Editing Contingency table (section)

===Odds ratio===
{{main|Odds ratio}}

The simplest measure of association for a 2&nbsp;×&nbsp;2 contingency table is the [[odds ratio]]. Given two events, A and B, the odds ratio is defined as the ratio of the odds of A in the presence of B and the odds of A in the absence of B, or equivalently (due to symmetry), the ratio of the odds of B in the presence of A and the odds of B in the absence of A. Two events are independent if and only if the odds ratio is 1; if the odds ratio is greater than 1, the events are positively associated; if the odds ratio is less than 1, the events are negatively associated.

The odds ratio has a simple expression in terms of probabilities; given the joint probability distribution:
:<math>
\begin{array}{c|cc}
& B = 1 & B = 0 \\
\hline
A = 1 & p_{11} & p_{10} \\
A = 0 & p_{01} & p_{00}
\end{array}
</math>
the odds ratio is:
:<math>OR = \frac{p_{11}p_{00}}{p_{10}p_{01}}.</math>