Parametric vs. Non-Parametric Hypothesis Testing: A Visual Decision Guide

Choosing the correct statistical hypothesis test is one of the most common inflection points in data analysis. Making the wrong assumption—such as assuming normality on heavily skewed e-commerce basket sizes—can lead to false positives and flawed product decisions.

Check Your Assumptions First

Before applying an Independent Samples T-Test, evaluate three key criteria:

• Normality: Does the distribution follow a Gaussian curve? (Shapiro-Wilk test or Q-Q plot).
• Homogeneity of Variance: Are the sample variances approximately equal? (Levene's test).
• Independence: Are the observations independent of each other?

# Automated verification routine in Clustey statistical core
from scipy import stats

stat, p_val = stats.shapiro(sample_data)
if p_val > 0.05:
    print("Normal distribution assumption holds")
else:
    print("Switch to Mann-Whitney U non-parametric test")

Summary Recommendation Matrix

• Continuous & Normal: Student's T-Test or Welch's T-Test
• Continuous & Skewed: Mann-Whitney U or Wilcoxon Rank-Sum
• Categorical Proportions: Chi-Square or Fisher's Exact Test