#### Description:

In this video, we’ll show you how to calculate the sample size needed to achieve a confidence interval for the difference between two proportions with a specified width and confidence level using PASS.

As an example, suppose we want to compute the sample size required for a two-sided 95% confidence interval if the difference in proportions is 0.2 and the desired margin of error is plus or minus 5%. We’ll assume that the sample proportion for group 2 is 0.45 and that there will be twice as many individuals in group 2 when compared to group 1.

To perform this calculation in PASS, first load the Confidence Intervals for the Difference Between Two Proportions procedure using the category tree or the search bar on the PASS Home Window.

For Solve For, select Sample Size. This procedure also allows you to solve for the interval width achieved at a given sample size.

The procedure includes a number of possible confidence interval formulas, but for this example, we’ll use the Pearson Chi-Square formula.

Select Two-Sided for Interval Type for a two-sided confidence interval.

For a 95% confidence interval, we set Confidence Level to 0.95.

Since we want twice as many individuals in group 2, change group allocation to Enter R and set R, which is equal to the number in group 2 divided by the number in group 1, to 2.

For a margin of error of plus or minus 5%, set the two-sided confidence interval width to 0.1.

Finally, set Input Type to differences and enter an assumed proportion difference of 0.2 and a group 2 proportion of 0.45. Remember that the sample size calculations assume that the value entered here will be the actual proportion estimate that is obtained from the sample. If the sample proportion is different from the one specified here, the width may be narrower or wider than specified.

Now, click the Calculate button to perform the calculations and get the results. The required sample sizes for the desired interval are 540 in group 1 and 1080 in group 2.