(meaning ≥ 10), then the following approximate formula for the 95 percent CI around an RR works

reasonably well:

where

.

For other confidence levels, you can replace the 1.96 in the Q formula with the appropriate critical z

value for the normal distribution.

So, for the 2023 adult Type II diabetes example, you would set

, and RR =  3.0. The

equation would be

, so the 95 percent lower and upper confidence limits would be

and

, meaning the CI of the RR would be from 1.75 to 5.13. You would interpret this

by saying that that 2023 RR for adult Type II diabetes incidence is 3.0 times the rate in City ABC

compared to City XYZ (95 percent CI 1.75 to 5.13).

Comparing two event rates

The examples in this chapter have compared incidence (or event) rates of adult Type II diabetes in

2023 between City XYZ and City ABC. These two event rates are represented as

for City XYZ, and

for City ABC. They are based on City XYZ having an

of 30 events and City ABC having an

of 24 events, and on exposures

and

for City XYZ and City ABC, respectively. The difference in

event rates between City XYZ and City ABC can be tested for significance by calculating the 95

percent CI around the RR, and observing whether that CI includes the value of 1.0. Because the RR is

a ratio, having 1.0 included in the CI indicates that City XYZ’s and City ABC’s rates could be

identical. If the 95 percent CI around the RR includes 1, the RR isn’t statistically significantly different

from 1, so the two rates aren’t significantly different from each other (assuming α = 0.05). But if the 95

percent CI is either entirely above or entirely below 1.0, the RR is statistically significantly different

from 1, so the two rates are significantly different from each other (assuming α = 0.05).

For the City ABC and City XYZ adult Type II diabetes 2023 rate comparison, the observed RR was

3.0, with a 95 percent confidence interval of 1.75 to 5.13. This CI does not include 1.0 — in fact, it is

entirely above 1.0. So, the RR is significantly greater than 1, and you would conclude that City ABC

has a statistically significantly higher adult Type II diabetes incidence rate than City XYZ (assuming α

= 0.05).

Comparing two event counts with identical exposure

If — and only if — the two exposures (

and

) are identical, there’s an extremely simple rule for

testing whether two event counts (

and

) are significantly different from each other at the level of

α = 0.05: If

, then the Ns are statistically significantly different (at α = 0.05).

To interpret the formula into words, if the square of the difference is more than four times the

sum, then the event counts are statistically significantly different at α = 0.05. The value of 4 in this

rule approximates 3.84, the chi-square value corresponding to p = 0.05.

Imagine you learned that in City XYZ, there were 30 fatal car accidents in 2022. In the following year,

2023, you learned City XYZ had 40 fatal car accidents. You may wonder: Is driving in City XYZ

getting more dangerous every year? Or was the observed increase from 2022 to 2023 due to random

fluctuations? Using the simple rule, you can calculate

, which is