Why You Should Use Non-Parametric Tests
By: Graham Waters
Tags: Statistics, Tests, Data, Non Parametric, Analysis

Why You Should Use Non-Parametric Tests

If your data insists on acting in non-normal ways then you may want to consider a non-parametric (NP) test. Why? Because, in contrast to parametric tests, non-parametric tests do not require data to be normally distributed. There can be many causal factors that made your data less than optimally distributed and in many cases, biases exist that are nearly impossible to eradicate. Andy Field (2013) calls these assumption-free tests which is a fantastic way of saying that they don’t assume as much about the state of your data as other tests do. They are less needy than their parametric counterparts.

Figure 1. Example of Non-Normal Data (Commute Times Graph, 2020).

How do they do this?

The mechanics behind the NP test allow the statistician to ignore the non-normal distribution of their data by transforming it. The data is transformed into an ordinal format. Because ordinal data is ranked it makes it much easier to analyze. Once ranked the data can be analyzed in a modular format. Each rank is considered individually which eliminates the problem of outliers in the data set (Field, 2013). It is actually an elegant statistical solution to the normality problem. Figure 2 shows a decision tree for inferential statistics. It gives context to the differences between parametric and non parametric tests.

Figure 2. Decision Tree for inferential statistics from Grosofsky (2009).

Okay, so why don’t we use Non-Parametric Tests all the time?

Statisticians avoid NP tests if at all possible because they eliminate some of the insights that Parametric tests provide. For example, the distances between scores in their original order is inaccessible once the data set is transformed and ranked. This is one reason that some have expressed that NP tests have less power than Parametric tests. In one sense this is true because of the lost insight into the differences; however, there are many times when the data is entirely unable to be analyzed by parametric tests and in those situations NP tests are much more powerful (Field, 2013).

There are cases where Parametric Tests may fail and yet still be useful. As an example consider ANOVA tests. The ANOVA assumptions being violated don’t necessarily render your analysis of no value. You can use the Welch and Brown-Forsythe Tests and check their significance. As Field (2013) points out in section 11.7.1, we can determine whether we need to use these tests by checking Levene’s Test. If Levene’s is not significant, as defined by the traditional threshold of 5% or 0.05), then the variances between your groups are not significantly different. If this were not the case, then the homogeneity of variance would be violated, necessitating changes. Welch’s F and the Brown-Forsythe F are good for this situation.

Finally, Non-Parametric Tests are used when your data is non-normal. That is their primary and best purpose. If your data can conform to a normal distribution then winsorize it, transform it or do anything you can to make parametric tests work. Don’t feel that all is lost if it proves to be impossible though, as non-parametric tests are ready and willing to help out.

References

Commute Times Graph. (2020). https://files.realpython.com/media/commute_times.621e5b1ce062.png

Field, A. (2013). Discovering Statistics Using IMB SPSS Statistics (4th ed.). SAGE Publications Ltd.

Grosofsky, A. (2009). Statistics Decision Aids [PDF]. Retrieved from http://teachpsych.org/resources/Documents/otrp/resources/grosofsky09.pdf