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

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)2110(

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)3950( 222

X

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)1425(

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)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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