I have several business units with a different amount of customers and we are tracking how many of these customers completed a requested task. I want to track who is performing the best but a simple % improvement will be skewed based on the total customer count, as a 1 task completion improvement in Chicago is weighted more than an improvement in Los Angeles. What would be the best way to calculate improvement statistatically?
| Business Unit | Customer Count | Task Completed Baseline | Task Completed after a Month |
|---|---|---|---|
| Los Angeles | 2,742 | 2,648 | 3,200 |
| Boston | 602 | 148 | 250 |
| Dallas | 1,006 | 198 | 450 |
| Chicago | 367 | 98 | 250 |
| Miami | 4,538 | 1,396 | 2,100 |
| Seattle | 7,001 | 3,207 | 5,000 |
I tried a simple % calculation but smaller customer bases are rewarded more than larger customer bases.
You're correct in pointing out that a simple percentage calculation may not accurately reflect the true improvement when dealing with business units of different sizes.
To address this issue, you can use a statistical method called "standardization" or "z-score normalization".
1.Calculate the percentage improvement for each business unit: Percentage Improvement = ((Task Completed after a Month - Task Completed Baseline) / Task Completed Baseline) * 100
2.Calculate the mean and standard deviation of the percentage improvements across all business units.
3.Calculate the z-score for each business unit's percentage improvement using the following formula:
Z-score = (Percentage Improvement - Mean of Percentage Improvements) / Standard Deviation of Percentage Improvements.
Business units with positive z-scores are performing better than the mean improvement, while those with negative z-scores are performing below the mean improvement.