SECTION 8.2 SUMMARY

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where and are the sample proportions:

and

where z* is the value for the standard Normal density curve with area C between −z* and z*. The large-sample level C confidence interval is

D ± m

We recommend using this interval for 90%, 95%, or 99% confidence when the number of successes and the number of failures in both samples are all at least 10. When sample sizes are smaller, alternative procedures such as the plus four estimate of the difference in two population proportions are recommended.

with P-values from the N(0, 1) distribution. In this statistic,

and is the pooled estimate of the common value of p1 and p2:

Use this test when the number of successes and the number of failures in each of the samples are at least 5.

Confidence intervals for relative risk are often used to summarize the comparison of two proportions.