F-Distributions

Question 1

What are f-tests used for?

Answer 1

To check if population variances are equal

Question 2

What are the Null and Alternative Hypotheses?

Answer 2

Null Hypothesis: Population variances are equal

Alternative hypothesis: Population variances are not equal

Can have two sided or one-sided tests

Question 3

What is the Test Statistic?

Answer 3

Ratio of sample variances

Numerator has to be the larger of the two

If null hypothesis is correct then the value of test statistic will be very close to1 (because numerator and denominator will be the same)

Question 4

What are the degrees of freedom for F-tests?

Answer 4

Degrees of freedom for variance is (n-1)

F-distribution has two different degrees of freedom for numerator and denominator

Question 5

How is the F distributions graph shaped?

Answer 5

Asymmetrical distribution

Always positive and skewed right

Question 6

What is the hypothesis testing for a two-sided analysis?

Answer 6

Split the significance level into halves

We only look at the values greater than 1 on the right side because the test statistic will never be less than one because the greater sample variance is always in the numerator

Question 7

What is the hypothesis testing for a one-sided analysis?

Answer 7

Will always be on the right side because we only look at values greater than one

Question 8

How is the p-value approximated?

Answer 8

Look at a lower significance levels to find a range for which the test statistic falls in