The field of statistics contains two types of variables: dependent and independent. Similarly, statisticians use various types of tests, parametric and non-parametric.
Key Takeaways
- Parametric tests are based on assumptions regarding the population’s underlying distribution, while nonparametric tests do not require such assumptions.
- Nonparametric tests are more robust to outliers and non-normal data than parametric tests.
- Parametric tests tend to have greater statistical power, but nonparametric tests are preferable when assumptions for parametric tests are not met.
Parametric vs Nonparametric
The main difference between these two tests is that one is dependent, and the other is independent to a certain extent from parameters like mean, standard deviation, variation, and Central Limit Theorem. All of these are different parameters calculated on the data available. However, every parametric test has a nonparametric counterpart or equivalent.
Parametric statistical procedures are described as those whose results rely on the assumption of the shape of the data distribution (Example: Normal Distribution) and the parameters of the assumed distribution.
Nonparametric statistical procedures are described as those whose results rely on no or few assumptions of the shape of the data distribution or about the parameters of the assumed distribution. Their application is more flexible and robust as they do not depend on any assumption or pre-defined conditions for the data.
Comparison Table
| Parameters of Comparison | Parametric | Nonparametric |
|---|---|---|
| Definition | The test whose outcomes depend on the distribution is called a parametric test. | The test whose outcomes do not depend on the distribution is called a nonparametric test. |
| Statistical power | Parametric tests have higher statistical power. | Nonparametric tests have lower statistical power. |
| Versatility | Parametric tests do not apply to all situations. | Nonparametric tests are more robust and can be applied to different situations. |
| Central Tendency value | The mean value is the central tendency value for this test. | The median value is the central tendency value for this test. |
| Type of distribution | It is used on data that follows a normal distribution. | It is used on data that follows any arbitrary distribution. |
What is Parametric Test?
A parametric statistical test assumes the parameters of the population and the distributions of the data it came from. The parametric test is used for quantitative data with continuous variables.
The most widely and commonly used parametric tests are the t-test (for sample size less than 30), Z-test (for sample size greater than 30), ANOVA, and Pearson’s rank Correlation. The central tendency value considered is the mean of the distribution and is mostly applicable to normal data distribution.
Continuous distributions like the data about various heights or weights of a species over time and data about temperatures are examples where parametric tests are used. Although, due to the assumptions about the data, its application is a little less versatile in real life.
What is Nonparametric Test?
Nonparametric tests are tests that aren’t dependent on any data distribution assumptions or parameters to analyze them. They are also sometimes referred to as “distribution-free tests”.
We use nonparametric tests because if the data doesn’t meet the assumptions for the population sample or when data is skewed, the population sample size is too small, or if the data being analyzed is nominal or ordinal.
It is more flexible in real-life applications as data found in real life is not necessarily normally distributed and is mostly clumped or non-linear. Due to their simplicity and robust nature, nonparametric tests are seen as less prone to improper use and misunderstanding.
Main Differences Between Parametric and Nonparametric Tests
The main difference between Parametric and Nonparametric tests is that parametric tests depend on the data following certain assumptions or conditions. In contrast, nonparametric tests need not be required to follow any such assumptions. Some of the other differences between the two tests are as follows:
- Parametric data follows a normal distribution, whereas normal distribution follows any arbitrary distribution.
- Parametric tests apply only to variables, whereas nonparametric tests can be applied to attributes and variables.
- The central tendency value for the parametric test is the mean, and for the nonparametric test is the median.
- In real-life situations, nonparametric tests are better fitting alternatives than parametric tests.
- In cases where the sample size is large, parametric tests show higher statistical power than nonparametric tests.
References
- http://people.umass.edu/~biep640w/pdf/HOSKIN%20Tonya%20Intro%20to%20Nonparametrics.pdf
- https://onlinelibrary.wiley.com/doi/abs/10.1002/j.1556-6676.1988.tb02007.x
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Yes, the comparison table makes it easier to understand the differences between these tests.
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Although it’s informative, this post overlooks the fact that nonparametric tests can be more powerful in certain scenarios due to their flexibility. The emphasis on parametric tests having greater statistical power is a bit misleading.
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The discussion about the statistical power can be further expanded and explained in more detail.