Data Analysis with Microsoft Excel: Updated for Office 2007

Chapter 7 Tables 293

The command generates some output in addition to the table of expected

counts shown in Figure 7-16, which we’ll discuss later. The values in the

Expected Counts table are the counts we would expect to see if a calculus

requirement were independent of department.

The Pearson Chi-Square Statistic

With our tables of observed counts and expected counts, we need to calculate

a single test statistic that will summarize the amount of difference between the

two tables. In 1900, the statistician Karl Pearson devised such a test statistic,

called the Pearson chi-square. The formula for the Pearson chi-square is

Pearson chi-square (^5) a
all cells
1 Observed count 2 Expected count 22
Expected count
If the frequencies all agreed with their expected values, this total would
be 0. If there is a substantial difference between the observed and expected
counts, this value will be large. For the data in Figure 7-16, this value is
Pearson chi-square 5
(^174273) .23 22
73.23
1
(^1152) 15.77 22
15.77
1
(^1252) 20.57 22
20.57
1 c 1
(^12217) .72 22
17.72
5 47.592
Is this value large or small? Pearson discovered that when the null
hypothesis is true, values of this test statistic approximately follow a dis-
tribution called the x^2 distribution (pronounced “chi-squared”). Therefore,
one needs to compare the observed value of the Pearson chi-square with the
x^2 distribution to decide whether the value is large enough to warrant rejec-
tion of the null hypothesis.

CONCEPT TUTORIALS

The^ x

(^2)

Distribution

To understand the x^2 distribution better, use the explore workbook for

Distributions.

To use the Distribution workbook:

1 Open the Distributions workbook, located in the Explore folder.

Enable the macros in the workbook.

2 Click Chi-squared from the Table of Contents column. Review the

material and scroll to the bottom of the worksheet. See Figure 7-17.