Explain the difference between Parametric and Non Parametric tests of Significance

November 01, 2019

In statistics, parametric and nonparametric methodologies refer to those in which a set of data has a normal vs. a non-normal distribution, respectively. Parametric tests make certain assumptions about a data set; namely, that the data are drawn from a population with a specific (normal) distribution. Non-parametric tests make fewer assumptions about the data set. The majority of elementary statistical methods are parametric, and parametric tests generally have higher statistical power. If the necessary assumptions cannot be made about a data set, non-parametric tests can be used. Here, you will be introduced to two parametric and two non-parametric statistical tests.
What is the difference between a parametric and a nonparametric test?
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. 

Nonparametric tests do not rely on any distribution. They can thus be applied even if parametric conditions of validity are not met.  Parametric tests often have nonparametric equivalents. You will find different parametric tests with their equivalents when they exist in this grid. The benefit of non-parametric tests over parametric tests is that they not make any assumptions about the data. Thus, they are well-suited in situations where the assumptions of parametric tests are not met, which is typically the case for small sample sizes.

Nonparametric tests don’t require that your data follow the normal distribution. They’re also known as distribution-free tests and can provide benefits in certain situations. Typically, people who perform statistical hypothesis tests are more comfortable with parametric tests than nonparametric tests.

You’ve probably heard it’s best to use nonparametric tests if your data are not normally distributed or something along these lines. That seems like an easy way to choose, but there’s more to the decision than that.

In this post, compare the advantages and disadvantages to help you decide between using the following types of statistical hypothesis tests:
Parametric analyses to assess group means
Nonparametric analyses to assess group medians

In particular,  like you to focus on one key reason to perform a nonparametric test that doesn’t get the attention it deserves! If you need a primer on the basics, read my hypothesis testing overview.
What is the advantage of using a nonparametric test?
Nonparametric tests are more robust than parametric tests. In other words, they are valid in a broader range of situations (fewer conditions of validity).
What is the advantage of using a parametric test?

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 with a parametric test will be lower than the p-value associated with a nonparametric equivalent that is run on the same data.

Many people aren’t aware of this fact, but parametric analyses can produce reliable results even when your continuous data are nonnormally distributed. You just have to be sure that your sample size meets the requirements for each analysis in the table below. Simulation studies have identified these requirements. Read here for more information about these studies.

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