LESSON 17: THE F-DISTRIBUTION Outline The F-distribution

THE F-DISTRIBUTION If you have two populations, and if you want to know if two populations have an identical variance, use F-distribution if each population has a normal distribution. The F-distribution also uses sample variance to make an inference about population variance. The F-distribution is used to compare the variances of two samples.

THE F-DISTRIBUTION Consider any two normally distributed populations and . Let = variance of a sample of size drawn from and = variance of a sample of size drawn from The F-statistic is as follows:

THE F-DISTRIBUTION The F-distribution is positively skewed and its shape depends on two parameters Degrees of freedom for numerator = Degrees of freedom for denominator =

THE F-DISTRIBUTION For each upper-tail probability , there is a critical value such that A large F-square statistic is usually undesirable. It is inferred at significance level that two population do not have an identical variance if

THE F-DISTRIBUTION Table J, Appendix A, pp. 546-553 gives the critical values F.05 (lightface) and F.01 (boldface) for various numerator and denominator degrees of freedoms. The relevant Excel commands are FDIST and FINV FDIST (critical value, d.f. numerator, d.f. denominator) returns the upper tail area FINV (upper tail area, d.f. numerator, d.f. denominator) returns the critical chi-square value. Thus, FINV does the same job as Table J.

THE F-DISTRIBUTION Example 1: Determine the critical values for the F-statistic in the following cases: a. b.

THE F-DISTRIBUTION Example 2: Does the following two population have an identical variance at 5% level of significance?

THE F-DISTRIBUTION Example 3: Does the following two population have an identical variance at 5% level of significance?

READING AND EXERCISES Lesson 17 Reading: Section 9-6, pp. 289-291 9-41, 9-42