Because <math>\left ( \dfrac{p\prime}{1-p\prime} \right )</math> and <math>\left ( \dfrac{p}{1-p} \right )</math> are odds of <math>p\prime</math> and <math>p</math>, respectively,
<math>\frac {\left ( \dfrac{p\prime}{1-p\prime} \right )}{ \left ( \dfrac{p}{1-p} \right ) }</math> is the '''odds ratio''' of [the probability when <math>1</math> is added to <math>X_1</math>] to [the probability before adding].