Parametric vs Nonparametric Statistical Tests
A key part of statistics is the process of using collected data to perform statistical inference. There are two types of statistical inferences: estimation and hypothesis testing. Estimation is using data from a sample to estimate or predict a parameter of interest in a population. Hypothesis testing is using data from a sample to assess the validity of a statement about a population parameter. Several statistical tests that can be used to determine if a statement is true. These tests can be classified into two types: parametric and nonparametric tests.
Review of Fundamental Statistical Concepts:
Before presenting the definitions of parametric and nonparametric tests, it is important to review some fundamental statistical concepts that serve as the basis for these tests.
The goal of statistics is to collect data from all individuals of interest, called a population. However, this is usually impossible since collecting data from an entire population can be too time-consuming and expensive. Because of this, the solution is to collect data from a subset of the population of interest. This is called a sample. This is done to discover some ‘truth’ about the population. When talking about a population, important values such as means, standard deviations, and proportions are called parameters. Since it is usually impossible to gather data from an entire population, we cannot know the true values of the parameters for a population. We can, however, use our sample to estimate these values. The estimates that come from a sample are called statistics. In other words, sample statistics are used to estimate population parameters.
Parametric vs Nonparametric Tests:
In a nutshell, a parametric statistical test assumes certain things about the population parameters and the distributions that the data come from. These tests include Student’s T-tests and ANOVA tests. Because these tests assume an underlying statistical distribution, a variety of conditions must be met for the results of a parametric test to be reliable. These include satisfying conditions for the randomness and size of a sample. However, the main assumption that these tests make is that the values are approximately normally distributed in the population. Note that it is not the data in the sample that is normally distributed, but rather it is the data in the full population that is assumed to be normal (i.e. most observations are in the center of the distribution while fewer are in the extremes).
On the other hand, a nonparametric statistical test does not assume anything about the population parameters. These are often called “distribution-free tests” since they do not assume an underlying distribution. These tests can be used even if the parametric conditions are not met. These tests include Wilcoxon tests and the Kruskal-Wallace test.
Every parametric test has a nonparametric equivalent. The table below, adapted from this Mayo Clinic article, illustrates this point.
To learn more about different parametric tests and see their nonparametric equivalent visit this link.
Why not use nonparametric tests all the time?
Since every parametric test has a nonparametric equivalent, it can be tempting to default to only using nonparametric tests. After all, they make fewer assumptions about the distribution and parameters of the population in question and can be used even if the parametric conditions are not met. While this is true, there are few drawbacks to nonparametric tests.
The first is that nonparametric tests tend to be less statistically powerful compared to their parametric equivalent. Statistical power is the probability that the tests will allow us to reject the null hypothesis when it is false. It is the probability of making the correct decision when the null hypothesis is false. Greater statistical power means that a test is more likely to detect significant differences if they truly exist. Simply put, statistical power is the probability of not making a Type II Error. Parametric tests are simply more statistically powerful. Nonparametric tests require slightly larger sample sizes to have the same statistical power as their parametric counterpart.
The second is that the results of nonparametric tests are less easy to interpret. Many nonparametric tests use rankings of values in the data rather than the actual data. This may not be intuitive or as useful as receiving actual data.
When your data allows for it, it is best to use a parametric test. Nonparametric tests have their uses but you must consider them carefully. Below you’ll find some reasons why one would use one test over the other.
Reasons to Use Parametric Tests:
- Parametric tests perform well with skewed and nonnormal distribution, provided that they meet the sample size conditions for the test. (e.g. a one-sample t-test requires that the sample size be greater than 20)
- Parametric tests perform well when the spread of each group is different. While nonparametric tests don’t assume normality, some require that all groups being compared have the same spread. This isn’t required for parametric tests.
- Parametric tests typically have more statistical power.
Reasons to Use Nonparametric Tests:
- Nonparametric tests are valid when data does not meet the assumptions associated with the desired parametric test.
- Nonparametric tests are often a good option for small sample sizes where parametric assumptions of normality are worrisome.
- Nonparametric tests can be used when an area of study is best represented by the median (e.g. income)
- Nonparametric tests can be used to analyze ordinal data, ranked data, or when outliers can’t be removed from the data.
Further Reading:
Click Here to learn more about different nonparametric tests and when to use them.
Sources:
Statistics How To — What are Parametric Statistics?
The Minitab Blog — Choosing Between a Nonparametric Test and a Parametric Test
Mayo Clinic — Parametric and Nonparametric: Demystifying the Terms
