Statistical tests come in two flavors: parametric and non-parametric. Parametric tests assume data follows specific distributions, while non-parametric tests are more flexible. Understanding when to use each type is crucial for accurate data analysis.
This section covers key non-parametric tests like Wilcoxon, Mann-Whitney U, and Kruskal-Wallis. These tests are vital when data doesn't meet parametric assumptions, offering robust alternatives for comparing groups and analyzing relationships in various research scenarios.
Parametric vs Non-parametric Tests
Assumptions of parametric tests
- Normal distribution of data assumes bell-shaped curve enables accurate statistical inferences
- Homogeneity of variance requires equal spread of data points across groups facilitates valid comparisons
- Independence of observations ensures each data point not influenced by others maintains statistical integrity
- Interval or ratio level of measurement allows meaningful arithmetic operations on data values
Wilcoxon test vs paired t-test
- Purpose compares two related samples or repeated measurements within same subjects
- Assumptions include paired observations from same population, ordinal or continuous data, symmetric distribution of differences
- Procedure calculates differences between pairs, ranks absolute differences, assigns signs to ranks, computes test statistic W
- Interpretation compares W to critical value or p-value, rejects null hypothesis if W ≤ critical value
- Applications include comparing pre-post treatment effects, evaluating matched pairs (twins)
Mann-Whitney U test for samples
- Purpose compares two independent groups when normality assumption violated
- Assumptions require independent observations, ordinal or continuous data, similar distribution shapes
- Procedure combines and ranks all observations, calculates rank sums for each group, computes U statistic
- Interpretation compares U to critical value or p-value, rejects null hypothesis if U ≤ critical value
- Applications include comparing median differences between groups (treatment vs control)
Kruskal-Wallis test vs ANOVA
- Purpose compares three or more independent groups when ANOVA assumptions not met
- Assumptions include independent observations, ordinal or continuous data, similar distribution shapes across groups
- Procedure combines and ranks all observations, calculates rank sums for each group, computes H statistic
- Interpretation compares H to chi-square distribution, rejects null hypothesis if H exceeds critical value
- Post-hoc analysis uses Dunn's test for pairwise comparisons, applies Bonferroni correction for multiple tests
- Applications include comparing median differences among multiple groups (different treatments)