LESSON 17: THE F-DISTRIBUTION

1. LESSON 17: THE F-DISTRIBUTION Outline • The F-distribution

2. 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.

3. 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:

4. 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 =

5. 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

6. 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.

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

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

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

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