Parametric vs. Non-Parametric Interactive Lab

Explore the mathematical mechanics and robustness of One-Way ANOVA, Kruskal-Wallis, t-tests, and Mann-Whitney U tests under skewed distributions and extreme outliers.

Interactive Multi-Group Distribution Kruskal-Wallis vs ANOVA

Adjust skewness or inject an extreme outlier to observe how One-Way ANOVA (Mean-based $F$-test) breaks down while Kruskal-Wallis (Rank-based $H$-test) remains robust.

Statistical Outputs & Rank Transformation

ANOVA F-Value
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p = 1.000
Kruskal H-Value
0.00
p = 1.000
Recommended
ANOVA
Based on normality

Key Insight: Equal Sensitivity

Both tests produce valid statistics under normal distributions. Observe what happens when an extreme outlier is injected.

Combined Rank Transformation Preview

Value Group Assigned Rank
# SPSS / Python Syntax Comparison # Parametric One-Way ANOVA: ONEWAY score BY group /STATISTICS DESCRIPTIVES. # Non-Parametric Kruskal-Wallis H Test: NPAR TESTS /K-W=score BY group(1 3).

Two Independent Groups t-test vs Mann-Whitney U

Compare the Independent Samples t-test (Parametric) with the Mann-Whitney U Test (Non-parametric Wilcoxon Rank-Sum).

Two-Sample Test Metrics

t-Statistic
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p = 1.000
Mann-Whitney U
0.00
p = 1.000
Mean Rank Diff
0.0
Group B vs A

Why Mann-Whitney U Handles Outliers

The t-test relies directly on sample means $ar{X}_1, ar{X}_2$ and pooled variance. A single extreme outlier dramaticallyinflates sample variance and pulls the mean. Mann-Whitney U converts values to ranks $(1, 2, \dots, N)$, capping the maximum influence of any extreme point to its rank position $N$.

# SPSS Syntax # Independent Samples t-test: T-TEST GROUPS=group(1 2) /VARIABLES=score. # Mann-Whitney U Test: NPAR TESTS /MANN-WHITNEY=score BY group(1 2).

Statistical Test Chooser Matrix

Design Context Parametric Test
(Normal Data / Scale)		 Non-Parametric Test
(Skewed / Ordinal / Ranks)
2 Independent Groups Independent Samples t-test Mann-Whitney U Test (Wilcoxon Rank-Sum)
3+ Independent Groups One-Way ANOVA Kruskal-Wallis H Test
2 Paired / Repeated Measures Paired Samples t-test Wilcoxon Signed-Rank Test
3+ Paired / Repeated Measures Repeated Measures ANOVA Friedman Test
Rule of Thumb for Academic Publishing:
  • Check normality using Shapiro-Wilk or Kolmogorov-Smirnov test alongside skewness/kurtosis evaluation.
  • If sample size per group $n > 30$, Central Limit Theorem provides some parametric robustness, but extreme outliers or ordinal scales (Likert) strongly warrant non-parametric testing.

Interactive Scenario Quiz