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 fulltime 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 oddratios 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
