dr. michael r. hyman, nmsu cross-tabulations and banners
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Dr. Michael R. Hyman, NMSU
Cross-tabulations and Banners
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Sample
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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 cross-tabulating 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 #2
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Looking for Differences Between Groups
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Type ofMeasurement
Differences between two independent groups
Nominal Chi-square test
When Chi-square Test Appropriate
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Men Women Total
Aware 50 10 60Unaware 15 25 40
65 35 100
Awareness of Tire Manufacturer’s Brand
Question: Do men differ from women in their awareness?
Example #3
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Chi-Square Test
i
ii )²( ²
E
EOx
x² = chi-square statisticsOi = observed frequency in the ith cellEi = expected frequency on the ith cell
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n
CRE ji
ij
Ri = total observed frequency in the ith rowCj = total observed frequency in the jth columnn = sample size
Chi-Square Test
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d.f.=(R-1)(C-1)
Degrees of Freedom
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Chi-Square Test
21
)2110(
39
)3950( 222
X
14
)1425(
26
)2615( 22
16.22
64.865.476.510.32
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Example #4
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Example #5
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Elaboration and Refinement
• Moderator variable
– Third variable that alters or has a contingent effect on the relationship between an independent variable and a dependent variable
– Spurious relationship
• An apparent relationship between two variables that is not authentic
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