Data Analysis with Microsoft Excel: Updated for Office 2007

Chapter 7 Tables 297

Breaking Down the Chi-Square Statistic

The value of the Pearson chi-square statistic is built up from every cell in

the table. You can get an idea of which cells contributed the most to the

total value by observing the table of standardized residuals. The value of

the standardized residual is

Standardized residual 5

Observed count 2 Expected count

"Expected count

Figure 7-19 displays the standardized residuals for the Calculus Requirement

by Department table. Note that the highest standardized residual, 4.56, is found

for the MathSci department under the Prereq column, leading us to believe that

this count had the highest impact on rejecting the null hypothesis.

Figure 7-19

Table of

standardized
residuals

Other Table Statistics

A common mistake is to use the value of x^2 to measure the degree of associa-

tion between the two categorical variables. However, the x^2 , along with the

p value, measures only the signifi cance of the association. This is because the

value of x^2 is partly dependent on sample size and the size of the table. For

example, in a 333 table, a x^2 value of 10 is signifi cant with a p value of 0.04,

but the same value in a 434 table is not signifi cant with a p value of 0.35.

A measure of association, on the other hand, gives a value to the asso-

ciation between the row and column variables that is not dependent on the

sample size or the size of the table. Generally, the higher the measure of asso-

ciation, the stronger the association between the two categorical variables.

Figure 7-20 shows other test statistics and measures of association

created by the StatPlus Table Statistics command.