Data Matters with SPSS®

Activity 6.3

Section 6.3 makes some very precise claims about the means of random samples. It says that if you gathered a bunch of random samples, you would find that they were roughly normally distributed and that the standard deviation of the means would be equal to the standard deviation of the observations in the population divided by the square root of the sample size. This standard deviation of sample means is called the standard error.

Your task in this project is to test those claims; these are the steps for this task.

1. Pick a variable to work with and find its mean and standard deviation in the population.
2. Take random samples, saving their means.
3. Find the mean and standard deviation of the means and get a histogram of the means to see whether these claims are correct.

Step 1: Pick a variable to work with and find its mean and standard deviation in the population.

Open RepUSSample.sav. Click on Analyze, Descriptive Statistics, Explore. Select the variable that you want to work with and click on the black triangle next to the Dependent List box. Click OK.

Step 2: Take random samples, saving their means.

Follow the steps for the project in Section 5.2 to produce a collection of random samples.

Step 3: Find the mean and standard deviation of the means and get a histogram of the means to see whether these claims are correct.

Select Analyze, Descriptives, Explore to explore the sample means.

What do you think? Does the standard error work? Does the standard deviation of the mean equal the standard deviation of the observations divided by the square root of the sample size?

Try other sample sizes. Does sample size affect how well the equation for the standard error works? Is sample size related to the shape of sample distributions?

Try other variables that start out with other distributions. Does the shape of the underlying distribution matter when there are small sample sizes? Does the shape of the population distribution matter when there are large sample sizes?