The Binomial Distribution and Test, Clearly Explained!!!

The binomial distribution and the related statistical test look really complicated, but a actually quite simple. Here I walk you through both, one step at a time, so that they are easily understood and applied.
If you would like to learn more about P-values, check out this StatQuest:
• Video
And if you would like to learn more about 2-sided P-values, check out this StatQuest:
• StatQuest: One or Two...
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#statquest #binomial

[@statquest]

Support StatQuest by buying my books The StatQuest Illustrated Guide to Machine Learning, The StatQuest Illustrated Guide to Neural Networks and AI, or a Study Guide or Merch!!! statquest.org/statquest-store/

[@aprajitasingh3206]

Can you please do a video on Poisson as well!

[@Jk-ki7tr]

Hi Stat Quest, Is it possible to complete a Binomial analysis on more than two options. I have received responses to a multiple choice survey and want to use Binomial Analysis to prove if the most popular answer is statistically more likely than chance.

[@statquest]

@@Jk-ki7tr Yes. It's called a "multinomial" test.

[@monicakulkarni3319]

On the entire internet, you're the only person who didn't do coins/cards example. God bless you! Thank you for this explanation.

[@statquest]

Hooray! I'm glad you appreciated the new perspective. :)

[@AmeyPanchpor02]

very true

[@DeViLTh0rn]

@@statquest DOUBLE BAM!

[@shanlin2359]

Yes, the example makes BAM more business sense!

[@pravin8419]

Agree! Cent percent.

[@mainulislam6765]

"The binomial distribution will tell us what to expect if there is no preference"- that statement just tied up in one string all the scattered information I had so far about binomial distributions. Thank you for this elegant explanation.

[@statquest]

Hooray! :)

[@yashthirani6849]

Exactly! Wonderful summary of the whole concept. Thanks StatQuest.

[@DeepROde]

It blows my mind thinking that future human generations will have such a great knowledge source on KZbin, I think generations to come will learn statistics from here, you will be remembered as a legend, sir!!

[@statquest]

Thank you!

[@samarthkalesh8984]

as someone from the future this video is much appreciated

[@ramprakash7872]

The way you have broken down the nasty looking formula into easily understandable and relatable stuff is mind blowing . Thanks for creating such videos. Super helpful tht waz. Pls do more of this sort :)

[@statquest]

Thanks and will do!

[@msawhney]

The world needs more educators like you. Please keep up the good work.

[@statquest]

Thank you very much! :)

[@ishamathstea9019]

Hye Mandeep, I love this video too..... Btw, I have just posted about how to find probability using Binomial Distribution.....i hope it's helpful...... 💓

[@vishalverma-wx7eo]

You really developed a genuine interest in me for statistics. Thanks a lot!

[@statquest]

Hooray! That is awesome! :)

[@saneeshcs6604]

I appreciate the explanation of the binomial distribution without using the example of flipping a coin (1000 times!!), instead you used a real-world example, it helped me understand the basic concepts of the binomial distribution. You did an amazing job.

[@statquest]

Thank you! :)

[@pranjalchakraborty364]

After watching your stat videos before exams my score got a double bam !! .... Thanks for what you do from the bottom of my heart

[@statquest]

Congratulations! BAM! :)

[@raycyst-k9v]

These videos blow my mind everyday . Again its 5 am and i am studying stats quest. I'll summarize my understanding for others to see here . What you learned in p value videos about the two sided p-value and the video on 'what are stats model' was used here . Here our model(which was also our null hypothesis) is that both flavours are EQUALLY loved , so both have a probability of 0.5(this is NOT p-value, this is just our model-Remember that a model can be an 'equation' or a 'relationship' between variables) And since are p-value came out to be larger than 0.05 we rejected the alternate hypothesis that one of them is more loved. Our p value was 1 so we FAILED to reject the null hypothesis. BAM!

[@statquest]

BAM!!! I'm so glad you like my videos. :)

[@TheOntheskies]

Just when i thought this formula is too complex. Revelation! Fantas brought it down to earth in human language. Thank you so much Josh!!

[@statquest]

Thanks!

[@innocentlord7985]

I have said it before and I will say it as many times as it needs to be, Josh, you are a blessing. Thank You. Usually there are certain small details which our professors often skip and those details are the ones upon which advance systems are based but you lacked the initial concept thus it gets difficult. But you put and explain every detail beautifully.

[@statquest]

Thank you very much! :)

[@ishamathstea9019]

Hello Muhammad Abbas, I have just posted how to find probability using Binomial Distribution..... I hope it's helpful.... 💓💓💓

[@anuragn.sharma4170]

This has to be the first comment (in a long time) that I've been inspired to write because of the sheer number of "light bulb" moments your tutorials give me. Great going and thank you!

[@statquest]

Awesome! I'm glad the video was helpful. :)

[@yutassmilehealsme6572]

Love your vids because they don’t use much terminology and explain it in the simplest way 🙌 Using diagrams to explain instead of spouting paragraphs makes stats so much easier to understand!

[@statquest]

Thank you very much! :)

[@im_karamo1907]

hahah the explanation was splendid.. using the pharase "nasty looking formular was the best caption of the presentation." thanks statsquest

[@statquest]

Hooray! :)

[@aezaa_]

Bro you don’t understand how much this video helped me 😭 I’m a homeschooler who’s in 9th grade and this was the work my mom gave me for today. Since I plan on taking college classes very soon, she wants to get me started on harder math problems. I was literally on the verge of tears while trying to use the nasty looking way for this. Thank you

[@statquest]

Happy to help! :)

[@dreamsbyiris]

CHUU MENTION!!

[@fmetaller]

Great video. At the beginning, I was a bit scared by the equation of bionomial distribution, but you have explained it very clearly and in the end it resulted to be very easy. Thank you very much for this video.

[@statquest]

You're welcome! I'm glad you like the video. :)

[@naruto5437]

man...u just need great teacher to make u fall in love with a subject world need great teachers

[@statquest]

Thank you!

[@emmanuelbankole5954]

I've watched 5 videos on this & yours is the only one i understood. Brilliantly explained!

[@statquest]

BAM! :)

[@yaluntan3643]

Thanks for explaining the binomial distribution in such a clear way and saving my fragile self-esteem in statistics :)

[@statquest]

BAM! :)

[@yogi4128]

i've listen only half of the presentation, and it's really clear and boiled down the formulas, that what i really need. thanks statquest

[@statquest]

Nice! I'm glad you got what you needed! :)

[@jaysonl3685]

The fanta example really helps understand the value of modelling via the binomial distribution, thanks a lot Josh!

[@statquest]

Glad it was helpful!

[@AmelyaSjahlim]

I just want to sincerely THANK YOU for not coming up with another example using coins, a deck of cards, and dice!

[@statquest]

bam! :)

[@redcat7467]

That moment where you randomly looking for someone to explain you binomial distribution and out of blue you click on some sodas videos and it turns out to be StatQuest video so now you can be sure you will'be explained the material well so you can invest saved time into procrastinating while buying some third party drink that doesn't fit into the model unless we deny any Fanta but the true one. BAM!

[@statquest]

BAM! :)

[@formula_person]

I've been watching your channel for like a year now, and realized I wasn't subscribed, and have now subscribed because of the amazing song 😆

[@statquest]

bam! :)

[@christopherivan1790]

Thank you for these Josh. You are doing an amazing job of making this stuff more accessible to people like me, struggling to improve and grow in my career :)

[@statquest]

Hooray! I hope you succeed in improving your career! :)

[@adrianairina7684]

Never been so focused and entertained at same time. Excellent video!

[@aditisoni2600]

Yes you are right

[@ExistentialNomad]

The video was great but I must say the opening jingle was even better :P :D ... Thanks a ton :)

[@statquest]

Glad you liked it!

[@pravin8419]

Josh, one more BAM!! You are the best Stats and ML tutor over the internet.

[@statquest]

Thanks! :)

[@SriHarshaBolisetti]

I cannot believe I prefer watching your videos over Netflix. I am learning to love Stats!

[@statquest]

TRIPLE BAM!!! And thank you for supporting me.

[@nirajkc224]

I really got a life after watching this. Appreciate it. Thank you so so much 😍

[@statquest]

BAM! :)

[@mayankbhatt1308]

Oh my man, Oh my man, i just dont know how to thank you, i just dont know how to thank you....let me be a living proof of it....the videos you have made are so well corelated that the moment you explain something new in new video my brain automatically knows, goes and wanders to all those past videos where it need to go to have a recall....its so good....thank u thank u thank u

[@statquest]

Glad I could help!

[@kanundash]

Love you

[@statquest]

Glad I could help!

[@asafvirin2181]

Thank you so much, this video was super helpful and really helped me get over the "nasty looking formula"

[@statquest]

Awesome! :)

[@vaibhavpandey7398]

Wow wat an explanation. Teaching the real use is of highest value. Please make more videos. M eagerly waiting.

[@statquest]

Thank you very much! :)

[@kf2606]

'Fanta'stic explanation! Loved the way you broke down the daunting equation and made it look simple.

[@statquest]

Thanks!

[@anandm6357]

Best explanation, Josh. Great work. Love from India.

[@statquest]

Thanks!

[@kiqmiq]

Lifesaver! So well explained!

[@statquest]

Glad it helped!

[@imdadood5705]

I don’t if my opinion is inversely correlated to yours. But statquest is not cool….. It is the coolest in the entire statistics universe found on KZbin.

[@statquest]

bam!

[@codebinding71]

Great video. It would be great if you could do a video on gradient descent or Monte Carlo with the mathematics clearly explained.

[@statquest]

Those are near the top of my to-do list. I'll get to them soon (I hope!)

[@mikalrain]

@@statquest What is the last status on this? Edit: Status on Monte Carlo?

[@revolution77N]

Thanks!

[@statquest]

Hooray!!! Thank you so much for supporting StatQuest!!! BAM! :)

[@sirvachjumani7215]

Great explanation for beginner with a simple product example.

[@statquest]

Thank you! :)

[@aimanasif6770]

Just wow!! The way you explained was amazingly mind blowing 👍

[@statquest]

Thank you so much 😀

[@TheAabbccddee12345]

was waiting for the BAM, got the BAM. Today was a good day.

[@statquest]

BAM! :)

[@jeevanmarg]

Just came to hear your intro song. I can't decide whether your Intro song is better or the actual content of the video. Awesome.

[@statquest]

BAM! :)

[@yulinliu850]

Yeah, I'm just looking for a good video on this topic. This is brilliant! Thanks a lot!

[@statquest]

Hooray!!! I'm glad you like it! :)

[@dipeshrathore8842]

God! Your Channel is just Awesome!! ♥ And the Fun Way of Explaining with 🤩wonderful Examples. You Got me Folks 😊

[@statquest]

Thank you! 😃

[@RastafarianRussian]

I had a lot of bam! moments watching this video. Thank you!

[@statquest]

Bam!

[@AlexanderPopusoi-i9m]

Thank you so much! This really helped me understand the formula.

[@statquest]

Glad it helped!

[@rohanthomas5434]

It was really helpful and intuitive. Felt good.

[@statquest]

Thanks!

[@anirbansaha1996]

I just came here for the Fanta, stayed for the content. BAM!

[@statquest]

bam!

[@rmiliming]

Tks for the clear explanation., especially the one on the factorial !

[@statquest]

Thank you!

[@nirajkc224]

I never had dreamt statistics would be this interesting ! BAM...

[@statquest]

BAM! :)

[@alanvillapando8821]

Dude, your videos are great! Thanks a lot for the tutorials!

[@statquest]

Glad you like them!

[@danielfreeman8136]

5:32 Alternatively, write out a few lines of Pascal's Triangle, and do a simple calculation. For this example 1,3,3,1. The second number corresponds to two orange one grape. Divide this 3 by the total 8 = 0.375

[@BRYANCASTANO-y4g]

@StatQuest , You really know how to ex'plain Statistic and Math Very Wll, You are Amazing.

[@statquest]

Thanks!

[@avinashcm]

Hey josh! Your doing a great job!!

[@statquest]

Thanks!

[@anashaat95]

Very clear explanation. Thanks a lot.

[@statquest]

Thanks!

[@archerdev]

Quad BAM! Thanks for this great lecture sir. Math bless you.

[@statquest]

Thanks!

[@dgytyt]

first of all, StatQuest is fantastic! One question: how do I compare if two binomial distributions are different from each other? What test should be applied?

[@ertugruledits3349]

BAM!:) you are our exam saviour 😅

[@statquest]

Good luck!

[@linalovesyou]

I JUST GOT IT. Thank you, internet statistics angel

[@statquest]

Hooray! :)

[@Lsazeh]

Again thank you so much for explaining this so simply

[@statquest]

Glad it was helpful!

[@ymighty001]

Oh god, this video is FUN. I need this!

[@statquest]

Bam!

[@ai_map]

Bam, feels interesting and by the way great explaination with live experience

[@statquest]

Thanks!

[@oliverkavanagh33]

You’re a life saver man :)

[@statquest]

Thanks!

[@maessonmlo]

Excellent explanation. See you!

[@statquest]

:)

[@earn4190]

The best explanation!

[@statquest]

Thank you!

[@jollyhateli5297]

Great work sir .. I loved the way you teach us .. mind blowing ❤❤❤

[@statquest]

Thank you very much! :)

[@shlokpunekar8503]

StatQuest is indeed very cool. I love what youre doing with this channel. A little constructive criticism from me would be that it sometimes get a little difficult to follow. When you link the math to the example and explain how the person preferring grape fanta fits into the formula, maybe try and be a little more informal about it. That is all i would like to say. Youre absolutely outstanding at what you do and i would love to see more videos from you. Keep up the good work.

[@statquest]

Thanks for the feedback! I'll keep it in mind when making future videos.

[@GravityGrid]

This video is amazing! Every thing make sense!

[@statquest]

Thank you! :)

[@soumojitchowdhury]

BAM. My favorite YT channel. :)

[@statquest]

Hooray! Thank you very much! :)

[@Cleisthenes2]

clearest explanation I've found. Also, grape Fanta

[@statquest]

bam! :)

[@BiranchiNarayanNayak]

Excellent... i loved the explanation.

[@statquest]

Thanks!

[@danielchacreton2401]

Fantastic as always.

[@statquest]

Thanks!

[@vilayatkhan331]

I hit the like button in the first 20 seconds of the video!

[@statquest]

Hooray! :)

[@JosueKEUTCH]

I laughed at the very beginning " then your opinion is inversely correlated with mine" 😂😂😂😂

[@statquest]

bam!

[@NadiaKh-o4r]

Thank you a lot! You just saved me❤

[@statquest]

Bam! :)

[@kaczucha3able]

StatQuest you're awesome!

[@statquest]

Hooray! :)

[@dhirenderpratapsingh5858]

No words to say thank you

[@statquest]

Most welcome 😊

[@poojapurohit1461]

I get this really well first time👍🏻

[@statquest]

Bam! :)

[@jacobm7026]

Hi, Josh, absolutely fantastic work! I was wondering if you could do something on Bayesian statistics? First off a frequentist vs bayesian perspective video, then a finding likelihood, prior, and posterior series!?

[@statquest]

Those are all on my to-do list. I hope to get to them as soon as I can, but it still might be a while.

[@aiaiaiyourlittlebutterfly.mp4]

SIR, I DON'T KNOW HOW I FOUND YOU, BUT YOU ARE CHANGING MY FATE THIS SEMESTER😭😭 THANK YOU. I am a musician too and I am emotional to finally find someone that takes me and my way of learning seriously!

[@statquest]

Thanks!

[@angadibharath5868]

Great explanation

[@statquest]

Thanks!

[@soldadopreciso]

thanks pal, very useful explanation, greetings from Ecuador.

[@statquest]

Thank you very much! :)

[@komaleshwarirani3731]

Your Bam hits!! thanks for clearly explaining statistical lingos.

[@statquest]

Thank you very much! :)

[@aditisoni2600]

Awesome👏👏 just loved it

[@statquest]

Thank you so much 😀!

[@dhirenderpratapsingh5858]

Best video on earth

[@statquest]

Thank you! :)

[@yiqiongxiao5255]

Amazing video. everything well explained! im so glad i found this on youtube...uGH wish my uni prof is half as good

[@statquest]

Thanks! :)

[@DreamCodeLove]

Plz do a series on Bayesian statistics...

[@mohsenpourjam6260]

Guys you're fantastic, always a recommendation

[@statquest]

:)

[@jessalinnguyen1504]

Thank you! This helped so much

[@statquest]

Glad it helped!

[@shiroe6969]

didn't knew grape fanta even existed 😂

[@statquest]

bam!

[@adnantarmizi6240]

Great content as always

[@statquest]

Thanks!

[@بسيطة-ف5ط]

wow! that's very clear and easy thank you

[@statquest]

You are welcome!

[@01anindyagita84]

Love your intro❣

[@statquest]

Thank you! :)

[@harshstrum]

Hi Josh, can you please please clarify the following: Why we don't we use combination instead of permutation...although I know the value would be same for both in this case where x = 1.......asking this because here ordering is not important so why (N)P(x) instead of (N)C(x)....I would be satisfied if I get to know this

[@statquest]

Permutations keeps track of all the different ways that 3 people can like grape fanta and 4 people can like orange fanta. Combinations does not do this.

[@harshstrum]

@@statquest understood the reason for using permutation. You are amazing!

[@ishamathstea9019]

Wow.... This is amazing... Btw I have just posted how to find probability using Binomial Distribution..... I hope it's helpful....

[@thomsondcruz]

Love the video Josh. Just the words Binomial Distribution used to scare me. You have explained so well. Kudos! But, just one thing. I've never met a person who actually loves Grape Fanta. Only in the world of Stats will someone equally prefer Grape Fanta to Orange Fanta.

[@statquest]

Ha! :)

[@aria124]

Dzang, thank you so very much

[@tarangt.8163]

6:08: we discuss the value of P for the Binomial Dist. Formula. The value of P should always be a constant 0.5 correct?

[@statquest]

'p' depends on the hypothesis you are testing. In this example, we are testing the hypothesis that p = 0.5. However, we could also test the hypothesis that p = 0.75 if we wanted.

[@tarangt.8163]

@@statquest Ah okay. Thank you for the clarification, Josh!