Introductory Biostatistics

2.Comparison of conditional probability and unconditional (or marginal)

probability: for example, PrðX¼þjY¼þÞversus PrðX¼þÞ.

3.Comparison of conditional probabilities: for example, PrðX¼þjY¼þÞ

versus PrðX¼þjY¼
Þ. The screening example above yields

PrðX¼þjY¼þÞ¼ 0 : 406

whereas

PrðX¼þjY¼
Þ¼

362

23 ; 724

¼ 0 : 015

again clearly indicating a statistical relationship. It should also be noted

that we illustrate the concepts using data from a cancer screening test but

that these concepts apply to any cross-classification of two binary factors

or variables. The primary aim is to determine whether a statistical rela-

tionship is present; Exercise 3.1, for example, deals with relationships

between health services and race.

The next two sections present some applications of those simple probability
rules introduced in Section 3.1.2: the problem ofwhento use screening tests and
the problem ofhowto measure agreement.

3.1.4 Using Screening Tests

We have introduced the concept of conditional probability. However, it is
important to distinguish the two conditional probabilities, PrðX¼þjY¼þÞ
and PrðY¼þjX¼þÞ. In Example 1.4, reintroduced in Section 3.1.3, we
have

PrðX¼þjY¼þÞ¼

154

379

¼ 0 : 406

whereas

PrðY¼þjX¼þÞ¼

154

516

¼ 0 : 298

Within the context of screening test evaluation:

PROBABILITY 115