162 PART 4 Comparing Groups

Figure 12-1 shows how this works out for the observed data taken from the exam-

ple in this chapter’s introduction. You can see from the marginal “Total” row that

the overall rate of pain relief (for both groups combined) is 43/100, or 43 percent.

Figure 12-1 presents the actual data you observed from your survey, where the

observed counts are placed in each of the four cells. As part of the chi-square test

statistic calculation, you now need to calculate an expected count for each cell. This

is done by taking the product of the row and column marginals and dividing them

by the total. So, to determine the expected count in the CBD/pain relief cell, you

would multiply 43 (row marginal) by 60 (column marginal), then divide this by

100 (total) which comes out 25.8. Figure 12-2 presents the fourfold table with the

expected counts in the cells.

The reason you need these expected counts is that they represent what would

happen under the null hypothesis (meaning if the null hypothesis were true). If

the null hypothesis were true:»

» ^{In the CBD-treated group, you’d expect about 25.8 participants to experience}

pain relief (43 percent of 60), with the remaining 34.2 reporting no pain relief.

FIGURE 12-1:

The observed

results comparing

CBD to NSAIDs

for the treatment

of pain from

chronic arthritis.

© John Wiley & Sons, Inc.

FIGURE 12-2:

Expected cell

counts if the null

hypothesis is true

(there is no

association

between either

drug and the

outcome).

© John Wiley & Sons, Inc.