Non-Parametric Inferential Statistics: Definition & Examples

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  • 0:01 Normal
  • 0:28 Parametric Methods
  • 1:26 Non-Parametric Methods
  • 2:25 Example of a…
  • 3:15 Lesson Summary
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Lesson Transcript
Instructor: Artem Cheprasov

Artem has a doctor of veterinary medicine degree.

In this lesson, you're going to learn about the major differences between parametric and non-parametric methods for dealing with inferential statistics, as well as see an example of the non-parametric method.


What is normal? At least in the world of statistics, this has nothing to do with how someone dresses, acts, or what their beliefs are. Normal data comes from a population with a normal distribution. A normal distribution is a distribution that has a symmetrical bell-shaped curve to it, which you're probably well aware of.

Keep this concept in mind as we go over the major differences between parametric and non-parametric statistics.

Parametric Methods

First, let's define our terms really simply. When we talk about parameters in statistics, what are we actually hinting at? Parameters are descriptive measures of population data, such as the population mean or population standard deviation.

When the variable we are considering is approximately (or completely) normally distributed, or the sample size is large, we can use two inferential methods that are concerned with parameters - appropriately called parametric methods - when performing a hypothesis test for a population mean. For instance, if we find that the distribution of the average salary of a sample looks like a bell curve, then parametric methods may be used.

These two methods are probably ones you've heard of before. They are the z-test, which we'd use when the population standard deviation is known to us; or the t-test, which we'd use when the population standard deviation is not known to us.

Non-Parametric Methods

Inferential methods that are not concerned with parameters are known, easily enough, as non-parametric methods. However, this term is also more broadly used to refer to many methods that are applied without assuming normality. So, for instance, if we find that the distribution of the average salary of a sample looks like the histogram you see on the screen now [see video], which is nothing close to that of a bell curve, then we will have to turn to non-parametric methods.

Such non-parametric methods have their pros and cons. On the pro side, these methods are usually simpler to compute and are more resistant to extreme values when compared to parametric methods. On the con side, if the requirements for the use of a parametric method are actually met, non-parametric methods do not have as much power as the z-test or t-test.

By power, I simply mean the probability of avoiding a type II error, which is an error where we fail to reject the false null hypothesis.

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