The Essentials of Biostatistics for Physicians, Nurses, and Clinicians

4.3 Student’s t-Distribution 53

4.2 STANDARD ERROR OF THE MEAN

The standard deviation of the sample mean is sometimes called the

standard error of the mean. We have seen in the previous section that

the standard error of the mean is σ/ n. This is very important, because

it indicates that the variance approaches 0 as n gets large.

4.3 STUDENT ’ S T - DISTRIBUTION

We have already explained some of the history regarding the t -

distribution. Now let ’ s look at it in more detail. The t is a symmetric

Figure 4.1. The effect of shape of population distribution and sample size on the
distribution of means of random samples.
Source: Kuzma, J. W. (1984). Basic Statistics for the Health Sciences. Mountain View, CA:
Mayfi eld Publishing Company, fi gure 7.2, p. 82.

142

SAMPLING DISTRIBUTIONS FOR MEANS

Population diatrlbutions

Values of X Values of X Values of X Values of X

Values of X Values of X Values of X Values of X

Values of X Values of X Values of X Values of X

Values of X Values of X Values of X Values of X

n = 2 n = 2 n = 2 n = 2

n = 5 n = 5 n = 5 n = 5

n = 30 n = 30 n = 30 n = 30