# Establish Whether populations have equal variance

#### Wrightomatic

##### New member
day 1
distance equals 52.175m, std = 0.015m and n = 10

day 2
distance equals 52.193m, std = 0.021m and n = 11

Establish whether the two populations have equal variance at the 0.05 signifcance level. Can someone help me out with how to get to the answer and what the answer actually is?

#### Klaas van Aarsen

##### MHB Seeker
Staff member
day 1
distance equals 52.175m, std = 0.015m and n = 10

day 2
distance equals 52.193m, std = 0.021m and n = 11

Establish whether the two populations have equal variance at the 0.05 signifcance level. Can someone help me out with how to get to the answer and what the answer actually is?
Welcome to MHB, Wrightomatic!

The F-test is the appropriate test to compare variances.
Do you know how to execute it?

#### Wrightomatic

##### New member
No sorry i don't know how that is why I am asking. Could you please demonstrate how to apply such a test for the given data?

#### Klaas van Aarsen

##### MHB Seeker
Staff member
No sorry i don't know how that is why I am asking. Could you please demonstrate how to apply such a test for the given data?

The F-test statistic is $F=\dfrac{s_1^2}{s_2^2}$, where $s_1^2$ is the larger of the 2 variances.
Can you calculate that?

#### Wrightomatic

##### New member
Yes I can calculate that but what does the F test mean? Like ill get the value for F then do i need to do anything else. As you can probably tell I have absolutely no idea how to do the test or how to implement it.

Could you possibly give me all the steps/formulas i will need and then I can work through it and check the final answer with you?

#### Klaas van Aarsen

##### MHB Seeker
Staff member
Yes I can calculate that but what does the F test mean? Like ill get the value for F then do i need to do anything else. As you can probably tell I have absolutely no idea how to do the test or how to implement it.

Could you possibly give me all the steps/formulas i will need and then I can work through it and check the final answer with you?
Well, you can find the steps/formulas for instance here.

The F-test tests if 2 variances are different.
You should look up the critical value in an F-table for the appropriate significance and degrees of freedom (see the article).
If your calculated F-value is greater than this critical value, your variances are different.
If it is lower, the variances are assumed equal.