Conducting hypothesis tests for the difference between two proportions with summary data
This tutorial covers the steps for computing hypothesis tests 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 Conducting hypothesis tests for the difference between two proportions with raw data.
Performing a two-sample proportion hypothesis test
Is there a significant difference between the proportion of Republicans and the proportion of Democrats that identify "Immigration" as the top problem? This can be considered by conducting a hypothesis test for the difference between the two proportions. To compute the appropriate two-sample proportion hypothesis test, 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, the Hypothesis test for p1 - p2 is selected by default. Leave the null value at 0 to directly compare the two proportions. The alternative hypothesis can be changed to > or < , but for this scenario leave the alternative hypothesis at since the goal is to detect any type of difference. Click Compute! to view the hypothesis test results. The hypothesis test output includes the difference of the observed sample proportion of Immigration responses between Republicans and Democrats, the test statistic (labeled as Z-Stat) and the P-value.

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