Data Matters with SPSS®

Activity 2.3

Section 2.3 makes some strong claims about the specifics of the bell curves that samples’ proportions fall into. It says that you can calculate something called the standard error with this equation:

This section also says that if you collect a lot of random samples and sort them from the smallest proportion to the largest, you will see this pattern.

• About 2.5% will be more than two standard errors below the probability.
• About 16% will be more than one standard error below the probability.
• About 50% will be below and about 50% will be above the probability.
• About 16% will be more than one standard error above the probability, so about 67% will be within one standard error of the probability.
• About 2.5% will be more than two standard errors above the probability, so about 95% will be within two standard errors of the probability and about 5% will be more than two standard errors away from the probability.

That’s a lot of claims. In this project you will check these claims to see where they hold up and where they don’t.

You are going to collect the same sorts of proportions you collected in Section 2.2. You will then sort them and work your way up, checking each of the claims.

Pick your probability and sample size. Before you proceed, calculate the standard error and find what you get when you add and subtract one and two standard errors from your probability.

Follow the same steps as in Section 2.2. You can use the same Syntax program altered only so it will use 1,000 samples. (See the LOOP #Sample line.) Notice that in the program you don’t include a comma in “1000.” A comma would confuse SPSS.

INPUT PROGRAM.
  LOOP #Sample = 1 TO 1000.
    LOOP #Case = 1 to 10.
      COMPUTE sample = #Sample.
      COMPUTE draw = RV.BINOMIAL(1,.5).
      END CASE.
    END LOOP.
  END LOOP.
  END FILE.
END INPUT PROGRAM.
EXECUTE.
AGGREGATE OUTFILE = *
  /BREAK = sample
  /percent1 = PIN(draw, 1,1).

In RV.BINOMIAL, set the probability wherever you want it.

Remember that this Syntax program requires a completely new data file to pour its numbers into. If it doesn’t run, get into the data editor and select File, New, Data.

Once you have your column of sample proportions, sort them by selecting Data, Sort Cases. Double-click on percent1, then click OK.

Now you can scroll down to check the claims.

Try other sample sizes and other probabilities. What sample sizes and/or proportions cause trouble for the claims about where the samples’ proportions fall? What kinds of trouble do they cause? Try other numbers of samples, such as 10. Does this cause trouble?