To test whether there is significant difference between population variances using R language

 

Aim: To test whether there is significant difference between population variances.

Problem:

Five Measurements of the output of two units have given the following results (in kilograms of

material per one hour of operation) .Assume that both samples have been obtained from normal

populations, test at 5% significance level if two populations have the same variance.

Unit A 14.1 10.1 14.7 13.7 14.0

Unit B 14.0 14.5 13.7 12.7 14.1

H0:S12=S22

H1: S12

S22

Level of Significance: 0.05

R-Code:-

> Unit_A=c(14.1,10.1,14.7,13.7,14.0)

> Unit_A

[1] 14.1 10.1 14.7 13.7 14.0

> Unit_B=c(14.0,14.5,13.7,12.7,14.1)

> Unit_B

[1] 14.0 14.5 13.7 12.7 14.1

> var.test(Unit_A,Unit_B)

F test to compare two variances

data: Unit_A and Unit_B

F = 7.3304, num df = 4, denom df = 4, p-value = 0.07954

alternative hypothesis: true ratio of variances is not equal to 1

95 percent confidence interval:

0.7632268 70.4053799

sample estimates:

ratio of variances

7.330435

> qt(0.975,4,4)

[1] 12.3232