Life is full of unexpected events and experiences that we might describe as anything but normal. It should come as no surprise then that data can behave in much the same way. When you encounter data with an underlying distribution that is unknown or non-normal, you can’t reach for your trusty parametric tools. Instead, you’ll need to stock your toolkit with non-parametric tools for robust analysis.
Chances are you’ve got questions about these tools and how to use them, so let’s jump right in and get them answered!
What are Non-Parametric Analysis Tools?
Non-Parametric analysis tools are your ticket to analyzing data that is unknown or non normal. Instead of using means, these tests use medians. Likewise, they make use of ranks instead of measurements and signs of differences instead of measured differences. While Non-Parametric tests do not have the power that parametric tests have, they are typically more robust to outliers and extreme values, making them useful for the analysis of non normal data.
So what do we mean when we refer to data that is not normal? Let’s look an example to best illustrate the concept. Imagine you’re working with order processing. The majority of the orders are processed and completed in less than a week’s time. However, a few orders take 2 weeks or longer. In this scenario, you would be looking at 3 Non-Parametric tools to aid your analysis:
1. 1-Sample Sign Test
2. The Mann-Whitney Test
3. Mood’s Median Test
If these 3 tools reminded you of the 1-Sample T-test, 2-Sample T-test, and the ANOVA, you’re right on target. They are the parametric equivalents in the toolbox.
Why Would I Perform a Non-Parametric Test?
Before we dive deeper into the Non-Parametric toolkit, we should review non-parametric tests themselves. These statistical tests are void of parameters and are often used to test a hypothesis. As discussed earlier, the data is non-normal and unlikely to transform. Generally speaking, it is better to use larger sample sizes for non-parametric tests to generate more powerful results.
Some of the most useful applications for these tests can be found in the analysis of data ranked in order, data lacking a normal distribution, and for data where information regarding the application is lacking.
How Should I Use the Non-Parametric Tools?
As for the tools themselves, the 1-Sample Sign Test looks for a notable difference between the proposed and sample medians. In these tests, the null hypothesis proposes that the null median and proposed median are the same.
If you are working with a null hypothesis that the two medians are equivalent, use the Mann-Whitney Test to analyze the two sample medians. For the analysis of multiple medians, use the Mood’s Median Test to determine if any of the medians are significantly different. The null hypothesis is that they are all equivalent.
Of course, in the case of normal data, standard parametric tools are preferable. However, non-parametric tools provide a much needed way to analyze nonnormal data and make conclusions based on the results.
Now that you’ve gotten your feet wet in non-parametric tools, dive right into the world of Lean measurement and analysis. We offer a course in partnership with the Portland State Center for Executive and Professional Education – SS511: Hypothesis Testing for Observational Data. Winter 2017/2018 registration is now open, so register today!