CHAPTER 12 Comparing Proportions and Analyzing Cross-Tabulations 167

Putting it all together with some

notation and formulas

The calculations of the Pearson chi-square test can be summarized concisely

using the cell-naming conventions shown in Figure 12-6, along with the standard

summation notation described in Chapter 2.

Using these conventions, the basic formulas for the Pearson chi-square test are as

follows:»

» ^{Expected values: Ex}

R

C

T

i

N j

M

i j

i

j

,

,

, , ...

;

, ,

...

1 2

1 2»

» ^{Chi-square statistic:}

2

2

1

1

(

)

,

,

,

Ob

Ex

Ex

i j

i j

i j

j

M

i

N»

» ^{Degrees of freedom: df}

(

)(

)

N

M

1

1

where i and j are array indices that indicate the row and column, respectively, of

each cell.

Pointing out the pros and cons

of the chi-square test

The Pearson chi-square test is very popular for several reasons:»

» ^{It’s easy! The calculations are simple to do manually in Microsoft Excel}

(although this is not recommended because the risk of making a typing

mistake is high). As described earlier, statistical software packages like

the ones discussed in Chapter 4 can perform the chi-square test for both

individual-level data as well as summarized cross-tabulated data. Also,

several websites can perform the test, and the test has been implemented

on smartphones and tablets.

FIGURE 12-6:

A general way of

naming the cells

of a cross-tab

table.

© John Wiley & Sons, Inc.