Five historical representations of the concept of confounding as a fallacy resulting from mixing strata of exposure to a third factor
| Author | Contrast | Stratum 1 | Stratum 2 | ALL | ||||||
| Exposure 1 | Exposure 2 | OR* | Exposure 1 | Exposure 2 | OR* | Exposure 1 | Exposure 2 | OR* | ||
| Yule1,† | Attribute present/absent | 0.25/0.25 | 0.25/0.25 | 1.0 | 0.1/0.9 | 0.1/0.9 | 1.0 | 0.13/0.17 | 0.17/0.53 | 2.4 |
| Greenwood21, ‡ | Dead/alive | 50/50 | 500/500 | 1.0 | 50/950 | 5/95 | 1.0 | 100/1000 | 505/595 | 0.12 |
| Hill22, § | Dead/alive | 16/64 | 6/24 | 1.0 | 16/24 | 24/36 | 1.0 | 32/88 | 30/60 | 0.7 |
| Simpson23, § | Dead/alive | 5/8 | 3/4 | 0.8 | 15/12 | 3/2 | 0.8 | 20/20 | 6/6 | 1.0 |
| Rothman24, ¶ | Fit/not fit | 9/1 | 17/3 | 1.6 | 3/17 | 1/9 | 1.6 | 12/18 | 18/12 | 0.4 |
↵* OR, computed by AM, not in the original publications.
↵† Stratum 1=fathers; stratum 2=mothers; exposure 1=attribute present; exposure 2=attribute absent.
↵‡ Stratum 1=group 1; stratum 2=group 2; exposure 1=inoculated; exposure 2=not inoculated.
↵§ Stratum 1=males; stratum 2=females; exposure 1=treatment; exposure 2=no treatment.
↵¶ Stratum 1=table 1; stratum 2=table 2; exposure 1=black hats; exposure 2=grey hats.