11.1. The F-Distribution and Testing Two Variances http://www.ck12.org
11.1 The F-Distribution and Testing Two Vari-
ances
Learning Objectives
- Understand the differences between theF- and the Student’st-distributions.
- Calculate a test statistic as a ratio of values derived from sample variances.
- Use random samples to test hypotheses about multiple independent population variances.
- Understand the limits of inferences derived from these methods.
Introduction
In previous lessons we learned how to conduct hypothesis tests examining the relationship between two variables.
Most of these tests simply evaluated the relationship of themeansof two variables. However, sometimes we also
want to test thevarianceor the degree to which observations are spread out within a distribution. In the figure below,
we see three samples with identical means (the samples in red, green and blue) but with very difference variances.
So why would we want to conduct a hypothesis test on variance? Let’s consider an example. Say that a teacher
wants to examine the effectiveness of two reading programs. She randomly assigns her students into two groups,
uses the different reading programs with each group and gives her students an achievement test. In deciding which
reading program is more effective, it would be helpful to not only look at the mean scores of each of the groups, but
also the “spreading out” of the achievement scores. To test hypotheses about variance, we use a statistical tool called
theF-distribution.