A company tested two vaccines (V1 and V2) at two locations (L1 and L2) and got the following success rates.
| L1 | L2 | |
| V1 | 80% | 70% |
| V2 | 75% | 60% |
Which one is a better vaccine? V1, without a doubt, eh? Because V1 beats V2 at L1 as well as at L2. At an average of 75% for V1 vs 67.5% for V2. Unfortunately, we cannot conclude which is better until we know the sample sizes. Now, the sample sizes
| L1 | L2 | |
| V1 | 100 | 900 |
| V2 | 900 | 100 |
Leading to total success
| L1 | L2 | Total | |
| V1 | 80 | 630 | 710 |
| V2 | 675 | 60 | 735 |
Leading to a success rate of 71% for V1 and 73.5% for V2. It is sometimes called Simpson’s paradox but is not a paradox. It is just a mistake for not paying attention to the format – percentage – of the result!
