Table 4 Third example of confounding
Unadventurous | Risk takers | Overall | |||||||||
5000 | 5000 | 10000 | |||||||||
4% use A | 40% use A | (Sum over unadventurous and risk takers) | |||||||||
↙ | ↘ | ↙ | ↘ | ↙ | ↘ | ||||||
A | Not A | A | Not A | A | Not A | ||||||
200 | 4800 | 2000 | 3000 | 2200 | 7800 | ||||||
5% use B | 3% use B | 50% use B | 30% use B | (sum) | (sum) | ||||||
↙ | ↘ | ↙ | ↘ | ↙ | ↘ | ↙ | ↘ | ↙ | ↘ | ↙ | ↘ |
B | Not B | B | Not B | B | Not B | B | Not B | B | Not B | B | Not B |
10 | 190 | 144 | 4656 | 1000 | 1000 | 900 | 2100 | 1010 | 1190 | 1044 | 6756 |
OR (within unadventurous) = (10/190)/(144/4656) = 1.70 | OR (within risk takers) = (1000/1000)/(900/2100) = 2.33 | OR (overall, unadjusted) = (1010/1196)/(1044/6756) = 5.49 | |||||||||
OR (overall, adjusted for risk taking) = ((10 × 4656)/5000 + (1000 × 2100)/5000)/((190 × 144)/5000 + (1000 × 900)/5000) = 2.31 | |||||||||||