Biostatistics

76 CHAPTER 3 SOME BASIC PROBABILITY CONCEPTS
Solution:
The variable age at onset is broken down into two categories, Early for onset
18 years or younger (E) and Later for onset occurring at an age over 18 years
(L). The variable family history of mood disorders is broken down into four
categories: negative family history (A), bipolar disorder only (B), unipolar
disorder only (C), and subjects with a history of both unipolar and bipolar
disorder (D). The category Early occurs jointly with all four categories of the
variable family history of mood disorders. The four joint probabilities that
may be computed are
PE\ ð AÞ ¼ 28=318 ¼ :0881
PE\ ð BÞ ¼ 19=318 ¼ :0597
PE\ ð CÞ ¼ 41=318 ¼ :1289
PE\ ð DÞ ¼ 53=318 ¼ :1667
We obtain the marginal probability P(E) by adding these four joint probabilities
as follows:
PE ð Þ ¼ PE\ ð AÞþPE\ ð BÞþPE\ ð CÞþPE\ ð DÞ
¼ :0881 þ :0597 þ :1289 þ :1667
¼ :4434
&
The result, as expected, is the same as the one obtained by using the marginal total for
Early as the numerator and the total number of subjects as the denominator.
EXERCISES
3.4.1 In a study of violent victimization of women and men, Porcerelli et al. (A-2) collected information
from 679 women and 345 men aged 18 to 64 years at several family practice centers in the
metropolitan Detroit area. Patients filled out a health history questionnaire that included a question
about victimization. The following table shows the sample subjects cross-classified by sex and the
type of violent victimization reported. The victimization categories are defined as no victimization,
partner victimization (and not by others), victimization by persons other than partners (friends,
family members, or strangers), and those who reported multiple victimization.
No Victimization Partners Nonpartners Multiple Victimization Total
Women 611 34 16 18 679
Men 308 10 17 10 345
Total 919 44 33 28 1024
Source: Data provided courtesy of John H. Porcerelli, Ph.D., Rosemary Cogan, Ph.D.
(a) Suppose we pick a subject at random from this group. What is the probability that this subject
will be a woman?
(b) What do we call the probability calculated in part a?
(c) Show how to calculate the probability asked for in part a by two additional methods.