CHAPTER 14 Analyzing Incidence and Prevalence Rates in Epidemiologic Data 197
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 (E1 and E2) are identical, there’s an extremely
simple rule for testing whether two event counts (N1 and N 2) are significantly dif-
ferent from each other at the level of α = 0.05: If N
N
N
N
1
2
2
1
2
4, 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 30
40
30
40
100 70
1 4
2
–
.
/
/
, which is less than 4. Having
30 events — which in this case are fatal car accidents — isn’t statistically signifi-
cantly different from having 40 events in the same time period. As you see from
the result, the increase of 10 in one year is likely statistical noise. But had
the number of events increased more dramatically — say from 30 to 50 events —
the increase would have been statistically significant. This is because
30
50
30
50
400 80
5 0
2 /
/
. , which is greater than 4.