Differentiate between parametric and nonparametric statistical analysis?

First of all, it is better to know each of them, then I want to elaborate to find the majors differences between both of them, in details. Indeed, inferential statistical procedures generally fall into two possible categorizations: parametric and non-parametric.

In the literal meaning of the terms, a parametric statistical test is one that makes assumptions about the parameters (defining properties) of the population distribution(s) from which one's data are drawn, while a non-parametric test is one that makes no such assumptions.

In this strict sense, "non-parametric" is essentially a null category, since virtually all statistical tests assume one thing or another about the properties of the source population(s). For practical purposes, you can think of "parametric" as referring to tests, such as t-tests and the analysis of variance, that assume the underlying source population(s) to be normally distributed; they generally also assume that one's measures derive from an equal-interval scale. And you can think of "non-parametric" as referring to tests that do not make on these particular assumptions. Non-parametric tests are sometimes spoken of as "distribution-free" tests.

In the other words, parametric tests assume underlying statistical distributions in the data. Therefore, several conditions of validity must be met so that the result of a parametric test is reliable. For example, Student’s t-test for two independent samples is reliable only if each sample follows a normal distribution and if sample variances are homogeneous. As well, nonparametric tests do not rely on any distribution. They can thus be applied even if parametric conditions of validity are not met. Nonparametric tests are more robust than parametric tests. In other words, they are valid in a broader range of situations (fewer conditions of validity). The advantage of using a parametric test instead of a nonparametric equivalent is that the former will have more statistical power than the latter. In other words, a parametric test is more able to lead to a rejection of H0. Most of the time, the p-value associated to a parametric test will be lower than the p-value associated to a nonparametric equivalent that is run on the same data.

To make the generalization about the population from the sample, statistical tests are used. A statistical test is a formal technique that relies on the probability distribution, for reaching the conclusion concerning the reasonableness of the hypothesis. These hypothetical testing related to differences are classified as parametric and nonparametric tests. The parametric test is one which has information about the population parameter. On the other hand, the nonparametric test is one where the researcher has no idea regarding the population parameter. So, take a full read of this article, to know the significant differences between parametric and nonparametric test.

The fundamental differences between parametric and nonparametric test are discussed in the following points:

  1. A statistical test, in which specific assumptions are made about the population parameter is known as the parametric test. A statistical test used in the case of non-metric independent variables is called nonparametric test.
  2. In the parametric test, the test statistic is based on distribution. On the other hand, the test statistic is arbitrary in the case of the nonparametric test.
  3. In the parametric test, it is assumed that the measurement of variables of interest is done on interval or ratio level. As opposed to the nonparametric test, wherein the variable of interest are measured on nominal or ordinal scale.
  4. In general, the measure of central tendency in the parametric test is mean, while in the case of the nonparametric test is median.
  5. In the parametric test, there is complete information about the population. Conversely, in the nonparametric test, there is no information about the population.
  6. The applicability of parametric test is for variables only, whereas nonparametric test applies to both variables and attributes.
  7. For measuring the degree of association between two quantitative variables, Pearsons coefficient of correlation is used in the parametric test, while spearmans rank correlation is used in the nonparametric test.

In sum, to make a choice between parametric and the nonparametric test is not easy for a researcher conducting statistical analysis. For performing hypothesis, if the information about the population is completely known, by way of parameters, then the test is said to be parametric test whereas, if there is no knowledge about population and it is needed to test the hypothesis on population, then the test conducted is considered as the nonparametric test.

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