What is the t-distribution? An extensive guide!

See all my videos at www.zstatistics.com/videos/
0:00 Introduction
2:17 Overview
6:06 Sampling RECAP
12:27 Visualising the t distribution
14:24 Calculating values from the t distribution (EXCEL and t-tables!)

[@lefttrade940]

If I make it through exams - I owe you a coffee or two. Best stats channel out there!

[@amols7184]

Only people like you who understand the concepts to their intuitive level should become teachers of statistics. I feel myself lucky to come across your videos to really understand real statistics

[@shehanijayalath9828]

Omg yes ikr! I hate learning formulas without understanding the intuition behind them. This channel is so good!

[@jadonlawrence4909]

You can say that for any class. Not everyone is supposed to teach, some people suck at it.

[@alphamehra6559]

Thank you! so much for explaining each and every concept so easily. Honestly, I struggle to get the concepts unless I understand their practical use. All these formulas started making sense after I watched your videos. I hope more people get benefit from your videos.

[@dwannahbee1341]

I CAN NOT THANK YOU ENOUGH FOR HOW PERFECTLY YOU EXPLAINED THIS !

[@lachiejg5838]

I couldn't quite grasp the concept of a T Distribution and watched a handful of other videos with no success, but then I came across this one and it was like a bolt of lightening. Thank you so much for your thorough explanation. Videos like this help students more than you know. Please keep up the good work.

[@shehanijayalath9828]

I watched a bunch of your videos and you made me appreciate statistics! When I learned with intuition, I realized how important these stat concepts are and how they can be applied. THANK YOU SO MUCH

[@oatmanbecauseilikeoatmeal]

my teacher just teaches to get random problems done with no or little explanation into what the terms mean or why we need them. Your channel has made me top of my class!

[@myramacarulay8715]

I study stat in a prestigious uni with brilliant lecturers but you explain the fundamentals more effectively and interesting. Thank you so much for sharing the knowledge, you are flawless - you truly have a gift in teaching.

[@arnoldstallone938]

Which university?

[@alexyordanov1844]

@@arnoldstallone938 Every fucking university.

[@optimusjam4981]

ngl I almost lost hope for my statistic until I watch you videos (sounds crazy but real) Having no hope catching back things others have learnt for 3 years in a couple months. Many thanks !

[@noniwinkler4953]

This is so helpful. I wish I could just call you on a Saturday afternoon to pick your brain about stats.

[@zedstatistics]

I love that you made a profile just to write this comment.

[@adityasatyam6300]

Your videos are great . PLZ MAKE MORE VIDEOS .

[@spearchew]

Great video. One of my top three "titan class" channels, alongside Sal Khan and Jeremy Balka

[@eduardobarbabosa4846]

thank you very much dude, you've no idea how this helps clarify everything

[@arushijha6543]

I can't tell you.. How much your videos mean to me.. Within a time of less than 2days for me.. You explained the basics of statistics.. Gave concepts that I can never forget.. Lots of love.. Thanku

[@zedstatistics]

Love hearing this Arushi! Stay safe and statistically savvy.

[@Competent00]

Thank you so much. Nobody could have explained this with this ease💯

[@doll3046]

your videos deserve millions viewers

[@hdanho3]

I don’t usually write comments but I had to. Thank you for these videos. You’ve saved me!

[@chyldstudios]

the musical intro was quite funky!

[@mohemmedansari8664]

Simply amazing explanation. Very helpful

[@mohemmedansari8664]

Made amazingly simple for so many of us and bringing life back to statistic. Elsewhere its death by formulae and math.

[@swghavoc]

Thank you for your work. You make this understandable

[@yogi4128]

this is gewd, keep making great statistics videos!

[@kanikabagree1084]

Keep up the good work. This helped me so much thankyouuu!!!

[@zurzakne-etra7069]

This video is seriously great!

[@antonbashkin6706]

Really great video, thank you professor!

[@marcoventura9451]

Very well explained. Thank you.

[@samuelkibet8031]

Thanks from kenya

[@fb3670]

thank you sooooo much. I finally get this

[@shahdanyal7542]

Excellent explaination.

[@allangallego3244]

Well explained Sir!

[@michaelcordova1803]

Excelente guía, felicitaciones. Saludos desde Lima Perú.

[@profritesh123]

Really an informative video, keep going

[@souvikbiswas284]

yout videos really helps to get the brief knowledge on these topics.. if you can please make videos on F and gamma distribution

[@JP-bo1nk]

Thank you, very helpful!

[@philipa706]

fantastic explanation!

[@lenaara4569]

Thank you for this awesome explanation! :)

[@holaola626]

Sir, that is genius explanations. All of them! That helped me much with my exam preparation. By the way, that goes well together with CFA quantitative volumes. One cool complements the other. You really should think of creating some courses helping with CFA preparation. For the present moment I would really to watch your videos with lognormal distribution. Thank's so much one more time for your job @zedstatistics P.S. Your videos replaced Netflix in my evenings =)))

[@hastins3514]

You're doing great. Thank You!! :)

[@aladeayomide62]

Very nice teaching claims. Thank you very much.

[@danielhamze8409]

thanks for explaining everything so methodically and clearly. I've watched and liked many of your videos and of course subscribed! Question: I'm confused about why we look for the height in PDF as we know this represents the gradient? Also why isn't the CDF an S curve? Keep up the good work!

[@rambaldotra2221]

Thanks A lot Man It's extremely useful 👍

[@aryamahima3]

Thank you sooo sooo much...respect from India...

[@MathManMcGreal]

Hey just want to say your videos are awesome, dude. Very well polished and easy to follow. Do you have a recommended order to watch of your videos? I'm currently in a master's in applied math program and know everything you're teaching, but I'm not nearly as fluent as you are in your ability to explain everything and as a teacher I'd like to get to your level.

[@zedstatistics]

Thanks Triple M, Check out my website, zstatistics.com. Everything is in nice categories up there!

[@khyatichouksey8927]

You’re amazing man!

[@rahulranjan3444]

Good work Can you please make videos on F and chi-square distributions as well.

[@zedstatistics]

They're comin!

[@eduardobarbabosa4846]

@@zedstatistics we neeed em maan, haha

[@pongwang9893]

How are these formulas derived? It’s amazing.

[@Weightingtablesafter]

Quality video !

[@jongcheulkim7284]

Thank you. this is good.

[@miaowenshi8822]

Something to supply: since we use the sample mean and the sample sd to calculate t, and they are so sensitive to outliers and strong skewness, it is IMPORTANT to check your sample data FIRST. If strong skewness exists or there are outliers, it is not recommended to use t-procedures(especially when the sample size is less than 30)

[@juanjosecabral5718]

if you have outliers or strong skewness your are not having normal distributed data so you are breaking one of the assumptions of T test (t distribution)

[@statisticsonsteroids]

​@@juanjosecabral5718no not really for sufficiently large n sample mean is still approx normally distributed regardless of whether we know population sd or not

[@uclalse]

Thank you! I love you!

[@escapiststupor]

Thank you so much for the video. Just my small wish - as helpful as these qualitative description of these common distributions, it will be super helpful to also touch base on how to arrive at the PDF (maybe in a separate video with more mathematical materials) instead of just saying "hay take a look, it's scary". Like for me, I am not particularly trained statistically, but looking at the gamma function I would assume that oh maybe this comes from a series summation that arises in the process of an analytical operation from a z distribution, but it is hard for me to chase it down further. If you can include this missing part, it will be awesome! (or at least include a reference as to where I can find the answer) Thank you again! this is by far one of the best video that clears explains what t distribution is and what it describes!

[@juanjosecabral5718]

that part is highly mathemathical and is teached in proability theory. Regarding PGF (Probability Generator Funcion) and MGF (Moments Generator Function). It would required a whole video and high level of math from the student to understand how it was arrived to things like PDF, E(X), Var(X) etc

[@devminsubasinghe4155]

Jesus Christ Man, thank you soo much for this. It all just suddenly clicked...

[@kyubeenkim9360]

Thank you!

[@abhay9994]

Thank you ❣

[@vinaylikhar6989]

Thankyou so much🙏

[@soumibhattacharyya8839]

too good! thankyou sir!

[@michelnakhla2327]

Are there any handouts for your videos or a reference book? Thanks. Excellent videos.

[@YRPortfolio]

Thanks so much for all your videos! One question though: You brushed over the explanation of the notation for the Normal distribution rather quickly around 7:45. Squaring the standard deviation (variance) is not what I remember to be the second parameter of any Normal distribution! What exactly is the story behind that?

[@srinivaschillara4023]

Excellent

[@Dubai_life_]

Thank you

[@MentalHealthMastery]

How do we work out the Sample standard deviation? it's 12.05 according to 10:00 in the video. are we given the sample standard deviation?

[@virgo8985]

I need a video on gamma distribution.

[@musheno]

Thanks!

[@nandiniagarwal9040]

Brilliant!!

[@karimullah593]

Very nice keep it up

[@alexadolfo4024]

I have a “silly” question, if anyone don’t mind answering. To use it on any value, I standardize it (“number”-mean/standard deviation of the sample), and then use the t.distribution? Thanks in advance.

[@marccepeci2980]

If the underlying population is normal then it doesn't matter how small your sample size happens to be. You can still use the CLT.

[@nathandupont8939]

Thanks for the great video! Small remark: at 9:50, I believe the standard deviation s of the sample should be s=10.778

[@danielh2833]

Thank you for the great explanation! Not sure if it is on my end or because of your recording setup, but i noticed a quiet but slightly annoying hum in the audio.

[@stephenburke9909]

At 13:00 is a visual representation of how the t-test converges towards the normal dist as DF increases. At 19:33 is a tabular representation of the same thing. Follow a column down. As he mentions at DF = 20, you are almost there. The difference between a DF 20 and the norm appears to be in the thousandth. I would have thought we would have need 50 data points to get close to that

[@zedstatistics]

Hi Even, there is still an appreciable difference at DF=20. You'll note from the table that the critical value for DF=20 is 2.086 for p=0.025. The equivalent z value (ie. the value from normal distribution) would be 1.96. This is not a difference of a thousandth. It is a difference of (2.086-1.96)=0.126.... which is not a percentage, but (roughly) a measure of standard deviations. So the t-distribution with 20 DF is 0.126 standard deviations "fatter" than the normal distribution at p=0.025. Or, if you like, the t-distribution is (0.126/1.96)=6.4% fatter than the normal distribution at p=0.025.

[@namishasharma9689]

To account for a sample, why aren't we taking root n-1 rather than root n in the t formula ?

[@bhavyabhandari3238]

Hey, thanks for all your efforts. I guess you could add F- distribution too.

[@takiyashir8712]

Thanks a lot...

[@ibrahimibnumar6270]

Hiii Brother,. Lovely Lectures. Question : If t distribution is Continuous then why are you calling Probability distribution function (PDF) instead of Probability Density Function?. I'm a Fan of you and your lectures. Thank you for this Knowledge. Love from India

[@MuhammadYousaf-hq2zh]

sir, How to the statistical table discover. for example t-test, f-test, z-test, chi square test etc

[@AR-vb4xy]

As we take sample with higher sample size wouldn't the distribution be more clustered around the population mean? Wouldn't this affect the 'Height' of our distribution?

[@superfreiheit1]

If we do not know the population standard deviation, why we know the population mean according this formular?

[@ImTheBoss619]

I just came across this channel and it's really awesome. The way he designs his videos is so damn cool and simple. I really wish he does some videos on applying the Statistics in R.

[@tamannajain533]

Hi, I have one doubt - in video u have said that the sample is too small to apply CLT.But, since population is assumed to be normal, CLT can be applied irrespective of sample size. Can u please clear that??? Thank you!

[@siulungsuen9107]

Same question here

[@YousufHussain]

can you make a video on log-normal distribution please

[@michaelh.6308]

How can I know whether or not the central limit theorem will apply? Is there some sort of cutoff below which I ought to use the t-distribution rather than the z-distribution?

[@andreafederer]

With a 40-50 sample size or more you can use the z table instead of the t table...as you increase your sample size you get closer to a normal distribution

[@Late4my8]

Nice video. I hear in a lot of videos (this included) the claim that the T distribution is is wider (fatter tails) due to the added variance of the sample standard deviation. I don't think this is true. I think it's fatter not because of the variance in the sample standard deviation, but because the sample standard deviation is biased low at low sampling. ...this is a very different mechanism as far as I can tell. If the sample standard deviation had a lot of variation, but tended to be balanced in its error (meaning sometimes its larger, and sometimes smaller in equal proportion), then I don't think there would be any need for the T distribution (in that situation we could just go with the maximum likelihood guess for sigma and all would be ok on average). Does that make any sense? ...and as far as I can tell, the mechanism that biases it low is nothing other than the mechanics of the square root (as even unbiased variance ends up biasing low after the square root). For a thought experiment, let's imagine there was another mechanism making our sample standard deviation come in too high on average (maybe someone was coming in and secretly multiplying our standard dev by 10, and we didn't notice). This would have a lot more variance from test to test, but if we were to redo Student's work under this condition (again we didn't notice our evil lab mate's trick), we would discover that we needed a new statistic that was a lot smaller than Z... ...even though the variance is higher. I think Student merely noticed the square root was playing the role of the evil lab mate, and worked out the correction factor needed for different population proportions. Thoughts?

[@gauranggarg549]

This really cleared the doubts I was having The main problem with using sample standard deviation (unbiased) as a estimator for sigma is that we are not standardizing (calculating z score) the sample distribution of mean by the correct factor But what if the that factor (our estimated std dev) is greater than actual population deviation, then logically we should be having a variable with lower values than z T-stat only makes sense when it is assumed that sample std dev (unbiased) would,on average, be smaller than population deviation And that is exactly the case as you mentioned

[@vslaykovsky]

5:40 are you sure, that the t statistic formula has n1 and n2 under square roots? Shouldn't the denominator look like sqrt(s1^2/n1 + s2^2/n2) instead?

[@fauziabegum6127]

How central limit theorem is applied in t test???

[@mishramn]

Can these videos be numbered sequentially for ease of understanding?

[@shresthaditya2950]

t-test: 1) It is used when sample size is too small for C.L.T to apply 2) Population standard deviation is unknown 3)Underlying distribution is normal

[@ShakespeareCafe]

Further history on the name, he came up with Student from his brand-named "Student's Notebook" he used in the lab.

[@Imrankhan-kn2lg]

Sir Is t distribution is leptokurtic or platykurtic? Plz explain this sir

[@aasthaarora0195]

pls create a video on random sampling and jointly distributed random variable 🙏🙏

[@user-yp1rg2jr5z]

Sir Thanks for the information... Now I have a little problem. I think you will give my answer.. Here, sometimes in example we use students t distribution table . But we use different sample size (n). But original sampling distribution may be based on a constant observation?!! I don,t know actually, I have a doubt in this case. When we make a sampling distribution then this will be a constant number observation let say n=5. Here we construct a distribution on the basis of these 5 observations mean taking various sample!! But why we check null hypothesis for various number of observations. How the students t table made?

[@edmondmalepane3141]

How was it derived ? Pleas helpe I need de proof

[@pongwang9893]

How are t-distribution derived? It’s amazing.

[@Time_Tales23]

The underlying distribution does not need to be normal, the sample mean (x-dash) needs to be normally distributed (and will be according to the CLT provided that the summation is done over a sufficiently large range of values) but the actual underlying distribution (from which you calculate the mean) DOES NOT have to be normally distributed.

[@jairishi2553]

you are a savior

[@karanarora225]

@zedstatistics why don't we divide sample mean by n-1 to adjust it for unknown population mean, like we do it for sample variance.

[@zedstatistics]

Great question! Check my video on this exact topic kzbin.info/www/bejne/raG8aqKVhN6rpbM

[@karanarora225]

@@zedstatistics Thank You!! :)

[@arunikapritimishra632]

can someone plz point out the formula for calculating standard deviation for sample

[@ais3153]

16:18 why the cumulative distribution function is not S-shaped?

[@deepjoybiswas2124]

When we use √n-1 ,tell me

[@HarshChoudhary-do9vm]

5:15 The variance term of difference is wrong, there are extra sqrts. at n1 and n2

[@marcellberto2538]

Perhaps I’m missing something, but what’s the point of testing the population mean when we already know what it is?

[@leogaussbell1622]

why 975 if 2.5