Non-Parametric Statistics
Partido, B.B.
When your data is non-parametric, there are tests that assess whether the medians of two groups are statistically different from each other (ordinal-scale data). These include the following:
- Mann-Whitney U-test (equivalent to the independent samples t-test)
- Wilcoxon matched pairs signed ranked test (equivalent to dependent samples t-test)
| Mann-Whitney U-test | Wilcoxon matched pairs test | |
| Independent variable (grouping) | nominal scale (dichotomous) | nominal scale (dichotomous) |
| Dependent variable (outcome of interest) | ordinal scale | ordinal scale |
| Purpose | Compares the medians of 2 unrelated groups | Compares the medians of 2 related groups |
| What the test reports | Median and interquartile range (IQR) of each group | Median and interquartile range (IQR) of each group |
An example of a Mann-Whitney U-test: You want to determine whether there are differences in oral health attitudes (dependent variable-ordinal scale) among teenage males and females (independent variable-nominal scale).
An example of a Wilcoxon matched paired test: You want to determine whether the oral health attitudes of teenagers (dependent variable-ordinal scale) would change from week 0 to week 2 (independent variable- nominal scale) upon visualizing their bacteria on a microscope.
Comparing 3 or more groups
A Kruskal-Wallis H-test compares the means of three or more independent groups defined by one factor (grouping variable) when the data is nonparametric (ordinal data).
| Kruskal-Wallis H-test | |
| Independent variable (grouping) | nominal scale |
| Dependent variable (outcome of interest) | at least ordinal scale, can be interval or ratio scale |
| Purpose | Compares the medians of 3 or more unrelated groups |
| What the test reports |
Reports if one or more of the means are statistically significantly different from the others. Post-hoc tests are completed to determine which groups are different.
|
An example of a Kruskal-Wallis H-test: You want to determine whether the oral health attitudes (dependent variable-ordinal scale) of male and female teenagers (independent variable- nominal scale) would change from week 0 to week 2 (independent variable- nominal scale) upon visualizing their bacteria on a microscope.