Risk Estimate

Figure 1. Crosstabulation for newspaper subscription by response

The relative risk is a ratio of event probabilities. The relative risk of a response to the mailing is the ratio of the probability that a newspaper subscriber responds to the probability that a nonsubscriber responds. Thus, the estimate of the relative risk is simply 17.2%/10.3% = 1.673. Likewise, the relative risk of nonresponse is the ratio of the probability that a subscriber does not respond to the probability that a nonsubscriber does not respond. Your estimate of this relative risk is 0.923. Given these results, you can estimate that a newspaper subscriber is 1.673 times as likely to respond to the mailing as a nonsubscriber, or 0.923 times as likely as a nonsubscriber not to respond.

The odds ratio is a ratio of event odds. The odds of an event is the ratio of the probability that the event occurs to the probability that the event does not occur. Thus, the estimate of the odds that a newspaper subscriber responds to the mailing is 17.2%/82.8% = 0.208. Likewise, the estimate of the odds that a nonsubscriber responds is 10.3%/89.7% = 0.115. The estimate of the odds ratio is therefore 0.208/0.115 = 1.812 (note there is some rounding error in the intervening steps). The odds ratio is also the ratio of the relative risk of responding to the relative risk of not responding, or 1.673/0.923 = 1.812.