Data Matters with Fathom! Dynamic Statistics™ software

Activity 3.1

Section 3.1 claims that if we take random samples from a population, 95% of the time the proportions in those samples will fall within two standard errors of their matching population proportions. That is a 95% prediction interval. A two-thirds prediction interval ranges from one standard error below the population’s proportion to one standard error above it.

To test this claim, use the RepUSSampleMarch2001.ftm file that you used in Section 2.1. Following the same steps as in Sections 2.2 and 2.3, you will take random samples and check whether these prediction intervals work.

The project in Section 3.1 requires these steps.

1. Find out some of the population’s proportions.
2. Pick a sample size and create prediction intervals for random samples’ proportions.
3. Use your software to take random samples.
4. Check what proportion fell within your prediction interval and what proportion fell outside.

Here’s how to do each step.

Step 1: Find out some of the population’s proportions.

Open RepUSSampleMarch2001.ftm. Select Analyze, Estimate Parameters and drag attribute names to find some proportions. Use whichever ones you wish.

Step 2: Pick a sample size and create prediction intervals for random samples’ proportions.

Check Section 3.1 in Data Matters if you’re not sure how to do this.

Step 3: Use your software to take random samples.

Open the Rep US Sample Collection and select Analyze, Sample Cases, Edit, and Inspect Collection. Pick a sample size and enter it in the Sample Size box. If you are using a very large sample size, you might want to turn off Animation to speed things up.

Click on the Measures tab and create a measure for each proportion you are interested in. For example, if you want to know the proportion of each sample that is female, click on <new>, type in a name (like femaleProportion), press “Enter,” right-click your name, and select Edit Formula. Type in the formula Proportion(Gender=”Female”) and click OK. Add as many attributes as you would like.

Select Analyze, Collect Measures, then drag a case table onto the workspace. To get more samples, click on the Measures Collection, then select Edit, Inspect Collection. Enter whatever number of measures you would like to work with. If you’re using a lot of measures, you might want to turn off Animation.

Step 4: Check what proportion fell within your prediction interval and what proportion fell outside.

Look at the case table of proportions. To check whether your prediction interval worked for a proportion, right-click on that proportion’s name and select Sort Ascending. Then scroll through to check how well your prediction interval worked.

Does your prediction interval work correctly? That is, for the 95% prediction interval, do 95% fall inside the interval and 5% fall outside? Do the samples’ proportions that fall outside the interval fall evenly, with 2.5% on each side? For the two-thirds prediction interval, do two-thirds fall inside? Does one-sixth fall below and one-sixth fall above the interval?

Try other sample sizes. Try other variables and measurements. Does the prediction interval work equally well for all population proportions? What if your prediction interval goes below 0 or above 100%? Is it sensible to adjust to those limits? Should you change the other side of the interval?