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Cross tabs, Chi Square, Follow-up (10/15/09)

Cross tabs—for viewing the relationship between two categorical variables, i.e., neither variable is continuous. Cross tabs tallies the percentages of cases in which characteristics occur together in the same individuals within pairs of variables. Examples:  ADHD vs nonADHD and sex—Does ADHD occur more often among boys than girls?; Obesity and Depression:  Are obese people more likely to have depression than non-obese people are? Race and hi vs lo income--Do blacks tend to have low income more often than whites do? (Note:  Both variables must be categorical, not continuous.)

Chi squared test of independence—provides a statistical test of some of the information tallied in cross tabs. Chi square provides a statistical comparison of two variables that, theoretically, are expected to be independent vs. whether they are actually observed to be independent of each other.  Issues: How often do individuals tend to share the same two characteristics? How does level of sharing compare with what you might expect? Is  the difference between the observed and the expected merely from chance, or is it  much less likely than chance?

• Based on the null hypothesis, you would expect boys and girls to have the same rate of ADHD. What is the actual rate? Is any difference in rate just due to chance?
• Based on the null hypothesis, one might expect that obese people have depression as often as non-obese people do. Is that actually the case? Might any discrepancy between the expected and the actual be due to chance alone?
• Based on the null hypothesis, you might expect blacks to have the same rate of low income as whites? What is actually observed? Was the discrepancy merely due to chance?

Analyze—Descriptive Statistics—Cross tabs

            Rows-Race Recode  RACREC_1  (From Adult Sample)

            Columns-Family Income </>$20,000  AB-BL20K

            Statistics—X-chi square—Continue

            Cells—Counts, Observed—check; Expected—no checks

                        Percentages-check

            Continue

            OK

Follow-up with interesting findings, if the overall Chi Squared is statistically significant.

Data—Select cases---If condition is satisfied

            IF—Race Recode-blacks  RACREC_1  = 2

            Continue

            Unselected cases—Filtered

            OK

Analyze—Nonparametric test—Chi Square

            Test variable—Family Income </>$20,000 AB_BL20K

Expected values   (**Be Careful Here**)

            Values—indicate proportion of cases (or actual number of cases) expected for each level of the test variable. E.g, Expectation:  % blacks above and below $20,000 should be same as %  whites (Copy % from your first cross tabs. In my example on the attached print out, I entered .759, .241).  Enter in those proportions in the order they appear. Use Add after entering each value.

OK

At the end,

Data—Selected cases—Reset—OK

GET

  FILE='H:\SEMINAR DATA FILES\SAM ADULT 02 17 09.sav'.

CROSSTABS

  /TABLES=RACREC_I BY AB_BL20K

  /FORMAT=AVALUE TABLES

  /STATISTICS=CHISQ

  /CELLS=COUNT ROW COLUMN

  /COUNT ROUND CELL.

SPSS Crosstabs and Chi Square Output

Comparison of Percentages of Whites vs. Blacks with Low Income

Select Cases--Blacks only – 3952 Cases

NPAR TESTS

  /CHISQUARE=AB_BL20K

  /EXPECTED=.759 .241

  /MISSING ANALYSIS.

From proportion .759, .241

Nonparametric test-Chi Square on Blacks

NPar Tests

Chi-Square Test

Frequencies

The expected N above is from proportions .759 and .241, the high income, low income split for whites.

The chi square is highly significant (p<.001).

Proportionally, many more blacks have low income than whites.

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