is also recommended that adjacent groups at the bottom of the table be com-
bined to avoid having any expected frequencies less than 1.
Example 10.4 The purpose of this study was to examine the data for 44
physicians working for an emergency department at a major hospital. The
response variable is the number of complaints received during the preceding
year; other details of the study are given in Example 10.5. For the purpose of
testing the goodness of fit, the data are summarized in Table 10.1.
To obtain the frequencies expected, we first obtain relative frequencies by
evaluating the Poisson probability for each value ofX¼x,
PrðX¼xÞ¼yxey
x!
forx¼ 0 ; 1 ; 2 ;...Since
yy^¼P
xi
44
¼ 3 : 34we have, for example,
PrðX¼ 2 Þ¼3 : 342 e^3 :^34
2!
¼ 0 : 198Each of the expected relative frequencies is multiplied by the sample size, 44, to
TABLE 10.1
Number of
Complaints ObservedOi ExpectedEi
0 1 1.54
1 12 5.19
2 12 8.71
3 5 9.68
4 1 8.10
5 4 5.46
6 2 2.99
7 2 1.45
8 2 0.62
9 1 0.22
10 1 0.09
11 1 0.04TESTING GOODNESS OF FIT 355