Risk estimate

Figure 1. Risk estimate for Newspaper subscription by Response
Risk estimate 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 13.7%/8.2% = 1.668. 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 0.940. Given these results, you can estimate that a newspaper subscriber is 1.668 times as likely to respond to the mailing as a nonsubscriber, or .940 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 13.7%/86.3% = 0.158. Likewise, the estimate of the odds that a nonsubscriber responds is 8.2%/91.8% = 0.089. The estimate of the odds ratio is therefore 0.158/0.089 = 1.775. Note that the odds ratio is the ratio of the relative risk of responding, to the relative risk of not responding, or 1.668/0.940 = 1.775.

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