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Visual Guides/Nonparametric Tests
STATISTICS·UNIT 8: COMPARING GROUPS

Nonparametric Tests: When Assumptions Fail

Use rank-based methods when your data violates normality or when you have ordinal outcomes. Explore Mann-Whitney U, Wilcoxon signed-rank, and Kruskal-Wallis tests.

Assumption checks: 0/2
Normality violation identified
Comparison panel viewed
Decision helper used

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Select Dataset

Each dataset exhibits a different reason to prefer nonparametric methods.

n=40 observations · showing first 10

IndexGroup 1Group 2
125
236
347
448
559
6511
7514
8617
9722
10829

Assumption Check

Check normality before choosing a test

Distribution

2.019375471

Q-Q Plot

Theoretical Quantiles02254871

Click "Run Assumption Check" to test for normality using the Q-Q plot correlation (how closely the sorted data track normal quantiles).

Parametric vs. Nonparametric

Compare the t-test and Mann-Whitney U results side by side.

Parametric

Independent t-test

Statistict = -2.81
p-value0.010
95% CI[-78.8, -14.0]
Normality violated; result may be unreliable
12345

Nonparametric

Mann-Whitney U

StatisticU = 99.00
p-value0.006
No normality assumption needed (still assumes independent observations)
AspectParametricNonparametric
Test Usedt-testMann-Whitney U
Statistict = -2.81U = 99
p-value0.0100.006
Assumption Met?NON/A
Reliable?QUESTIONABLEYES

Test Selection Helper

Answer 5 questions to find the right test

Q 1/5

How many groups are you comparing?

Test Calculations

Step-by-step breakdown of each nonparametric test

When to Use

Two independent groups (e.g. Group A vs Group B). Tests whether the rank distribution of one group is stochastically greater than the other.

Dataset: Skewed Data
Group 1: n=20, mean=17.90
Group 2: n=20, mean=64.30

Calculation Steps

  • 1. Combine all values from both groups into one list
  • 2. Sort combined list and assign ranks (average ties)
  • 3. Compute R₁ = sum of ranks for group 1
  • 4. U₁ = n₁·n₂ + n₁(n₁+1)/2 − R₁
  • 5. U = min(U₁, U₂) where U₂ = n₁·n₂ − U₁
  • 6. μᵤ = n₁·n₂/2, σᵤ = √(n₁·n₂·(n₁+n₂+1)/12)
  • 7. z = (U − μᵤ) / σᵤ, p = 2·Φ(z)
← ANOVA: Comparing Many GroupsCorrelation & Covariance →