Hypothesis Tests for Equality of Two Variances

I discuss the F test for equality of two population variances, based on the assumption of normally distributed populations, then work through an example. Note that these methods do not work well when the populations are not normally distributed.

[flipnoBS]

As a graduate student and educator, I really appreciate your clarity of instruction and tone of voice. This video helped me understand more clearly!

[alzaraure]

How do I find the p-value using the critical values in the F distribution table?

[jbstatistics]

When I first discuss hypothesis testing, I bring up both the rejection region approach (comparing the test statistic to a critical value from a table) and the p-value approach. I feel the p-value approach is better, so I use it the rest of the way. The p-value gives more information about how much evidence there is against the null hypothesis, rather than simply "reject Ho at alpha = 0.05". In practice, typically the p-value approach is used (p-values are included in software output).

[mohammadrezanargesi]

A similar approach was used in chi2 square tests.
Thank you for your comprehensive presentation

[jbstatistics]

Had I used a two-sided alternative in the example, then I would have doubled the tail area to get the p-value. The alpha level would stay at 0.05, if that's what we felt was an appropriate alpha level.

The other option would be to use the rejection region approach (which I don't typically use). In that setting, we would divide the alpha level of .05 by 2, put .025 into both tails, then find the appropriate rejection region. We'd reject Ho if the test statistic fell in the rejection region.

[jbstatistics]

The critical value of F, with 3 and 14 DF, for an alpha level of 0.10 is 2.52. (The area to the right of 2.52 under this distribution is 0.10.) The p-value of the test in this video is the area to the right of the test statistic (2.448). 2.448 lies to the left of 2.52, and so p-value must therefore be greater than 0.10. Using software, we can find that it's 0.107. I have a video ("Finding areas under the F distribution using the table", or something along those lines) if you need more help.

[jbstatistics]

You're welcome. I'm glad to be of help!

[bijoudeaux]

How do you get the p-value to be 0.10 using the table? I checked df 3 and 14 in my F table at 5% alpha [and even for the other alpha %'s] and for the 5% alpha, I get 3.34. I'm confused.

[AR-gcdr]

Hi

This is great.

How do you calculate the degrees of freedom in this case? In other questions like population means testing when variance is unkown, we would use a t table but I didn't understand how you would do that if you had both a numerator and a denominator in the degrees of freedom

Thanks!!

[universaltunes]

Merci, pourriez-vous nous envoyer des tests d’homogénéité des moyennes, des proportions et des variances svp? ... concernant ces dernières justement, il y a 2 enseignements différentes auxquels nous voudrions recouper auprès de vous, celui du test F= Variance 1 / Variance 2 comme formule et le second F = Variance 1* (n1/n-1) / Variance 2* (n2/n-2). Laquelle des 2 formules est la plus exacte? et pourriez vous envoyer une illustration (tant en bilatéral qu'en unilatérale) Merci

[keithndlovu]

WHAT A GOOD WAY TO REVISE THE NIGHT BEFORE THE TEST

[abellara]

Hi there,
Excellent video. I have a question. What is the difference between 2 variance test vs test for equal variance?
Kind Regards.

[theodoresweger]

I have trouble with where the p values is when using my HP Prime its to the left and we are dealing with the right.

[preritgoyal]

Sir may I know if you find sample variance by dividing sum of squares of deviations from mean with (n) or (n-1) ?

[MintedGeek]

Very helpful videos. I appreciate your time and effort. Thanks a lot.

[MysticMD]

Your voice here 4 years back sounded more enthusiastic than in your recent videos.. Stats wears out your voice eh..

[fin-pundit]

Hi
If we are using Sample data (VARIANCE)
Then NUll HYPOTHESIS should be
Ho:s squarex = S squarey??
Since sample data is being used for representation of population

2)Also Ifwe use above notaion as Null hypothesis and it gets" failed to reject "cant we indirectly say
Ho=population variance x = population vataraince y
Since we are assuming Equaliance of variance as per F table based on sample data



Kindly solve my query

[mzee]

when do you make the assumption the variances are equal or not equal? during the test of two population means

[PrabhanjanMangalgi]

Hello, is this test always right tailed?

[iam_a.maestro]

sometimes you should show us how you are using the table to arrive at a p value, some like me are absolutely blank right there given a strike ended all the studies and no lecturer bothers about exam time