- Calculate a confidence interval for the difference in proportions of two groups.
- Make conclusions based on a confidence interval.
Confidence interval for the difference in proportions
To estimate a difference between two population proportions (or the size of a treatment effect), we select two independent random samples and use the difference in sample proportions as an estimate. Of course, random samples vary, so we want to include a statement about the amount of error that may be present. Because the differences in sample proportions vary in a predictable way, we can also make a probability statement about how confident we are in the process that we used to estimate the difference between the population proportions. This describes a confidence interval.
Let’s focus on using technology to calculate the confidence interval for the difference between two population proportions for independent groups.
Step 1: To enter the summary data at the beginning of this preview assignment, select Number of Successes under Enter Data on the left-hand side.
Step 2: Since we are interested in calculating the confidence interval for [latex]\hat{p}_{group1} - \hat{p}_{group2}[/latex], assign the correct variable to Group 1 and Group 2.
Step 3: Enter the number of successes and sample sizes for each group in the tool. You can add informative group labels by clicking Provide Labels for: Groups.
Step 4: Change the confidence interval using the slider on the left-hand side accordingly.