Understanding when and how to use the right statistical test is a critical skill for data scientists. Whether analyzing clinical trials, A/B test results, or user behavior data, choosing the wrong test can lead to misleading conclusions. Here’s a practical guide to the most common statistical tests, when to use them, and how to decide based on your data’s characteristics.
🔹 Decision Framework: How Do Data Scientists Choose a Test?
The choice of a statistical test depends on three key factors:
- Type of data (continuous, categorical)
- Normality of the distribution (assessed using QQ plots, Shapiro-Wilk test)
- Variance homogeneity (tested using Levene’s or Bartlett’s tests)
General Rule of Thumb:
- If your data is normal and homoscedastic (equal variance), use parametric tests.
- If assumptions are violated, opt for non-parametric tests.
🧪 1. Tests for Normality
a. QQ Plot Purpose: Visual inspection of normality Use When: You need a quick check before applying parametric tests Interpretation: Points should follow a diagonal line if data is normal.
b. Shapiro-Wilk Test Purpose: Formal test for normality Null Hypothesis: Data is normally distributed Decision: If p > 0.05, data is normal
🌀 2. Tests for Equal Variance
a. Levene’s Test Use When: Before t-test or ANOVA to test equality of variances
b. Bartlett’s Test Use When: Similar to Levene’s but more sensitive to non-normal data
👥 3. Comparing Two Groups
a. Independent t-test Use: Two independent groups, normal data, equal variance
b. Welch’s t-test Use: Normal data, unequal variance
c. Mann-Whitney U Test Use: Two independent groups, non-normal data
d. Paired t-test Use: Two related samples, normal distribution
e. Wilcoxon Signed-Rank Test Use: Paired non-parametric alternative
📊 4. Comparing More Than Two Groups
a. One-way ANOVA Use: >2 groups, normal data, equal variance
b. Welch’s ANOVA Use: >2 groups, normal data, unequal variance
c. Kruskal-Wallis Test Use: >2 groups, non-normal data
🌍 5. Post-hoc Tests (After ANOVA or Kruskal-Wallis)
a. Tukey’s HSD Use: After significant ANOVA result
b. Games-Howell Use: After Welch’s ANOVA (unequal variance)
c. Dunn’s Test Use: After Kruskal-Wallis (non-parametric post-hoc)
🔢 6. Correlation Tests
TestWhen to UseParametric?PearsonNormal, linear dataYesSpearmanRanked/ordinal or skewedNoKendall’s TauSmall
Final Thoughts
Choosing the right test isn’t just about plugging numbers into a formula. It requires understanding the structure of your data, verifying assumptions, and selecting the test that provides valid, interpretable results.
Feel free to save this guide or share it with your data science network. If you’d like visual examples (QQ plots, ANOVA vs Kruskal visualizations, etc.), drop a comment – I’d be happy to generate a full set!
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