Non-parametric methods
Intro
Parametric vs Non-parametric
- parametric methods:
- a set of fixed parameters
- assume the distribution is Gaussian and set the significance level
- the result or outputs generated can be easily affected by outliers
- non-parametric methods:
- no assumption of parameters
- no assumption of the distribution
- the result or outputs generated cannot be easily affected by outliers
Benefits of Non-parametric
- avoid Type I error
- 30% trials would be already enough to show the effects
Non-parametric methods
| NONPARAMETRIC TEST | PARAMETRIC ALTERNATIVE | DESCRPTION |
|---|---|---|
| 1-sample sign test Paired-data Tests#the sign test | One-sample Z-test, One sample t-test | estimate the median of a population and compare it to a reference value |
| 1-sample Wilcoxon Signed Rank test | One sample Z-test, One sample t-test | same as sign test, but requiring a symmetric distribution |
| Friedman test | Two-way ANOVA | by ranks: tests whether n treatments in randomized block designs have identical effects |
| Kruskal-Wallis test | One-way ANOVA | tests whether > 2 independent samples are drawn from the same distribution |
| Mann-Whitney test | Independent samples t-test | compare differences between two independent groups, or Wilcoxon rank sum test |
| Mood’s Median test | One-way ANOVA | Use this test instead of the sign test when you have two independent samples |
Permutation test
- not assuming any distribution
- test whether the obeserved data differ from the randomly shuffled data
- any statistical tests can be applied to the shuffled data