Module Review: Non-Parametric Methods
[!NOTE] This module explores the core principles of Module Review: Non-Parametric Methods, deriving solutions from first principles and hardware constraints to build world-class, production-ready expertise.
1. Cheat Sheet: Parametric vs Non-Parametric
| If you have… | And you want to test… | Parametric (Normal) | Non-Parametric (Any) |
|---|---|---|---|
| 2 Independent Groups | Difference in Means/Medians | Independent t-test | Mann-Whitney U Test |
| 2 Paired Groups | Difference in Means/Medians | Paired t-test | Wilcoxon Signed-Rank Test |
| 3+ Independent Groups | Difference in Means/Medians | One-way ANOVA | Kruskal-Wallis H Test |
| Correlation | Linear Relationship | Pearson Correlation | Spearman Rank Correlation |
2. Interactive Flashcards
Click a card to reveal the answer.
Bootstrap Method
What is the core mechanism of the Bootstrap method?
Resampling with Replacement
It involves repeatedly drawing samples of size n from the original dataset, allowing the same observation to be picked multiple times, to estimate the sampling distribution.
Bandwidth (h)
In Kernel Density Estimation (KDE), what happens if the bandwidth is too small?
Overfitting (High Variance)
The estimated density curve becomes "spiky" and noisy, capturing random fluctuations in the data rather than the underlying structure.
Mann-Whitney U Test
What is the Null Hypothesis (H0) for the Mann-Whitney U test?
Identical Distributions
The null hypothesis states that the two populations have the same distribution (specifically, that a randomly selected value from one population is equally likely to be greater or less than a value from the other).
Wilcoxon Signed-Rank
When should you use the Wilcoxon Signed-Rank test instead of the Mann-Whitney U test?
Paired Data
Use Wilcoxon when the data samples are dependent or paired (e.g., measuring the same subjects "Before" and "After" a treatment).
Kruskal-Wallis Test
The Kruskal-Wallis test is the non-parametric equivalent of which parametric test?
One-Way ANOVA
It extends the Mann-Whitney U test to compare more than two independent groups.
Rank Transformation
Why is rank transformation robust to outliers?
Magnitude is Ignored
The largest value in a dataset gets the highest rank (e.g., N), regardless of whether it is slightly larger or exponentially larger than the second-largest value.
3. Next Steps
Now that you’ve mastered non-parametric methods, you are well-equipped to handle real-world data distributions.