The Sampling Distribution of the Sample Variance

A discussion of the sampling distribution of the sample variance. I begin by discussing the sampling distribution of the sample variance when sampling from a normally distributed population, and then illustrate, through simulation, the sampling distribution of the sample variance for a few other distributions.

[@BMadClown]

this is the best tutorial video I have ever seen, very clear and concise, you basically saved my life

[@jbstatistics]

Thanks! I'm glad to be of help!

[@sushantpatil7950]

Sorry but I didn't understood it properly :(

[@resey1999]

Hi! Thank you for your video but I was wondering if someone can explain to me why does it equal to 4s^2

[@ridazouga4144]

Hello sir, I just want say thank you for this beautiful explanation, I just have one single question, we know that the mean of the sampling distribution = sigma^2 but what about the variance formula

[@AbhishekJain-bv6vv]

That's the best video, one can find on the internet, clearly explaining the sampling distribution of the sample variance. Great work. Keep it up.

[@lesahoffman-quantmethods]

Fantastic! I have been confused by the original quantity on the x-axis, but now it makes much more sense -- thank you!

[@DorothySeaman]

Thank you for making these videos! Very helpful.
Do you know if these caveats apply to distributions of sample means as well? Whether some inference procedures for the mean work better than others depending on violations of the normality assumption?

[@anasfrh]

I think in general the sampling distribution of the mean will be normal unless the population is a cauchy distribution and then the sampling distribution of the means will follow a cauchy distribution. stats.stackexchange.com/questions/238246/what-is-the-distribution-of-sample-means-of-a-cauchy-distribution but the mean for a cauchy distribution is undefined so I guess there is no point in trying to estimate the sampling distribution of the "mean". I could be wrong.

[@sudharshanr4997]

Beautiful visuals💛

[@lucasf.v.n.4197]

what if the population isn't normal?

[@delcapslock100]

Isn't the t distribution already a sampling distribution, i.e., the ratio of a normally distributed sample statistic and a chi-square distributed sample statistic? So in your 3rd example is that the same as saying you are sampling from a sampling distribution? It might not matter, but I want to make sure I have my concepts right.

[@hehehehhe2011]

It is just one of the examples of sampling from a non-normal distribution to show you the effect of non-normality on sampling variance accuracy. Normal distribution has perfect fit. Uniform, t-distributions have skews.

[@t3hb3r7]

Just a slight correction, that the uniform and t-distributions do not have skews. Rather, these distributions have different kurtosis (tail behaviour) compared to the normal distribution. This changes the sampling distribution of s^2.

[@fakhtehsaadatniaki5531]

Agree with all the replies. Answering your question specifically: You’re not wrong with respect to the random variable (RV) underlying the t distribution being the ratio of a normally distributed RV & a Chi-Squared RV.