F test for variance

• Assumptions

1. Data is normally distributed.

• 5-Step Hypothesis
  

Null and Alternative Hypothesis

• Ho: σ1=σ2
• Ha1: σ1≠σ2 (Two tailed test)

Ha2: σ1<σ2 (Left tailed test)

Ha3: σ1>σ2 (Right tailed test)

Test Statistic

Critical value

• -F(1-a/2,n1-1,n2-1), F(1-a/2,n1-1,n2-1) (Two tailed test)
• F(1-a,n1-1,n2-1) (Left tailed test)
• F(a,n1-1,n2-1) (Right tailed test)

P-value

• 2*(1-P(F≤|f|) (Two tailed test)
• P(F≤f) (Left tailed test)
• P(F≥f) (Right tailed test)

Decision rule

• Reject Ho if F < F(1-a/2,n1-1,n2-1)  or F > F(a/2,n1-1,n2-1)  or p-value < alpha (two tailed test)
• Reject Ho if F < F(1-a,n1-1,n2-1) or p-value < alpha (left tailed test)
• Reject Ho if F > F(a,n1-1,n2-1) or p-value < alpha (right tailed test)

• Confidence Interval

100(1-alpha)% Confidence interval for the population variance is given by:

This implies I am 100(1-alpha)% confident that estimated difference in the population variance of two samples lie in the obtained interval.