Computing confidence intervals for the difference between two proportions with summary data

This tutorial covers the steps for computing confidence intervals for the difference between two proportions in StatCrunch.
This example will look at a Gallup survey taken in July and August 2014 which asked 945 Republicans and 854 Democrats to name biggest problem facing the United States. The number of Republicans classifying each item as a top problem is as follows: Immigration 208; Dysfunctional Government 189; Economy 161; Unemployment 113; Other 274. The number of Democrats classifying each item as a top problem is as follows: Immigration 94; Dysfunctional Government 137; Economy 111; Unemployment 111; Other 401.
For this example, results will be computed using these summary counts. To compute two-sample proportion results using the corresponding raw data set with individual measurements, see Computing confidence intervals for the difference between two proportions with raw data.

Calculating a confidence interval for difference in proportions

A confidence interval can be calculated for the difference between the proportion of Republicans and the proportion of Democrats that identify "Immigration" as the top problem. Choose the Stat > Proportion Stats > Two Sample > With Summary menu option. In StatCrunch, a "success" is used to define the outcome of interest. In this case, consider an Immigration response to be a success. We will use Sample 1 for Republicans and Sample 2 for Democrats.
Under Sample 1, enter 208 for the # of successes and 945 for the # of observations.
Under Sample 2, enter 94 for the # of successes and 854 for the # of observations.
Under Perform, choose Confidence interval for p_{1} - p_{2}. By default, StatCrunch has a value of 0.95 for the Level input which will produce a 95% confidence interval for the difference between the two proportions. Enter 0.99 for this input to produce a 99% confidence interval instead and click Compute!. The results below show a 99% confidence interval for the difference between population proportions with "L. Limit" representing the lower limit and "U. Limit" representing the upper limit of this interval.

Always Learning
Pearson