Non-parametric tests are essential when data doesn't follow normal distribution. They use ranks instead of actual values, making them less sensitive to outliers and useful for ordinal data.
These tests include Mann-Whitney U, Wilcoxon signed-rank, Kruskal-Wallis, and Friedman tests. They're great alternatives when parametric test assumptions aren't met, though they're generally less powerful.
Rank-Based Tests for Two Groups
Mann-Whitney U Test and Wilcoxon Signed-Rank Test
- Mann-Whitney U test compares two independent groups when the data is ordinal or continuous but not normally distributed
- Calculates the difference between the mean ranks of the two groups to determine if they are significantly different
- Wilcoxon signed-rank test compares two related samples (paired data) when the data is ordinal or continuous but not normally distributed
- Calculates the differences between each set of paired observations, ranks the absolute differences, and compares the sum of positive and negative ranks
Ordinal Data and Rank-Based Methods
- Ordinal data represents categories with a natural order or ranking (Likert scales, performance ratings)
- Rank-based methods convert the original data values into ranks before performing the statistical analysis
- Ranks are assigned by ordering the data from smallest to largest and assigning each value a rank based on its position
- Rank-based methods are less sensitive to outliers and can be used when the assumptions of parametric tests are not met
Rank-Based Tests for Multiple Groups
Kruskal-Wallis Test and Friedman Test
- Kruskal-Wallis test compares three or more independent groups when the data is ordinal or continuous but not normally distributed
- Calculates the differences between the mean ranks of the groups to determine if at least one group is significantly different from the others
- Friedman test compares three or more related samples (repeated measures) when the data is ordinal or continuous but not normally distributed
- Calculates the differences between the mean ranks of the groups across multiple measurements to determine if there are significant differences
Distribution-Free Methods
- Distribution-free methods, also known as non-parametric methods, do not assume that the data follows a specific probability distribution (normal distribution)
- These methods are useful when the assumptions of parametric tests, such as normality and homogeneity of variance, are not met
- Distribution-free methods are generally less powerful than parametric tests when the assumptions are met, but they provide valid results when the assumptions are violated
Non-Parametric Correlation
Spearman's Rank Correlation
- Spearman's rank correlation measures the strength and direction of the monotonic relationship between two ordinal or continuous variables
- Monotonic relationship means that as one variable increases, the other variable either consistently increases (positive correlation) or consistently decreases (negative correlation)
- Calculates the Pearson correlation coefficient on the ranked values of the two variables instead of the original data values
- Spearman's rank correlation coefficient ranges from -1 (perfect negative correlation) to +1 (perfect positive correlation), with 0 indicating no correlation
Ordinal Data and Rank-Based Methods in Correlation
- Ordinal data can be used to calculate non-parametric correlations when the relationship between variables is not strictly linear
- Rank-based methods are employed in Spearman's rank correlation to convert the original data values into ranks before calculating the correlation coefficient
- Rank-based methods in correlation are less sensitive to outliers and can be used when the assumptions of Pearson's correlation (linearity, normality, and homoscedasticity) are not met