Parametric and Non-Parametric Tests

In statistics, the choice between parametric and non-parametric tests depends on the nature of the data and the assumptions the researcher can reasonably make about the population distribution.

1. Parametric Tests

Parametric tests are statistical methods that assume the data follows a specific probability distribution, usually the normal (Gaussian) distribution. These tests are more powerful when their assumptions are met because they use the actual values of the data.

Key Assumptions

• Normality: The data should be approximately normally distributed.
• Homogeneity of Variance: The variance (spread) of the data should be similar across groups.
• Interval/Ratio Scale: The data must be measured on a continuous scale.
• Independence: Observations must be independent of one another.

Common Examples

• • Student’s t-test: Compares the means of two groups.
  • ANOVA (Analysis of Variance): Compares the means of three or more groups.
  • Pearson Correlation: Measures the linear relationship between two continuous variables.

2. Non-Parametric Tests

Non-parametric tests, often called “distribution-free” tests, do not assume that the data follows a normal distribution. They are generally based on the ranks of the data rather than the raw values, making them robust against outliers and skewed data.

Key Assumptions

• No assumption of normality: They work well with skewed data or ordinal (ranked) data.
• Independence: Still requires observations to be independent.
• Flexibility: Can be used with ordinal data, where the exact interval between values is unknown.

Common Examples

• Mann-Whitney U test: The non-parametric equivalent of the independent t-test.
• Wilcoxon Signed-Rank test: The non-parametric equivalent of the paired t-test.
• Kruskal-Wallis test: The non-parametric equivalent of one-way ANOVA.
• Spearman Rank Correlation: Measures the monotonic relationship between variables.

3. Comparative Overview

4. Which One to Choose?

Deciding between the two involves evaluating your data’s characteristics:

1. Check for Normality: Use graphical methods (like histograms or Q-Q plots) or statistical tests (like the Shapiro-Wilk test). If the p-value is > 0.05, you may assume normality.
2. Sample Size: Parametric tests are generally robust to minor violations of normality with large sample sizes (Central Limit Theorem). With small samples, non-parametric tests are safer if normality is not confirmed.
3. Presence of Outliers: If your data contains extreme values that you cannot exclude, non-parametric tests are preferred as they use ranks rather than magnitudes.
4. Measurement Scale: If your data is ordinal (e.g., Likert scales from 1–5), non-parametric tests are the standard choice.

Statistical Fact

The Central Limit Theorem states that as your sample size increases (typically n > 30), the sampling distribution of the mean will approach a normal distribution, regardless of the population’s underlying distribution. This is why researchers often use parametric tests on large datasets even when the raw data is not perfectly normal.