The Essentials of Biostatistics for Physicians, Nurses, and Clinicians

82 CHAPTER 6 Hypothesis Testing

in Section 6.7 relating confi dence intervals and to hypothesis tests, we
reject H 0 if μ 0 < 727.1, or if μ 0 > 1558.9, and do not reject if
727.1 ≤ μ 0 ≤ 1558.9. There are many other bootstrap confi dence inter-
vals, and each can be used to construct a test. See Efron and Tibshirani
( 1993 ) or Chernick ( 2007 ) for details.

6.10 MEDICAL DIAGNOSIS: SENSITIVITY

AND SPECIFICITY

Screening tests are used to identify patients who should be referred for

further diagnostic evaluation. To determine the quality of a screening

test, it is best to have a gold standard to compare it with. The gold

standard provides a defi nitive diagnosis of the disease. For healthy

individuals, the tests, if they are numerical, there is a range called the

normal range.

Formulating the screening test as a statistical hypothesis testing

problem, we would see that these two types of error could be the type

I and type II errors for the hypothesis test. In medical diagnosis, we

have special terminology. Table 6.2 shows the possible results.

In this case, we apply a screening test to n patients with the fol-

lowing outcomes. Based on the gold standard, m of the patients had the

disease, and n − m did not. Of the m diseased patients, “ a ” were found

positive based on the test, and c were found negative. So m = a + c.

Of the n − m patients that were not diseased based on the gold standard

b tested positive, and d were found negative. So b + d = n − m. The

off - diagonal terms represent the two types of error. The number of false

positives is b , and the number of false negatives is c.

Table 6.2

Sensitivity and Specifi city for a Diagnostic Test Compared to a

Gold Standard

Test results True condition of the patient

based on gold standard

Total

Diseased Not diseased

Positive for disease A b s = a + b
Negative for disease C d n − s = c + d
Total m = a + c n − m = b + d n = a + b + c + d