Chapter 7 Tables 291
On the basis of this table, almost 18% of the professors in the survey teach
a class that has calculus as a prerequisite whereas more than 82% do not.
To reformat the table to show counts again:
1 Right-click any of the percentages in the PivotTable; then click Value
Field Settings in the pop-up menu.
2 Click the Show values as tab and select Normal from the Show values
as list box. Click the OK button.
Computing Expected Counts
If a calculus prerequisite were the same in each department, we would ex-
pect to fi nd the column percentages (shown in Figure 7-14) to be about the
same for each department. We would then say that department and calculus
prerequisite are independent of each other, so that the pattern of usage does
not depend on the department. It’s the same for all of them. On the other
hand, if there is a difference between departments, we would say that de-
partment and calculus prerequisite use are related. We cannot say anything
about whether knowledge of calculus is usually required without knowing
which department is being examined.
You’ve seen that there might be a relationship between the calculus vari-
ables and department. Is this difference signifi cant? We could formulate the
following hypotheses:
H 0 : The calculus requirement is the same in all departments
Ha: The calculus requirement is related to the department
How can you test the null hypothesis? Essentially, you want a test statis-
tic that will examine the calculus requirement across departments and then
compare it to what we would expect to see if the calculus requirement and
department type were independent variables.
How do you compute the expected counts? Under the null hypothesis, the
percentage of courses requiring calculus should be the same across depart-
ments. Our best estimate of these percentages comes from the percentage of
the grand total, shown in Figure 7-14. Thus we expect about 82.28% of the
courses to require calculus and about 17.72% not to. To express this value
in terms of counts, we multiply the expected percentage by the total number
of courses in each department. For example, there are 119 courses in the
MathSci departments, and if 17.72% of these had a calculus prerequisite,
this would be 11 930 .177 2 , or about 21.08, courses. Note that the actual
observed value is 42 (cell C7 in Figure 7-13), so the number of courses that
