Chapter 7 Tables 295Like the normal and t distributions, the x^2 distribution has a critical
boundary for rejecting the null hypothesis, but unlike those distributions,
it’s a one-sided boundary. There are a few situations where one might use
upper and lower critical boundaries.
The critical boundary is shown in your chart with a vertical red line.
Currently, the critical boundary is set for a5 0. 0 5. In Figure 7-18, this is
equal to 7.815. You can change the value of a in this worksheet to see the
critical boundary for other p values.
To change the critical boundary:1 Click the p value box, type 0.10, and press Enter.
The critical boundary changes, moving back to 6.251.Experiment with other values for the degrees of freedom and the critical
boundary.
When you’re fi nished with the worksheet:1 Close the Distributions workbook. Do not save any changes.
2 Return to the Survey Table Statistics workbook, displaying the
Calculus Department Table worksheet.
The degrees of freedom for the Pearson chi-square are determined by
the numbers of rows and columns in the table. If there are r rows and
c columns, the number of degrees of freedom are^1 r 21231 c 212. For our
table of calculus requirement by department, there are 4 rows and 2 col-
umns, and the number of degrees of freedom for the Pearson chi-square
statistic is 14212312212 , or 3.
Where does the formula for degrees of freedom come from? The Pearson
chi-square is based on the differences between the observed and expected
counts. Note that the sum of these differences is 0 for each row and column
in the table. For example, in the fi rst column of the table, the expected and
observed counts are as shown in Table 7-2: