11.1. The F-Distribution and Testing Two Variances http://www.ck12.org
F-Max Test: Calculating the Sample Test Statistic
We use theF-ratiotest statistic when testing the hypothesis that there is no difference between population variances.
When calculating this ratio, we really just need the variance from each of the samples. It is recommended that the
larger sample variance be placed in the numerator of theF-ratio and the smaller sample variance in the denominator.
By doing this, the ratio will always be greater than 1.00 and will simplify the hypothesis test.
Example:
Suppose a teacher administered two different reading programs to two groups of students and collected the following
achievement score data:
Program 1 Program 2
n 1 = 31 n 2 = 41
X ̄ 1 = 43. 6 X ̄ 2 = 43. 8
s 12 = 105. 96 s 22 = 36. 42What is theF-ratio for these data?
Solution:
F=
s 12
s 22=
105. 96
36. 42
≈ 2. 909
F-Max Test: Testing Hypotheses about Multiple Independent Population Variances
As mentioned, in certain situations we are interested in determining if there is a difference in the population variances
between two independent samples. We can conduct a hypothesis test of no difference between the population
variances with the null hypothesis ofH 0 :σ 12 =σ 22. Therefore, our alternative hypothesis would beHa:σ 126 =σ 22.