Extension D: Equivalence between ORs <1 and ORs >1
The way odds ratios (ORs) are expressed depends on the baseline or comparison category. For example, consider the association of gender with aspiration to continue in full-time education after the age of 16, the example we described on Page 4.2. Suppose boys form the base or comparator category, the analysis shows that the odd-ratios of girls:boys is 2:1, i.e. girls are twice as likely to aspire as boys. We can also simply invert the base category to be girls rather than boys. This gives a ratio of 1:0.50, i.e. boys are half as likely to aspire as girls. These two ratios (2:1 and 1:0.50) are exactly equivalent, they just differ in the base category. The table below (Figure D1) shows:
(a) the equivalent OR <1 given a particular OR>1, and
(b) the equivalent OR >1 given a particular OR<1.
Figure D1: Equivalent Odds Ratios