I also do too. It is peaceful yet authoritative.

You are very welcome!

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.

You are very welcome.

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 kzfaq.info/get/bejne/ba2Iod2Cl6m8ZWw.html

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

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

I hope your test went well!

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

Thanks!

You are welcome!

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

@@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 👌👌.

@@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.

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.

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.