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Description

**Q: By comparison, which of the main assumptions of the parametric test is more critical?**

Parametric and Nonparametric Test.

In statistics, a parameter means an aspect of a population, for instance, a population mean, which is quite different from a statistic that means an aspect regarding a sample, for instance, a sample mean. Before performing any parametric analyses, it is important to evaluate the data and ascertain that some specific assumptions have been fulfilled (Derrick et al., 2020). Parametric statistical tests use analytical tools to compare data groups with continuous variables, for instance, the Analysis of Variance (ANOVA) test and the Students test (Derrick et al., 2020). Parametric statistical testing makes assumptions regarding a populations parameter and the allotments that the data originated from.

Examples of assumptions made in parametric statistical testing are that data in each group being compared displays a normal or Gaussian distribution (Derrick et al., 2020). Another assumption is that data in each group being compared displays identical degrees of homogeneity of variance or homoscedasticity ((Derrick et al., 2020). While parametric tests require a population for assumptions, non-parametric tests do not require any populations for assumptions (Nahm, 2016). Non-parametric or distribution-free tests do not rely on a certain data set describing a specific parametric group of probability (Nahm, 2016). Thus, the main assumptions in non-parametric tests are independence and randomness (Nahm, 2016).

From the assumptions listed, it is pretty clear that a researcher may decide to use a parametric test when the data presented follows a certain distribution, such as normal distributions (Derrick et al., 2020). Parametric tests are generally considered more powerful (Derrick et al., 2020). Non-parametric tests, on the other hand, are used when the data presented is not normally distributed. In addition to the type of data, the type of variables collected in the dataset determine which method to use. Normally, non-parametric tests are used on nominal values or values that lack quantitative significance (Nahm, 2016). On the other hand, Parametric tests require interval or ratio data, i.e., quantifiable data (Derrick et al., 2020).

**References.**

Derrick, B., White, P., & Toher, D. (2020). Parametric and non-parametric tests for the comparison of two samples which both include paired and unpaired observations. *Journal of modern applied statistical methods*, *18*(1), 9.

Nahm, F. S. (2016). Nonparametric statistical tests for the continuous data: the basic concept and the practical use. *Korean journal of anesthesiology*, *69*(1), 8.

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