Question

Below are sets of summary statistics for two sets of samples. You want to compare the variances. How can you compare them?

	Mean	Variance	Range	Sample size
Set 1	43.6	10.2	23-62	17
Set 2	31.2	5.7	25-39	26

Answer 1

we can use f test to compare the two variance

let Ho: $\sigma _{set 1}^{2} = \sigma _{set 2}^{2}$

H1:$\sigma _{set 1}^{2} \neq \sigma _{set 2}^{2}$

using minitab>stat>basic stat> two variance

Test and CI for Two Variances

Method

Null hypothesis σ(First) / σ(Second) = 1
Alternative hypothesis σ(First) / σ(Second) ≠ 1
Significance level α = 0.05

F method was used. This method is accurate for normal data only.

Statistics

95% CI for
Sample N StDev Variance StDevs
First 17 3.194 10.200 (2.379, 4.861)
Second 26 2.387 5.700 (1.872, 3.296)

Ratio of standard deviations = 1.338
Ratio of variances = 1.789

95% Confidence Intervals

CI for
CI for StDev Variance
Method Ratio Ratio
F (0.866, 2.163) (0.751, 4.677)

Tests

Test
Method DF1 DF2 Statistic P-Value
F 16 25 1.79 0.186

since p value is large so we accept H0 and can conclude that the two variance are same