An Introduction to the F Distribution

A brief introduction to the F distribution, an important continuous probability distribution that frequently arises in statistical inference. I discuss how the F distribution arises, its pdf, mean, median, and shape.

[@paulam.9582]

THANK YOU SO MUCH for all of your videos!! you will be the reason I dont fail this class!

[@PunmasterSTP]

How'd your class end up going?

[@thinklikeanant]

These videos have really helped me understand probability and statistics... Got more out of them than I did in the classroom.. Thank you so much

[@ck-nguyen-dotcom]

watching this in 2018 and probably someone else will in years to come. thanks!

[@jbstatistics]

You're welcome! I definitely hope they provide a little value to the world for a long time. Cheers.

[@doggy79900]

Yessir

[@jbstatistics]

I'm glad to be of help!

[@siqili204]

this is fantastic !!! I will watch this all the time before my homework

[@PunmasterSTP]

Out of curiosity, how did your class go?

[@sheenusharma6137]

These videos are very helpful. You have made it so easy for us to learn statistics. Truly appreciate....

[@jbstatistics]

sheenu sharma I'm glad you've found them helpful! All the best.

[@sheenusharma6137]

Please can I request you to upload a video for Bayes theorem.

[@mfanafuthifortunenene2792]

Thank you, I can understand every vedio you upload very clearly keep it up

[@phymath-jisanislam9639]

I have learnt many things from your channel....Thank you....

[@jbstatistics]

You are very welcome.

[@huizizhang6244]

you're a life savior, seriously!

[@immortalpuffin6643]

Thanks for the explanation, interesting to see that the F distribution is the ratio of variances and how the gamma function comes into play with the definition of the probability density function of F

[@belgiemijntweedehuis3256]

Thanks for your video.
I saw that the F distribution is also widely used in ANOVA and Regression in which the F test is used to test for many things.
Could you make some videos about the application of F test in this field and also the video about MANOVA. I found it was very difficult to understand MANOVA and how to interpret the result.
Thank you so much and hope to see more video.

[@jbstatistics]

Thanks! I'm glad you liked it!

[@chevasflorian4055]

Thanks for your video. I have a question: Why F distribution is important for?

[@qianw4785]

Thank you for being way much more helpful than my teacherssss! There is a small error at 2:50. V should have a minus sign in the denominator - google. This explains why mu is smaller than 1, but I don't know why mu is negative.

[@jbstatistics]

The expression I give for mu at 2:50 is correct. Mu can't possibly be negative, as none of the possible values of the random variable are negative.

[@qianw4785]

@@jbstatistics I agree that mu is positive. I was confused because the mu looked less than 1, but actually, I was looking at the mode. anyway, I understand now :) thank you~

[@pranavpatel9135]

nice job jb!!! I like your all videos its short and unstandable easyly.......keep it up...

[@jbstatistics]

Thanks Pranav. I'm glad you like my videos. I'll definitely be adding more in the not-too-distant future.

[@hanzelmejia6722]

Do you have discussion for Weibul and Erlang distribution?

[@ParagSen1988]

Your videos are simply outstanding. I have only one question. While conducting F test, F statistic is usually given by σa2/σb2. However, while deriving the pdf of F distribution two independent variables' (with some dof) ratio are considered with χ2 distribution. How do we come to know that σa2 or σb2 follows χ2 distribution? Otherwise, σa2/σb2 ratio cannot be expressed by F statistic.

[@jbstatistics]

First, sigma^2 is a fixed-value parameter, whereas S^2 is a statistic. So it is only S^2 that is a random variable with a probability distribution. But, with the appropriate changes to notation, the answer is that it is a consequence of sampling from a normal distribution. If we're sampling n observations from a normally distributed population that has a variance of sigma^2, then the quantity S^2(n-1)/sigma^2 has a chi-square distribution with n-1 degrees of freedom. This is often covered in a first course in mathematical statistics.
So when sampling from normally-distributed populations A and B, S_a^2(n_a -1)/sigma_a^2 ~ chi-square with n_a-1 DF, and S_b^2(n_b -1)/sigma_b^2 ~ chi-square with n_b-1 DF. If the samples are independent, then under the null hypothesis of equality of population variances (sigma_a^2 = sigma_b^2, and let's just call this sigma^2), this quantity is a ratio of independent chi-squares divided by their respective degrees of freedom: [S_a^2(n_a -1)/sigma^2/(n_a-1)] /[S_b^2(n_b -1)/sigma^2/(n_b-1)], which reduces to S_a^2/S_b^2. Since S_a^2/S_b^2 is a ratio of independent chi-squares over their respective degrees of freedom (n_a -1, and n_b-1), S_a^2/S_b^2 ~ F(n_a -1, n_b-1).
If we're not sampling from normally distributed populations, then all bets are off.

[@ParagSen1988]

@@jbstatistics Thank you so much for your lucid explanation. Now it's clear.

[@k.happinesschapadiya3299]

Is it Snedecor's f distribution? Or fisher's?

[@AlienBlade51]

Dude, I have watched a few of your videos and I have to say that you are a very good explainer (if that is even a word!) of things please keep it up! can i request videos on Moment Generating Functions and Probability Generating Functions if possible?

[@oAbraksas]

So for fit statistics, If i want to compare two models, its F= (x1^2)/v1 / (x2^2)/v2 ?

[@lemyul]

thanks for the playlist but #9 video is private/missing

[@ajufsd]

useful video and macho voice, bro.

[@tigerking5546]

very good

[@gauravgregrath6606]

how to calculate f distribution probability using tables? do you have a video for that

[@jbstatistics]

+gaurav gregrath I show how to use the F table in this video: th-cam.com/video/mSn55vREkIw/w-d-xo.html.

[@fatimafam6219]

Watching in 2024

[@TheBlackCatFromHell]

Thank you! great video :)

[@praisethankgivingworshipsongs]

Thank you very Much.

[@jbstatistics]

+Benjamin Franklin You are very welcome.

[@DaraDara-kw1up]

it was useful... thank you

[@jbstatistics]

You are very welcome!

[@rahulpradeep926]

Rahul Pradeep session watched👍

[@TheProblembaer2]

I love you.

[@surabhishinde7788]

thank you !

[@snazmi1019]

thank you so much..

[@jbstatistics]

You are very welcome!

[@randomdude9135]

Why you stopped making videos?

[@dihasfarz2836]

Cuz he deaad

[@PunmasterSTP]

F-this, but in the best way possible! 👍

[@nalinjain7343]

Fuck I still don't understand

[@MindFixingTV]

Thank you so much