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Cross tabs, Chi Square, Followup (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 nonobese people are? Race and hi vs lo incomeDo 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
RowsRace Recode RACREC_1 (From Adult Sample)
ColumnsFamily Income </>$20,000 ABBL20K
Statistics—Xchi square—Continue
Cells—Counts, Observed—check; Expected—no checks
Percentagescheck
Continue
OK
Followup with interesting findings, if the overall Chi Squared is statistically significant.
Data—Select casesIf condition is satisfied
IF—Race Recodeblacks 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
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% 
ChiSquare Tests 


Value 
df 
Asymp. Sig. (2sided) 
Exact Sig. (2sided) 
Exact Sig. (1sided) 
Pearson ChiSquare 
407.657^{a} 
1 
.000 


Continuity Correction^{b} 
406.869 
1 
.000 


Likelihood Ratio 
380.670 
1 
.000 


Fisher's Exact Test 



.000 
.000 
LinearbyLinear 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 CasesBlacks only – 3952 Cases
NPAR TESTS
/CHISQUARE=AB_BL20K
/EXPECTED=.759 .241
/MISSING ANALYSIS.
From proportion .759, .241
Nonparametric testChi Square on Blacks
NPar Tests
ChiSquare 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 
ChiSquare 
510.639^{a} 
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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