Cross-tabulations and Banners

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

Example #1

Example #2

Looking for Differences Between Groups

Type ofMeasurement

Differences between two independent groups

Nominal Chi-square test

When Chi-square Test Appropriate

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

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

n

CRE ji

ij

Ri = total observed frequency in the ith rowCj = total observed frequency in the jth columnn = sample size

Chi-Square Test

d.f.=(R-1)(C-1)

Degrees of Freedom

Chi-Square Test

21

)2110(

39

)3950( 222

X

14

)1425(

26

)2615( 22

161.22

643.8654.4762.5102.32

2

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

TwoTworatingratingscalesscales 4 quadrants4 quadrants

two-dimensionaltwo-dimensionaltabletable Importance-Importance-

PerformancePerformanceAnalysis)Analysis)

Quadrant Analysis