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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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Risk Estimate |