Basic Statistics

CHAPTER 9

VARIANCES: ESTIMATION AND TESTS

In Chapter 5 we discussed the importance of variability, and by now it should be

apparent that one of the major problems in working with any type of data is assessing

its variability. Even if the ultimate goal is to estimate the mean of a population, we

need to obtain an estimate of its variance and standard deviation, and then use this

estimate in testing hypotheses or developing confidence intervals for the mean. When

the t test is used to test whether two population means are equal, we assume that the

population variances are equal, so it is important to know how to perform this test.

In Chapters 7 and 8 we presented confidence intervals and tests of hypotheses

for population means. This chapter gives tests of hypotheses concerning population

variances. In Section 9.1 we review how to make point estimates of a pooled variance

from two samples and give a comparable formula for the pooled estimate from more

than two samples. In Section 9.2 we describe how to test whether two population

variances are equal. The test for equality of the variances is needed since we assume

equal variances when doing a t test of equal means. Also, a treatment that gives

consistent results may be preferred over one that has highly variable results. In

Section 9.3 an approximate t test for the equality of two means is given that can be

used if we find that the population variances are unequal. Finally, in Section 9.4 a

Basic Statistics: A Primer for the Biomedical Sciences, Fourth Edition.

By Olive Jean Dunn and Virginia A. Clark

Copyright @ 2009 John Wiley & Sons, Inc.

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