Parametric vs Nonparametric Tests

Whether a test is parametric or nonparametric depends on whether the data set assumes a normal distribution or not. If the data was drawn from a population that is normally distributed, then the subsequent test is known as a subsequent test. However, if the data comes from a non-normal distribution, then the tests conducted are nonparametric. Parametric tests are more common and statistical since some assumptions can be made about the parameters. If this is not possible, then one uses nonparametric tests.

Advantages of Parametric Tests

  1. They produce trustworthy results even for non-normal distributions

For these results to be reliable even when the continuous data is skewed and not normally distributed, some conditions must be met. In the 1-sample t-test, the sample size should be greater than 20 while in the 2-sample t-test it should exceed 15 observations in each group. One-way ANOVA requires 15 observations for each group if the groups range from 2-9. If the groups are in the range of 10-12, each group requires at least 20 observations for the one-way ANOVA. The central limit theorem makes it possible to conduct non-normally distributed data using parametric tests

  1. Reliable results can be obtained from data even if it differs in variability unlike in nonparametric tests
  2. Parametric tests have more statistical power and they can easily identify an underlying effect

Advantages of Nonparametric Tests

  1. They can be better in some fields of study because they use the median as opposed to the mean used in parametric tests.
  2. They can be used for non-normally distributed data even with a small sample size
  3. These tests can analyze ordinal, and ranked data and outliers

Parametric and Nonparametric Tests for comparing two or more groups

It is essential to consider whether the mean or median is the perfect estimate for the sample at hand. The following tests are the equivalents of parametric and nonparametric tests but proper consideration should be made first. Statisticians tend to use parametric tests because they are a stronger statistical tool.

Parametric test Nonparametric equivalent
Paired t-test Wilcoxon rank sum test
Unpaired t-test Mann-Whitney U test
Pearson correlation Spearman correlation
One-way ANOVA Kruskal Wallis test, Mood’s median test

Differences between parametric and nonparametric tests

Parametric tests Nonparametric tests
Rely on normal distribution Rely on any distribution, even non-normal
Use the mean Use median
Require large sample size Can be used even for small samples
More statistical power Less chances of detecting effects

Before settling on a test, one should consider if there exists a hypothesis or not, and the type of data under observation. If the mean is an ideal estimate and you have a small sample size, consider increasing it where possible. However, if the sample is small and the median is the most suitable measure, then proceed with it despite the lower statistical power.

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