Data Matters with SPSS®

Activity 5.2

There are two tasks in this project.

1. Take many random samples from the representative U.S. sample and save the samples’ means, then get a histogram of the samples’ means.
2. Collect a distribution of proportions that is normally distributed and check the symmetry.

Here’s how to do them.

Step 1. Take many random samples from the representative U.S. sample and save the samples’ means. Get a histogram of the samples’ means.

For this project, follow the same steps as for the project in Section 3.1. You will sort randomly, then add a variable, sample, that assigns the first bunch of observations to the first sample, the second bunch to the second sample, and so on.

You may recall that this approach is not ideal and that there are some fixes (found at the end of Section 3.1), which you may use if you would like.

Sorting Randomly

Open RepUSSample.sav and get into the data editor.

To add the random number, click on Transform, Compute. Name your new target variable random, name the numeric expression RV.UNIFORM(0,100), and click OK.

To sort, click on Data, then select Sort Cases. Double-click on random and click OK.

Adding the Sample Variable

You won’t be able to take more samples than 50,000 divided by your sample size. Use Transform, Compute to add the new target variable, sample. Before you enter a numeric expression, click on If, Include if case satisfies condition: and enter an equation so that SPSS doesn’t add sample to more people than you want to consider. For example, if you want 50 samples of 10 people each, then you want to consider 500 people, so you would enter the equation $CASENUM <= 50*10 .

Click on Continue and you’re ready to enter your numeric expression. If your sample size is 55, then the expression is TRUNC(($CASENUM-1)/55) .

To get the means, click on Data, Aggregate. Scroll down, select sample, and click on the triangle next to the Break Variable(s) box. Select the variable you are interested in and click on the triangle next to the Aggregate Variable(s) box. The default summary is mean. Select Replace working data file and click OK.

SPSS returns a mean for the variables you didn’t assign a sample for. They appear at the top and have “.” (a period) for sample. You can select and delete that row.

Get a histogram of the samples’ means (Graphs, Histogram, and so forth). How would you describe the distribution? What is the mean? What is the median?

You can change the sample size by using a different equation when you add the sample variable. Does the sample size make a difference?

Step 2. Collect a distribution of proportions that is normally distributed and check the symmetry.

Call up the data set of one of the projects for which you took samples and recorded their proportions. For example, the project in Section 3.3 has proportions from random samples. If your probability was near 0 or 100% and your sample size is small, the distribution won’t be normal. In that case, edit the program to set the probability to 50%.

If you don’t have a copy of a data set with proportions from random samples, go back and follow the steps to collect proportions from random samples.

Get the mean and median of one of the proportions by selecting Analyze, Descriptive Statistics, Explore.

Does it appear that the distribution is symmetrical? Try other sample sizes. Does sample size matter? Try other probabilities. How do sample size and probability affect the symmetry?