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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?

 

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

            IFRace Recode-blacks  RACREC_1  = 2

            Continue

            Unselected cases—Filtered

            OK

 

Analyze—Nonparametric test—Chi Square

            Test variableFamily 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

 

 

Case Processing Summary

 

Cases

Valid

Missing

Total

N

Percent

N

Percent

N

Percent

Race Recode * Fam inc at/above vs. below $20,000

26829

86.4%

4215

13.6%

31044

100.0%

 

 

Race Recode * Fam inc at/above vs. below $20,000 Crosstabulation

 

Fam inc at/above vs. below $20,000

Total

$20,000 or more

Less than $20,000

Race Recode

White

Count

17354

5523

22877

% within Race Recode

75.9%

24.1%

100.0%

% within Fam inc at/above vs. below $20,000

87.9%

78.0%

85.3%

Black

Count

2392

1560

3952

% within Race Recode

60.5%

39.5%

100.0%

% within Fam inc at/above vs. below $20,000

12.1%

22.0%

14.7%

Total

Count

19746

7083

26829

% within Race Recode

73.6%

26.4%

100.0%

% within Fam inc at/above vs. below $20,000

100.0%

100.0%

100.0%

 

 

Chi-Square Tests

 

Value

df

Asymp. Sig. (2-sided)

Exact Sig. (2-sided)

Exact Sig. (1-sided)

Pearson Chi-Square

407.657a

1

.000

 

 

Continuity Correctionb

406.869

1

.000

 

 

Likelihood Ratio

380.670

1

.000

 

 

Fisher's Exact Test

 

 

 

.000

.000

Linear-by-Linear Association

407.642

1

.000

 

 

N of Valid Cases

26829

 

 

 

 

a. 0 cells (.0%) have expected count less than 5. The minimum expected count is 1043.35.

b. Computed only for a 2x2 table

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

 

Fam inc at/above vs. below $20,000

 

Observed N

Expected N

Residual

$20,000 or more

2392

2999.6

-607.6

Less than $20,000

1560

952.4

607.6

Total

3952

 

 

 

 

 

 

 

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

Test Statistics

 

Fam inc at/above vs. below $20,000

Chi-Square

510.639a

df

1

Asymp. Sig.

.000

 

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

Proportionally, many more blacks have low income than whites.

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