Parametric and non-parametric tests are two broad categories of statistical tests used to analyze data, and they differ mainly in their assumptions about the underlying data and the nature of the data being analyzed. Here’s a detailed comparison:
Parametric Tests
Definition: Parametric tests are statistical tests that assume a specific distribution for the data, usually the normal distribution. These tests rely on parameters like the mean and standard deviation to make inferences.
Assumptions:
- Distribution: Data should follow a known distribution, typically normal.
- Homogeneity of Variance: The variance among groups should be approximately equal.
- Scale of Measurement: The data should be measured on an interval or ratio scale.
Examples:
- t-Test: Compares the means of two groups (independent or paired) to determine if they are significantly different from each other.
- ANOVA (Analysis of Variance): Compares the means of three or more groups to assess if at least one group mean is significantly different from the others.
- Pearson Correlation: Measures the strength and direction of the linear relationship between two continuous variables.
Advantages:
- Power: Generally, parametric tests are more powerful (i.e., more likely to detect a true effect) if the assumptions are met.
- Interpretability: Parameters like means and variances are straightforward and easy to interpret.
Disadvantages:
- Assumptions: If the assumptions are violated, the results can be misleading.
Non-Parametric Tests
Definition: Non-parametric tests do not assume a specific distribution for the data and are used for data that does not meet the assumptions required for parametric tests. They are often based on ranks or other non-parametric measures.
Assumptions:
- Distribution: No specific distribution is assumed; they are more flexible regarding the shape of the data distribution.
- Scale of Measurement: Often used with ordinal data or non-normal interval/ratio data.
Examples:
- Mann-Whitney U Test: Non-parametric alternative to the independent t-test; compares the distributions of two independent groups.
- Wilcoxon Signed-Rank Test: Non-parametric alternative to the paired t-test; used for comparing two related samples.
- Kruskal-Wallis Test: Non-parametric alternative to one-way ANOVA; compares medians among three or more independent groups.
- Spearman's Rank Correlation: Measures the strength and direction of the association between two variables, using rank values instead of raw data.
Advantages:
- Flexibility: They can be used with ordinal data, and they do not require the assumption of a specific data distribution.
- Robustness: Less sensitive to outliers and violations of assumptions compared to parametric tests.
Disadvantages:
- Power: Generally less powerful than parametric tests if the parametric test assumptions are met.
- Interpretability: Results are often less straightforward and may involve ranks or other transformations rather than raw data values.
Summary
- Parametric Tests: Assume a specific distribution (usually normal), require interval or ratio data, and are generally more powerful and interpretable if assumptions are met.
- Non-Parametric Tests: Do not assume a specific distribution, can handle ordinal data and non-normal distributions, and are more flexible but often less powerful and harder to interpret.
Choosing between parametric and non-parametric tests depends on the nature of the data and whether the assumptions of the parametric tests are met. In practice, if your data meets the assumptions for parametric tests, they are typically preferred due to their greater statistical power. If the assumptions are not met, non-parametric tests provide a robust alternative.