In another flu prevention experiment like Example 14.5, the experimenter decides to search the clinic records for 300 patients in each of the three treatment categories: no vaccine, one shot, and two shots. The n5900 patients will then be surveyed regarding their winter flu history.

The experiment results in a 233 table with the column totals fixed at 300, shown in Table 14.8.

By fixing the column totals, the experimenter no longer has a multinomial experiment with 23356 cells. Instead, there are three separate binomial experiments—call them 1, 2, and 3—each with a given probability pj of contracting the flu and qj of not contracting the flu.

(Remember that for a binomial population, p 1q 51 j j .)

Suppose you used the chi-square test to test for the independence of row and column classifications. If a particular treatment (column level) does not affect the incidence of flu, then each of the three binomial populations should have the same incidence of flu so that 5 5 1 2 3 p p p and 5 5 1 2 3 q q q .

Table 14.8 Cases of Flu for Three Treatments No Vaccine One Shot Two Shots Total Flu " No Flu 12 Total 300 300 300 n