The Essentials of Biostatistics for Physicians, Nurses, and Clinicians

74 CHAPTER 6 Hypothesis Testing

Figure 6.1. Power functions for a normal distribution with mean δ and sample sizes 25
and 100. Null hypothesis δ = 0.

Power Function for two sample sizes

Power

Alternative Mean

–1.5 –1 –0.5 0 0.5 1 1.5

1. 2

1

0.8

0.6

0

0.4

0.2

N=100 N=25

6.2 ONE - TAILED AND TWO - TAILED TESTS

The test described with the power function in Figure 6.1 is an example

of a two - tailed test. Two - tailed tests are test where we consider both

δ > 0 and δ < 0 as part of the alternative. A one - tailed test is a test

where only one side is of interest for the alternative. So, for example,

if you want to show drug A is better than drug B at lowering cholesterol,

we would only be interested to see if drug A had a larger drop from

baseline in cholesterol than drug B. Then, if we take δ = change from

baseline for A − change from baseline for B, we are interested if δ < 0.

But δ > 0 is no more interesting than δ = 0. So in this case, δ > 0 is as

much a part of the null hypothesis as δ = 0. There are also cases where

δ ≤ 0 is not interesting, and is included in the null hypothesis because

we are only interested if we believe δ > 0.

6.3 P - VALUES

The p - value is simply the probability of getting a value as extreme or

more extreme than the actual value of the observed statistic when the