| Concept | Description |
|---|---|
| Two Families | |
| Hypothesis Testing | Using sample data to decide whether an assumption about a population is supported by evidence |
| Parametric Tests | Tests that assume the data follow a specific distribution, usually normal, and require interval or ratio data |
| Non-Parametric Tests | Tests that make no strict distributional assumptions and can accept ordinal, ranked, or skewed data |
| Key Assumptions | |
| Normality Assumption | The assumption that the observations are drawn from a normally distributed population |
| Homogeneity of Variance | The assumption that different groups being compared share the same variance |
| Measurement Scale | The level of measurement of the variable, from nominal through ordinal to interval and ratio |
| Parametric Examples | |
| t-test | Parametric test comparing the means of two groups |
| ANOVA | Parametric test comparing the means of three or more groups |
| Pearson Correlation | Parametric measure of linear association between two numerical variables |
| Linear Regression | Parametric model for predicting a numerical outcome from one or more predictors |
| Non-Parametric Examples | |
| Mann-Whitney U | Non-parametric alternative to the independent samples t-test |
| Kruskal-Wallis | Non-parametric alternative to one-way ANOVA |
| Wilcoxon Signed-Rank | Non-parametric alternative to the paired samples t-test |
| Spearman Correlation | Non-parametric measure of monotonic association based on ranks |
| Chi-square | Non-parametric test for association between categorical variables |
| Choosing Between Them | |
| Statistical Power | The probability that a test correctly detects a real effect when one exists |
| Robustness to Outliers | The extent to which a test remains valid when extreme values are present |
| Sample Size Consideration | Parametric tests perform better with large samples, non-parametric tests with small samples |
| Data Integrity | Non-parametric tests are preferred when data are imprecise, ranked, or heavily tied |
14 Parametric vs Non-Parametric Tests
TipParametric vs Non-Parametric Tests
Parametric and non-parametric tests are two broad categories of statistical tests used in hypothesis testing. The choice between them depends on the type of data you’re analyzing, its distribution, and the assumptions that can reasonably be made about that data. Both play a crucial role in statistical inference helping analysts move from observed patterns to meaningful conclusions.
| Aspect | Parametric Tests | Non-Parametric Tests |
|---|---|---|
| Assumptions | Assume the data follows a specific probability distribution (commonly normal). Also require homogeneity of variances and that data is measured on an interval or ratio scale. | Do not assume any specific distribution. They are distribution-free and less restrictive about variance and measurement scale assumptions. |
| Data Requirements | Require quantitative data that typically meets assumptions about distribution (e.g., normality). Most suitable for interval or ratio scale data. | Can be used with ordinal data, ranked data, or non-normally distributed data. Often useful when sample sizes are small or when data contain outliers. |
| Examples | t-test (compare means of two groups), ANOVA (compare means of three or more groups), Pearson correlation (measure strength and direction of a linear relationship), Linear regression. | Mann–Whitney U test (compare two independent groups), Kruskal–Wallis test (compare three or more groups), Wilcoxon signed-rank test (paired samples), Spearman rank correlation, Chi-square test (categorical associations). |
| Advantages | When assumptions are met, parametric tests are more powerful — more likely to detect a true effect. They provide estimates of population parameters (mean, standard deviation). | More robust to violations of normality and outliers. Applicable to ordinal and categorical data. Provide insights when data fail to meet parametric assumptions. |
| Disadvantages | Results may be invalid if assumptions are violated. Sensitive to outliers and skewed distributions. | Generally less powerful when parametric assumptions hold true. May not provide detailed parameter estimates. |
14.1 Choosing Between Parametric and Non-Parametric Tests
The decision depends on the nature of your data, sample characteristics, and research objectives.
1. Data Distribution and Scale
- Use parametric tests when data are normally distributed, measured on interval or ratio scales, and assumptions of equal variances are satisfied.
- Use non-parametric tests when data are ordinal, categorical, skewed, or contain outliers that cannot be corrected through transformation.
2. Sample Size
- Parametric tests typically perform better with larger samples, as normality approximations become more reliable.
- Non-parametric tests are useful with small samples or when normality cannot be assumed.
3. Data Integrity and Quality
- Non-parametric tests are safer when data are imprecise, contain extreme values, or are based on ranks or categories.
4. Research Question and Objective
- Use parametric tests for estimating population parameters (e.g., mean differences, regression coefficients).
- Use non-parametric tests for ranking, ordinal comparisons, or testing medians instead of means.
14.2 Consideratioins
Parametric and non-parametric tests complement each other in statistical analysis.
-
Parametric tests are preferred when assumptions hold — they provide precision and statistical power.
- Non-parametric tests act as reliable alternatives when those assumptions fail offering flexibility and robustness.
A wise analyst chooses the test not based on preference but on data characteristics and research purpose.
Understanding both families of tests ensures analytical accuracy, methodological rigor, and credible results.