Cross-tabulations and
Banners: Part I
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Dr. Michael R. Hyman, NMSU
Sample SPSS Cross-tabulation Output
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Cross-tabulation
• Way to organize data by groups or
categories, thus facilitating comparisons;
joint frequency distribution of observations
on two or more sets of variables
• Contingency table: Result of crosstabulating two variables, such as survey
questions
• Relative to univariate analyses, bivariate
analyses can provide more insights
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Example #1
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Example #2a
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Banner
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Looking for Differences Between Groups
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When Chi-square Test
Appropriate
Type of
Measurement
Differences between
two independent groups
Nominal
Chi-square test
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Example #3
Awareness of Tire
Manufacturer’s Brand
Men
Aware
Unaware
50
15
65
Women
10
25
35
Total
60
40
100
Question: Do men differ from women in
their awareness?
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Chi-Square Test
(Oi  Ei )²
x²  
Ei
x² = chi-square statistics
Oi = observed frequency in the ith cell
Ei = expected frequency on the ith cell
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Calculation for Expected Count
in a Cell for Unrelated Variables
E ij 
R iC
j
n
Ri = total observed frequency in the ith row
Cj = total observed frequency in the jth
column
n = sample size
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Degrees of Freedom
d.f.=(R-1)(C-1)
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Chi-Square Test
( 50  39 )
(10  21)


39
21
2
2
(15  26 )
( 25  14 )


26
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2
X
2
2
  3.10  5.76  4.65  8.64 
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  22.16
2
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Example #2b
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