4-1.1 Odds of field value agreement.

Refer now to figure 4 of the first chapter as here augmented in figure 1. These figures illustrate Bayes' theorem as it relates to record linkage. The probability of field value agreement when the comparison is matched is here related to the probability that it agrees in any event. This is the agreement ratio. It follows from the theorem of total probability that the probability of the data agreeing is #1 + #3. Branch #1 is the probability of agreement when matched as represented by the reliability; branch # 3 is a probability of agreement when unmatched as represented by the coincidence. The agreement ratio is #1 ÷ (#1 + #3).

The agreement odds, which we give in equation (4.2), translate directly from the agreement ratio.

(4.2)