Data Matters with SPSS®

Activity 4.3

Section 4.3 makes a set of claims about p-values of chi-square statistics. They are summarized in Table 4.3.3 from Data Matters.

Your task in this project is to check those critical values. You will do that by collecting measures from random samples from a simulation in which the null hypothesis is true, saving the chi-square values. You can then sort the chi-square values and make sure that only 5% are above each critical value.

Here is how to check the critical value for df of 1.

First, modify the Syntax program from Section 4.1. The changes are in bold.

INPUT PROGRAM.
  LOOP #Sample = 1 TO 100.
    LOOP #Case = 1 to 60.
      COMPUTE sample = #Sample.
      COMPUTE row = TRUNC(RV.UNIFORM(0,2)).
      COMPUTE column = TRUNC(RV.UNIFORM(0,2)).
      COMPUTE select = MOD($CASENUM,7).
      END CASE.
    END LOOP.
  END LOOP.
  END FILE.
END INPUT PROGRAM.
EXECUTE.

In addition to creating the variable that indicates which sample an observation is in as it did in the Section 4.1 version, this Syntax creates three other variables: a row variable, row, a column variable, column, and a third variable, select, that we won’t use for a while.

The row variable is set in two steps. RV.UNIFORM(0,2) draws a random number from 0 to just under 2. TRUNC then strips off the decimal, leaving 0 or 1. The same two steps create random 0’s or 1’s for column. Look at what appears in the data editor to see what this Syntax does.

To get the chi-square values, select Analyze, Descriptive Statistics, Crosstabs. Select the variable row and click on the black triangle next to the Row(s) box. Select column and click on the black triangle next to the Column(s) box. Select Sample and click on the black triangle next to the Layer 1 of 1 box. Click on Statistics, select Chi-Square, click on Continue, then click OK.

SPSS returns results on 100 chi-square tests. Scroll down through the output until you see the chi-square tests. Double-click on the Chi-Square Tests table. There are a variety of chi-square values that can be used to test cross-tabs. We are interested in the Pearson chi-square value. Select the top Pearson chi-square value. Scroll to the last sample, hold down “Shift,” and click on the last Pearson chi-square value. That will select the column of values. Do not worry that it is selecting more than Pearson chi-square values. We will get to that.

Right-click on the selected column and select Copy. Open the data editor, right-click a cell in the column next to the select variable, and select Paste. Now the Select column has a 1 in each row that has a Pearson chi-square value. You need to get rid of the rest of the values. Click on Data, Select Cases, If condition is satisfied, If. Enter select=1 and click on Continue, Deleted, OK. Now the other kinds of chi-square values are deleted.

To check the cutoffs in Table 4.3.3, sort the chi-square values. Click on Data, Sort Cases and double-click on the variable that is holding your chi-square values. (It is probably called “var00001.”) Click OK.

Now you can find the chi-square values that were higher than 95% of the chi-square values.

How did the table do? Is 3.84 a good cutoff?

For Degrees of Freedom Over One

To work with cross-tabs with more rows and/or more columns, empty the data file (File, New, Data) and edit the Syntax program to create more rows, more columns, or both. COMPUTE row = TRUNC(RV.UNIFORM(0,3)). would create three rows. COMPUTE row = TRUNC(RV.UNIFORM(0,4)). would create four rows, and so on.

Check all five rows of Table 4.3.3. Find the critical cutoff for six degrees of freedom.

Try different cross-tab designs that have the same degrees of freedom, like a three-column-by-three-row design and a two-row-by-five-column design. Do the cutoffs stay in the same place? Do the chi-square values really have the same distribution when the null hypothesis is true?

Check whether sample size matters.

Check whether it is really true that the expected counts must be at least 5. You can do this by using a two-column-by-two-row design with 19 observations in each sample.

In the last section, you found the chi-square values for tests of correlations in the U.S. population. You were working with the representative U.S. sample that is available from the Data Matters web site at www.keycollege.com/dm. Now get the p-values and report those tests in two ways: once in the style of the popular press and once in the complete style of the sciences.