Hypothesis Tests for Equality of Two Variances

[@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).

[@flipnoBS3]

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

[@KT2ify]

I also do too. It is peaceful yet authoritative.

[@alzaraure4259]

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

[@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.

[@mohammadrezanargesi2439]

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

[@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!

[@MichaelSeethaler]

1000x better than my professor.

[@TheActurialRepository]

Great video! How would you calculate the sample size for each sample in order to reduce the length of the interval in "x" amount? To make things simpler we can choose a sample size for each set that is the same.

[@theodoresweger4948]

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.

[@keithndlovu44]

WHAT A GOOD WAY TO REVISE THE NIGHT BEFORE THE TEST

[@jbstatistics]

I hope your test went well!

[@keithndlovu44]

Thank you and yes it went very well, all thanks to you i now qualify to proceed to second year in my Actuarial Science studies

[@AR-gc7dr]

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!!

[@jbstatistics]

In this video I describe the F test for equality of variances. The test statistic is the ratio of sample variances, and the F statistic has DF for the numerator and DF for the denominator. The DF for the sample variance in the numerator is the DF for the numerator, and the DF for the sample variance in the denominator is the DF for the denominator. In each case, DF = sample size - 1.

[@MintedGeek22]

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

[@bijoudeaux1]

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.

[@hovhadovah]

Anyone else watching this video, the p-value of 0.107 is indeed correct. Verified with R.

[@Abner3]

I believe 3.34 is the critical value of alpha. This video is showing the p-value method.

[@MysticMD]

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

[@abellara9169]

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

[@universaltunes9606]

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

[@preritgoyal9293]

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

[@jbstatistics]

I'm using a divisor of n-1 in the sample variance formula.

[@preritgoyal9293]

@@jbstatistics Sir I think we should not call it "sample variance" because in general we divide by (n) to find variance. We should call it (S^2) itself. Calling it sample variance may create confusions. Because in some questions of my book sample variance (s^2) is given in questions and we first need to find (S^2) from that, using (S^2) = (n/(n-1)) (s^2) and then solve the question. I appreciate your efforts of making these excellent videos 👌👌.

[@jbstatistics]

@@preritgoyal9293 ​ @Prerit Goyal That's a very weird strange take, IMO. This statement of yours is simply not true: "in general we divide by (n) to find variance." At least in my neck of the woods and line of work, using the term "sample variance" to refer to sum (x_i - x bar)^2/(n-1) is pretty much as common as using "sample mean" to refer to sum x_i /n. In variance calculations we typically divide by the appropriate degrees of freedom. In one sample problems, there are n-1 degrees of freedom. The *vast* majority of people use n - 1 as the divisor, as that gives an unbiased estimator of sigma^2. We *could* use n as the divisor (and that's what comes up as the MLE when sampling from a normal pop), but that results in a negatively biased estimator. Not the end of the world, and not a big issue for large sample sizes. Sure, if your book is sticking to n as the divisor, then you'd need to make an adjustment. But it's not common, at all, to use n as the divisor. My use of the term "sample variance" is consistent with its common usage around the globe (as far as I can tell). Just do a quick google search of "sample variance" and have a look. Let me know if it's somehow treated differently where you are. I'd be very surprised. The difference between capital S^2 and lower case s^2 won't be in the divisor, as that's extremely confusing. If we are drawing a distinction between S^2 and s^2, it is that the capital version is the random variable itself, and the lower case is a realization of the random variable. Having different formulas for something that looks that similar would be a wildly weird choice of notation. I'm not sure if you're meaning sigma^2 rather than S^2. I've seen some terrible notation in my day, and even foolishly used some on occasion, but having different formulas for S^2 and s^2 would take the cake. In any event, I wish you the best, and thanks for the kind words, but my terminology and notation here is very standard.

[@preritgoyal9293]

Yes sir you are right. I read a question: It is known that mean diameters of rivets produced by two firms A and B are practically the same but their S.D. may differ. For 22 rivets produced by A, S.D is 2.9 while for 16 rivets produced by B, the S.D. is 3.8 Test whether products of A have same variability as those of B ? In ans it gives : (S2)^2 = 15.40 and (S1)^2 = 8.81 So (S2/S1)^2 = 1.748 Deg. of freedom = (15, 21) So, F (tab. at 0.05 ) = 2.18 > F (calculated) Thus we can say that variability of the products from the firms may be same. Thanks for giving the detailed response.

[@kanacaredes]

Excellent video!!!

[@hovhadovah]

Another great video! Thanks :)

[@jbstatistics]

You are very welcome!

[@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

[@badriaahmed4858]

Very Informative. Thank you

[@jbstatistics]

You are very welcome.

[@mzee8866]

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

[@jbstatistics]

I discuss that in quite a bit of detail in my video: Pooled or Unpooled Variance t Tests and Confidence Intervals? (To Pool or not to Pool?), which is available at kzbin.info/www/bejne/bXi7n62HZ6iLa5o

[@vidthai0202]

If it was two sided then we would use alpha as 0.05/2=0.025, right?

[@CybersecurityandCigars]

Nice, brief tutorial.

[@jbstatistics]

Thanks!

[@fin-pundit9631]

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

[@jbstatistics]

Hypotheses never, ever, ever, ever involve statistics. We make hypotheses about *parameters*. The null hypothesis is that the population variances are equal. We use sample data to determine how much evidence we have against the null hypothesis, but the null hypothesis always involves parameters and never sample statistics.

[@JoaoVitorBRgomes]

How do I like this video 2 times?

[@alaeeddinesamhi405]

PLEASE HOW CAN CALCUL S1 SQUARE

[@jopell9631]

Thank you so much, finally understand this!

[@PrabhanjanMangalgi]

Hello, is this test always right tailed?

[@chaitanyatuckley4666]

Thanks a lot.

[@favprince]

Thank you.

[@jbstatistics]

You are welcome!

[@aitaisakura4281]

HHAHAHAHAHAH F dist , Get it?? Oh god I have no life