideas like if the two approaches are equally effective. If it is found that the two approaches are the same, then the null hypothesis is good. Otherwise, an alternative hypothesis such as the two approaches not being equally effective may hold. However, each dataset may require a different type of comparison as well as parametric or non-parametric test. However, as illustrated above, the parametric and non-parametric tests kind of run parallel depending on the statistical analysis selected by the researcher that best fits the nature of the research question and data collected.
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