was 12.0 (95 percent CI = 9.24 – 14.76) per month.”

To calculate the CI around the event count itself, you estimate the SE of the count N as

, then

calculate the CI around the observed count using the formulas in the earlier section “Before you begin:

Formulas for confidence limits in large samples.” So the SE of the 36 observed serious falls in a

three-month period is simply

, which equals 6.0. So for the confidence limits, we have

and CLU = 36.0 + 1.96 × 6.0. In this case, the ME is 11.76, which works

out to a 95 percent CI of 24.2 to 47.8 serious falls in the three-month period.

Many other approximate formulas for CIs around observed event counts and rates are

available, most of which are more reliable when your N is small. These formulas are too

complicated to attempt by hand, but fortunately, many statistical packages can do these

calculations for you. Your best bet is to get the name of the formula, and then look in the

documentation for the statistical software you’re using to see if it supports a command for that

particular CI formula.

Relating Confidence Intervals and Significance

Testing

In Chapter 3, we introduce the concepts and terminology of significance testing, and in Chapters 11

through 14, we describe specific significance tests. If you read these chapters, you may have come to

the correct conclusion that it is possible to assess statistical significance by using CIs. To do this, you

first select a number that measures the amount of effect for which you are testing (known as the effect

size). This effect size can be the difference between two means or the difference between two

proportions. The effect size can also be a ratio, such as the ratio of two means, or other ratios that

provide a comparison, such as an odds ratio, a relative risk ratio, or a hazard ratio (to name a few).

The complete absence of any effect corresponds to a difference of 0, or a ratio of 1, so we call these

the “no-effect” values.

The following statements are always true:

If the 95 percent CI around the observed effect size includes the no-effect value, then the effect is

not statistically significant. This means that if the 95 percent CI of a difference includes 0 or of a

ratio includes 1, the difference is not large enough to be statistically significant at α = 0.05, and we

fail to reject the null.

If the 95 percent CI around the observed effect size does not include the no-effect value, then the

effect is statistically significant. This means that if the 95 percent CI of a difference is entirely

above or entirely below 0, or is entirely above or entirely below 1 with respect to a ratio, the

difference is statistically significant at α = 0.05, and we reject the null.