BIO 500 W8 Discussion Question 1
BIO 500 W8 Discussion Question 1
Discuss the differences between parametric and nonparametric tests.
Nonparametric tests don’t require that your data follow the normal distribution. They’re also known as distribution-free tests and can provide benefits in certain situations. Typically, people who perform statistical hypothesis tests are more comfortable with parametric tests than nonparametric tests.
You’ve probably heard it’s best to use nonparametric tests if your data are not normally distributed—or something along these lines. That seems like an easy way to choose, but there’s more to the decision than that.
In this post, I’ll compare the advantages and disadvantages to help you decide between using the following types of statistical hypothesis tests:
Nonparametric Tests vs. Parametric Tests
Nonparametric tests don’t require that your data follow the normal distribution. They’re also known as distribution-free tests and can provide benefits in certain situations. Typically, people who perform statistical hypothesis tests are more comfortable with parametric tests than nonparametric tests.
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You’ve probably heard it’s best to use nonparametric tests if your data are not normally distributed—or something along these lines. That seems like an easy way to choose, but there’s more to the decision than that.
In this post, I’ll compare the advantages and disadvantages to help you decide between using the following types of statistical hypothesis tests:
- Parametric analyses to assess group means
- Nonparametric analyses to assess group medians
In particular, I’d like you to focus on one key reason to perform a nonparametric test that doesn’t get the attention it deserves! If you need a primer on the basics, read my hypothesis testing overview.
Related Pairs of Parametric and Nonparametric Tests
Nonparametric tests are a shadow world of parametric tests. In the table below, I show linked pairs of statistical hypothesis tests
| Parametric tests of means | Nonparametric tests of medians |
| 1-sample t-test | 1-sample Sign, 1-sample Wilcoxon |
| 2-sample t-test | Mann-Whitney test |
| One-Way ANOVA | Kruskal-Wallis, Mood’s median test |
| Factorial DOE with a factor and a blocking variable | Friedman test |
Additionally, Spearman’s correlation is a nonparametric alternative to Pearson’s correlation. Use Spearman’s correlation for nonlinear, monotonic relationships and for ordinal data. For more information, read my post Spearman’s Correlation Explained!
For this topic, it’s crucial you understand the concept of robust statistical analyses. For more information, read my post, What are Robust Statistics?
Advantages of Parametric Tests
Advantage 1: Parametric tests can provide trustworthy results with distributions that are skewed and nonnormal
Many people aren’t aware of this fact, but parametric analyses can produce reliable results even when your continuous data are nonnormally distributed. You just have to be sure that your sample size meets the requirements for each analysis in the table below. Simulation studies have identified these requirements. Read here for more information about these studies.
| Parametric analyses | Sample size requirements for nonnormal data |
| 1-sample t-test | Greater than 20 |
| 2-sample t-test | Each group should have more than 15 observations |
| One-Way ANOVA |
|
You can use these parametric tests with nonnormally distributed data thanks to the central limit theorem. For more information about it, read my post: Central Limit Theorem Explained.
Related posts: The Normal Distribution and How to Identify the Distribution of Your Data.
Advantage 2: Parametric tests can provide trustworthy results when the groups have different amounts of variability
It’s true that nonparametric tests don’t require data that are normally distributed. However, nonparametric tests have the disadvantage of an additional requirement that can be very hard to satisfy. The groups in a nonparametric analysis typically must all have the same variability (dispersion). Nonparametric analyses might not provide accurate results when variability differs between groups.
Conversely, parametric analyses, like the 2-sample t-test or one-way ANOVA, allow you to analyze groups with unequal variances. In most statistical software, it’s as easy as checking the correct box! You don’t have to worry about groups having different amounts of variability when you use a parametric analysis.
Related post: Measures of Variability
Advantage 3: Parametric tests have greater statistical power
In most cases, parametric tests have more power. If an effect actually exists, a parametric analysis is more likely to detect it.