LibraryPirate

EXERCISES 627
If we wish to test the same hypothesis using the chi-square approach, our contingency
table will be
Characteristic Present
Sample Yes No Total
1 60 40 100
2 48 72 120
Total 108 112 220
By Equation 12.4.1 we compute
X 2 =
220316021722 - 1402148242
11082111221100211202
= 8.7302
which is significant at the .05 level because it is greater than the critical value of
3.841. We see, therefore, that we reach the same conclusion by both methods. This
is not surprising because, as explained in Section 12.2, x We note that
8.7302 = 12.954692 2 and that 3.841 = 11.962 2 112 2 = z 2 .
.
EXERCISES
In the exercises that follow perform the test at the indicated level of significance and determine
the p value.
12.5.1 Refer to the study by Carter et al. (A-9), who investigated the effect of age at onset of bipolar disorder
on the course of the illness. One of the variables studied was subjects’ family history. Table
3.4.1 shows the frequency of a family history of mood disorders in the two groups of interest:
early age at onset (18 years or younger) and later age at onset (later than 18 years).
Family History of Mood
Disorders Early … 181E2 Later 7 181L2 Total
Negative (A) 28 35 63
Bipolar disorder (B) 19 38 57
Unipolar (C) 41 44 85
Unipolar and bipolar (D) 53 60 113
Total 141 177 318
Source: Tasha D. Carter, Emanuela Mundo, Sagar V. Parkh, and James L. Kennedy,
“Early Age at Onset as a Risk Factor for Poor Outcome of Bipolar Disorder,” Journal
of Psychiatric Research, 37 (2003), 297–303.
Can we conclude on the basis of these data that subjects 18 or younger differ from subjects older
than 18 with respect to family histories of mood disorders Let a = .05.