Nonparametric Tests

Parametric data

In the past, if our data wasn’t normally distributed, we’d likely have resorted to using nonparametric statistics or unnecessary forms of data transformation. Statistics that rely on normally distributed data are called parametric. Most people would now agree that these techniques are generally outdated and unnecessary. That said, there may be times when we find them helpful, and they’re good to know about.

Nonparametric data

Let’s start by considering why nonparametric statistics were considered beneficial, and why they might still be considered such under some conditions. The primary reason is that nonparametric statistics make no assumptions about our data. We can pretty much have any data and still analyze it with nonparametric statistics. They don’t need to be normal. They don’t need to be anything. And therein lies their beauty. When all else fails, we can use nonparametric statistics.

Importance of non-parametric statistics

Now, let’s discuss why nonparametric statistics are frowned upon nowadays. For one thing, we aren’t analyzing our data anymore. Seriously, we don’t analyze our actual data. Instead, we’re usually testing the difference in the ranked order of our data.

What does that mean? Well, imagine we take all the data we’ve painstakingly collected and line the numbers up and order them from smallest to most significant. Then, we assign them ranks (for example, 1, 2, 3, and so on). When it’s time to run the analysis, we’re no longer analyzing the numbers themselves but their ranks. It’s like asking, “Does group A have more big numbers than group B?” as opposed to asking if the values in group A are different from those in group B.

More importantly, nonparametric tests are generally considered to have low power, meaning that their ability to distinguish between two groups that aren’t extremely different isn’t very good. Presumably, we want statistics that can discriminate the differences between our treatment groups, and nonparametric statistics can only really do that if the differences are enormous. The good thing about nonparametric statistics is that they’re very conservative and unlikely to give us a false-positive result. Using these methods, we can be pretty confident that our groups are indeed ...