📊 Statistical Analysis · Python

Marketing Statistical Test

Determining optimal promotional strategies through A/B Testing and ANOVA analysis

🧪 One-Way ANOVA 🔬 Bonferroni Post-Hoc 📈 Trend Analysis 🗂 3 Promotions · 4 Weeks
1

Initial Observations

Promotion 1
$58.1K
Avg Weekly Sales
✅ Best Weekly Avg
Promotion 2
$47.3K
Avg Weekly Sales
❌ Lowest Performer
Promotion 3
$55.4K
Avg Weekly Sales
🏆 Highest Total Rev

Despite Promotion 2 having the lowest average weekly sales, Promotion 3 generated the highest total revenue at $10.4M, outperforming both Promotion 1 ($9.99M) and Promotion 2 ($8.90M) — due to broader deployment across more market locations. Promotion 1 generates $10.77K more per week than Promotion 2 on average.

2

One-Way ANOVA Test

Before recommending which promotion works better, we need to verify these differences are statistically significant and not just random variation. The ANOVA test answers: "Are these differences real or due to chance?"

F-Statistic
21.95
Large → meaningful difference
p-value
< 0.001
Highly significant
Eta-squared (η²)
Moderate
Practical effect size

✅ Normality: While Shapiro-Wilk detected non-normality, all groups have n > 170. Under the Central Limit Theorem, ANOVA remains robust at this sample size.

✅ Levene's Test (Equal Variances): p = 0.2818 > 0.05 → the equal variances assumption is satisfied. ANOVA results are trustworthy.

⚠️ ANOVA confirms at least one promotion differs significantly from the others (F = 21.95, p < 0.001), but does not specify which pairs differ — that requires Post-Hoc analysis.

3

Post-Hoc Analysis — Bonferroni Correction

Pairwise t-tests with Bonferroni correction were applied to identify which specific promotions differ. The adjusted significance threshold is α = 0.0167 (0.05 ÷ 3 comparisons).

Promo 1 vs Promo 2
+$10.77K
t-statistic: 6.4537
p-value: < 0.0001
Result: p < 0.0167
✅ Significant

Promotion 1 significantly outperforms Promotion 2.

Promo 1 vs Promo 3
+$2.73K
t-statistic: 1.5551
p-value: 0.1208
Result: p > 0.0167
⚠️ Not Significant

No strong evidence that Promos 1 and 3 differ in performance.

Promo 2 vs Promo 3
−$8.04K
t-statistic: −4.8814
p-value: 0.000002
Result: p < 0.0167
✅ Significant

Promotion 3 significantly outperforms Promotion 2.

4

Weekly Trend Analysis by Promotion

📈
Promotion 1
Slope: +0.25 → +$250/week
R²: 0.15 (15% explained)
p-value: 0.6088 (not sig.)
Slight upward trend, not yet statistically reliable — but the most promising direction.
📉
Promotion 2
Slope: −0.42 → −$420/week
R²: 0.60 (60% explained)
p-value: 0.2261 (not sig.)
Strong declining pattern with high R². Clear warning signal even without statistical significance.
📉
Promotion 3
Slope: −0.28 → −$280/week
R²: 0.27 (27% explained)
p-value: 0.4796 (not sig.)
Moderate declining trend. Good overall performer but requires close monitoring over time.

None of the trends reached statistical significance (all p > 0.05), likely due to the short 4-week observation window. However, Promotion 2's R² of 0.60 indicates a meaningfully consistent decline that warrants concern regardless of significance. More data would help confirm these patterns.

5

Strategic Recommendations

🚫
Discontinue Promo 2
Lowest weekly average, statistically inferior to both alternatives, and declining at $420/week. Reallocate its budget immediately.
🚀
Scale Up Promo 1
Top weekly performer with the only positive trend slope. Clear statistical superiority over Promotion 2. Primary candidate for budget reallocation.
👁️
Monitor Promo 3
Statistically equivalent to Promotion 1 and highest total revenue generator — but declining weekly. May offer operational or cost advantages worth investigating.

🚩 Promotion Fatigue Signal: Trends suggest Promotions 2 & 3 may be suffering from promotional fatigue, while Promotion 1 shows promise for sustained performance. Collect more data to achieve statistical significance on trend analysis and investigate external factors contributing to the decline.

6

Final Conclusion

🏆

The evidence is clear across all tests

One-Way ANOVA (F = 21.95, p < 0.001) confirmed statistically significant differences between promotions. Bonferroni post-hoc analysis revealed that Promotions 1 and 3 perform equivalently, while both significantly outperform Promotion 2. Weekly trend data further supports pivoting investment toward Promotion 1.

Promotion 1 ≈ Promotion 3  ≫  Promotion 2