How to calculate p-values

[@statquest]

NOTE: If you are still wondering why we add rarer events to the p-value, consider this: At the start of the video I got 2 heads and though, "wow! This is special!!!". However, if I got 2 tails, I would have thought the exact same thing. We tend to think that whatever we see is special, even though there are other events that are just as rare, or rarer. Adding them to the p-value compensates for our observational bias. 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/

[@xnoreq]

The idea of NHST or null hypotheses as used here is, to be frank, nonsense. These are point hypotheses because the p-value assumes that the coin is _perfectly_ fair. (Also see my comment on the other p-value video why the p-value shouldn't even be used.) Combine both and you got a testing regime that is GUARANTEED to reject the null hypothesis eventually. Even if you deem the coin "fair". Also, 2 heads in a row is very little information but it is still information which a Bayesian approach does not throw away.

[@lcoandrade]

Why the standard is 0.05? What can you say about making changes in the significance value to prove a point? Why 5%?

[@giuseppedejanlucido]

@CogitoErgoCogitoSum seriously? if you toss a coin 100 times and obtain 99 heads, what do you think between theese 2 options? 1) this is absolutely possible because the result belong to the set of possible events, so I can say the coin is fair; 2) even if this is possible, this result it's so rare than I can conclude ALMOST CERTAINLY that the coin it's not balanced (so belong to another distribution, the distribution of not balanced coins)

[@av3499]

I'm still trying to wrap my head why "or rarer" is added to p-value, and how that's related to 1 & 2 tailed tests. Suppose a baseball company claims their bats are 100 cm long, with std.dev of 5 cm. Assuming Normal, that means if we look at 100 random bats, 95 of them should be between 90 - 110 cm, while 2.5 bats < 90cm and 2.5 bats > 110cm. Now I'm an investigator who wants to test if the company is lying. To do that - if I sample 100 bats, and more than 5 bats are outside the 90-110 cm range, I can sue them. Right ? If I find a random bat that is 110cm long, I'd think 'wow that's rare, but not impossible'. But I'm struggling to see how or why I'd suddenly start thinking along the lines of 'I found a bat that is 110cm. What are the chances of finding > 110cm or < 90cm bats'. Why would/should I think that way ?

[@youssefdirani]

@@av3499 I think regardless of the samples you took, your example is very important. Finding a really extreme value could result in suing the company according to 95% confidence.

[@Nihit-n5n]

god gifted or extremely hard working teacher. good to live in the times where such education is freely available. you are really a gift to the humanity as I believe a lot of people in future will make things (after learning from your videos and not giving up).

[@statquest]

Thank you very much! :)

[@MrG0olden]

The P-value of this content being normal is less than 0.05, it's super!

[@statquest]

BAM! Thank you very much! :)

[@boahgeil465]

Lets hope it is a one sided p-value and H0 is this content is not better than normal ;) Otherwise (for a two sided p value), it could be that the content was super bad, which is definitely not the case :D

[@offchan]

we can safely reject the null hypothesis that this content is no different than other people's content

[@letseconomics2938]

It means we will reject that the content is normal right?

[@DreamCodeLove]

The p-value that your lectures are special < 0.000001.

[@statquest]

Bam! :)

[@thangible]

wait a minute

[@JonesingUSAF]

Triple Bam!!!

[@A_Proud_Indian]

H0 - your lectures are normal (null hypothesis) H1 - your lectures are brilliant (alternate hypothesis) P value < 0.05 means H1 is true and we can reject h0 right?

[@dustinshepherd-hoppis2322]

@@A_Proud_Indian yes. He saying StatQuest is 1 in a million. Rare to find such quality. Extremely low probability that StatQuest is of a normal distribution of stat teachers.

[@papername1237]

My life would be SO different if I had seen this video 10 years ago. My heart brakes thinking where I could be today and fills me with anger to think that this was simple and my teachers didn't care to teach me and people publishing the class textbooks only cared about impressing their colleagues but never cared about the students. Thank you, Josh. Thank you for bringing this to the world. You're changing lives.

[@statquest]

Thank you!

[@sandeepsahu7950]

I am watching this video today and need to use this concept in research but i am dumb enough to understand these things.. How stupid i am.

[@rajkumars8573]

That's why they bad teacher spoils lives of millions of students.

[@vamanieperumal5262]

I can't believe how concepts can be made so simple and at the same time so comprehensive. this is mindblowing :)

[@statquest]

Hooray!!! :)

[@sanghoonkim2351]

Ever since my sister highly recommended StatQuest, it has been my favorite KZbin channel since it clears up every concept magically. But the old p-value video still let me confused about what p-value really is... and BAMMM. This video came out! It is fantastic and deserves a million views. Thanks always.

[@statquest]

Awesome! :)

[@writtenlike]

@@statquest BAMMM.

[@anfelaidoud3455]

This is by far one of the best explanations i've ever seen...keep up the amazing work !

[@statquest]

Thank you! 😊

[@josephravi7722]

Triple BAM!!! I learned so much as a teacher from this video. Those classroom learning during my graduating time did not come with this excitement and visuals. So lucid and easy you made it. Not just to understand but also to take away the teaching method -- TRIPLE BAM!!!

[@statquest]

Hooray! I'm glad the videos are helpful.

[@binishrajkhanal8429]

You should be given a Nobel Prize for all the efforts you put into your illustration guided lectures. I wish I had learnt Statistics from you during my undergrad studies, I would not be scared away and would learn enthusiastically like I am doing right now. Hat’s off to you with immense respect and thanks ❤

[@statquest]

Thank you!

[@Also_sprach_Zarathustra.]

I support this idea. @@statquest

[@elizabethjoy934]

Finally happy to realise what the p value actually means. Thank you Josh for all the great efforts to make it so simple and showing that anything complex can be made simple if explained in the way it should be.

[@statquest]

Thank you very much!

[@chasemcdonald7250]

Oh, my god. I just had the most satisfying aha! moment of my life. What a comprehensive, yet concise, and easy to understand explanation. This deserves more likes, you deserve more subscribers. Incredible content.

[@statquest]

Thank you very much! :)

[@joserobertopacheco298]

It is extremely rare to find a so comprenhensive explanation like this one.

[@statquest]

Thank you!

[@damienhackney6499]

This deserves a million likes. Brilliant!

[@statquest]

Thank you very much! :)

[@wesleysbr]

You are incredible josh, and since you mentioned brazil, know that we brazilians see your videos a lot, they are the best, and it's very good that you write what you say in the videos, it helps a lot of non-natives who besides learning statistics still want train english. Your work is commendable, I really appreciate your dedication of time and effort. Thank you very much.

[@statquest]

Muito obrigado! Eu amo do Brasil!

[@gfocaraccio]

"..and since failing to detect that SuperDrug is making things worse would be bad, one sided p-values are tricky and should be avoided..." .. that final line helped clarify your position on one sided p-values, thank you.

[@statquest]

Hooray!

[@biplabkar1391]

I have told this concept to my professor. He was very happy to see this explanation. He is on the list of the top 2% of scientists in the world. But as a statistician, he seeks clarification of the statement that "one-sided p values have the potential to be dangerous".

[@statquest]

Happy to help! :)

[@drpkmath12345]

Nice video! One thing I notice while teaching statistics to students is that many of them are confused between confidence interval and p-value. This video elaborates nicely about what p-value is. As someone who is also teaching statistics, this video inspires me a lot.

[@statquest]

Awesome! Thank you very much! :)

[@somia_ashraf]

After I finished college, I would like to remember when I was studying and listening to these videos, which made things much easier for me and increased my love for the field.

[@statquest]

bam! :)

[@konstantinlevin8651]

I couldn't help but dreaming a scenario where they want contenders to find as much special coins as possible from a bag mixed with normal coins and I calculate p values to find special coins. Thanks a lot Josh, it's always a pleasure to learn with you

[@statquest]

Thank you very much! :)

[@anirbandey8999]

This is true the best video to understand p-value, not just the statistical implication, but understand it's actual application.

[@statquest]

Thanks!

[@zahramanafi4793]

since I was a student, I didn't like statistics much. I think the reason for that was I've never understood these topics well. You are the best teacher I have ever had. :)

[@statquest]

Wow! Thank you! :)

[@ota_vioo704]

Hooray! I just got accepted at Statistics College and my classes starts only in August! Your videos has proved to be very much helpful and i shall keep studying then till there! I'm brazilian by the way and wanted to thank you for the enlightening content!

[@statquest]

Muito obrigado!!! :)

[@varunparuchuri9544]

@StatQuest with Josh Stammer .. you are literally saving many student asses who are trying to learn data science . Love from India(Andhra Pradesh) in telugu : Devudu pampina dootha Dandam ra dootha niku .

[@statquest]

BAM!!! What's "BAM" in telugu?

[@novacannnne]

This is one of the best explanations I've seen, I can finally understand how the p-value and the hypothesis test works. Thank you so much for your work!!

[@statquest]

Glad it was helpful!

[@sushantrauthan5704]

Josh Barmer may you live upto 200 years and please keep spreading the joy as you are right now

[@statquest]

Thank you! :)

[@mohamed.hfathy3717]

„These values are considered equal to or more extreme, because they are as far from the mean or further“ this sentence explained the missing part from the last videos and the saved my day :D .. Great as usual!! thanks a lot

[@statquest]

Hooray!

[@ThalesBrunoM]

Two days in a row watching your videos and learning a lot! Thank you from Brazil!

[@statquest]

Muito obrigado!

[@XuanJr.]

Thanks, I have learnt 2 important things as a master. First, you use the height between 155.4 and 156 cm to tell us why we should include equal rare and more rare things. This is so AMAZING! Good idea! I understand why we should include equal rare and more rare things for the first time in my life! Second, you use a bad drug as a example to tell us why One-Sided p-values test avoid something bad.

[@statquest]

bam!

[@SrujanSingh]

Although I really love these videos and concepts, I think the true motivation comes from anticipation of the opening song. No doubt these videos are highly insightful and educational due to the way Josh explains them but it's uncanny how Josh's voice is so under-appreciated. Great job. Keep them videos coming!! :)

[@statquest]

Wow! Thank you! :)

[@fatemehsh1391]

This is the finest content I've got in my whole education years

[@statquest]

Wow! Thanks!

[@umangsukhadia99]

omg you are truly legend idk who else teaches stats more clearlyyyy

[@statquest]

Thank you!

[@pierre-marcshinkaretzky8851]

Il m'a fallu attendre cette video en anglais pour comprendre la Valeur-p : Excellent ! All other videos failed to clearly explain what p-value really means. Bravo!!!!!!

[@statquest]

Merci beaucoup!

[@pierre-marcshinkaretzky8851]

@@statquest You clearly explained that P-value is not validating a theory but can only tell if we can trust it or not ... Of course we know that p(x/Ho) is not p(Ho/x) while we have so many temptations to cheat and accept p(x/Ho) = p(Ho/x). The point that enlighted my brain came when you associated the HHHHT serie to the TTTTH.... Yes, both are equally weird and HHHHH or TTTTT are worst. We cannot doubt about our coin because of funny series until reaching a certain threshold. I've made a colored simulation to illustrate this docs.google.com/spreadsheets/d/1zWzQfMPUtCmbcS7_DB8l9VKO5SMMuUteAZxWRGxlVa4/edit?usp=sharing Then when Ho is rejected , our test doesn't give us a clue about "what is the acceptable theory?" question . We just have to test a new theory and apply to it the same torture. I think this is frustrating because we think such a rigorous test can do it. Finally hypothesis test aim is quite modest but smart. I spend so much time to understand the deep meaning of it.... Not intuitive at all but you have done the job perfectly.

[@magtazeum4071]

I love this guy. Heaven is there for beautiful people like Josh. He is a gem of a person.. protect him at all costs.

[@statquest]

Thank you!

[@r.prasannavenkatesan9879]

These lectures are worth binge-watching! Thanks a lot Sir!

[@statquest]

Glad you like them!

[@ankitjobanputra5680]

The way you are making videos and explaining these concepts with such an ease....it shows how passionate you are to pass on the knowledge.....!! Keep up the great work....You have earned a Subscriber....!!!

[@statquest]

Thank you so much 😀

[@chelsie292]

I'm currently in IB and recently they rolled out a new Math system and I joined Applications and Interpretations which means that there's gonna be lots of stats going on, from descriptive stats, uncertainty, to testing for Spearman's and X2 tests. this youtube channel has been such a blessing for learning those concepts because the new book that I've been using (Oxford book) has lots of mistakes and was incredibly confusing. Thank you!!

[@statquest]

Hooray! I'm glad the videos are helpful.

[@lcoandrade]

Best statistics teacher on KZbin!!!!

[@statquest]

Thank you! :)

[@sepehretminan8683]

Man, your work is so awesome that the words can't even describe it!

[@statquest]

Thank you so much 😀

[@mostinho7]

12:50 p value calculation for probability density functions. P value = probability of the event happening + probability of all events equally rare + probability of all events rarer Rarer here means “more extreme”, farther away from the mean

[@statquest]

Yep

[@farzanehmahmoudi8717]

Unlike other videos of 66 days of Data this video was not clear completely. Thank you

[@statquest]

What time point (minutes and seconds) was hard to understand?

[@felixbecker6059]

Really good explanation. Already understood it by text book reading, which took me way longer than 20 minutes.. Nice too see I understood it correctly though. Keep up the nice work.

[@statquest]

Awesome! :)

[@kevinshao9148]

So surprised at 19:43 that we obtain p-value=1 ... Thanks for the great video again!

[@statquest]

bam!

[@HgrAhmd-l6u]

currently , after a month watching this channel I react with bam and double bam on every thing😅 u have your own effect tbh😂😂

[@statquest]

BAM! :)

[@mrcharm767]

really great channel !! clears doubts also within less time better than a paid course .. your just brilliant and unique from what others do .. A warm hearthly thank you sir

[@statquest]

I'm so glad you are enjoying my videos. :)

[@mrcharm767]

@@statquest yea really my intuition has become even stronger

[@mrcharm767]

@@statquest yes really btw why not upload projects on the concepts u teach

[@amorevera4988]

I understood more from this video than I did from one semester of lectures.

[@statquest]

BAM! :)

[@shanggao9970]

I love the tricky one-side p value explanation part!

[@statquest]

Thanks!

[@akashmanojchoudhary3290]

I cannot thank you enough, lots of love from India ❤❤❤

[@statquest]

Thanks!

[@aadeshtiwari7532]

So many videos, but this summarizes and I think is best video to understand P value

[@statquest]

Thank you! :)

[@arieljiang8198]

wow this is the best explanation of p value I have seen

[@statquest]

Thank you!

[@andypeters2115]

Best StatQuest I have seen yet! Crystal clear!

[@statquest]

Thank you!

[@LS-py1ry]

Thanks!

[@statquest]

TRIPLE BAM!!! Thank you so much for supporting StatQuest!

[@kayhankashi9970]

After watching this video I told my self BAAAM!! that was a great explanation.

[@statquest]

BAM! :)

[@chiragpalan9780]

I have seen many videos and read so much about p-values. I never felt such plesent experience. Why dont Prof wont teach at universities like this? Love you Josh. Please recommend some good reference for ML and Statistics.

[@statquest]

Thank you! A great book for ML is An introduction to statistical learning in R.

[@chiragpalan9780]

@@statquest Thanks Josh.

[@HenriqueMizuno]

This is the best explanation I've ever seen! Thank you so much for it!

[@statquest]

Thank you!

[@nitkap441]

Finally I am getting a fair idea of what p value means

[@statquest]

To learn what it means, see: kzbin.info/www/bejne/rJbQi6d7gptmfbs

[@nitkap441]

@@statquest thanks. I did watch that too 👍

[@balamira297]

Deserves million likes.

[@statquest]

Thank you!

[@r_chauhan]

I can't help but jam out when the opening song comes on StatQuest videos.

[@statquest]

BAM! :)

[@aramvs8818]

This channel is absolutely epic dude

[@statquest]

Thank you!

[@AthulRamkumar]

Beautiful! Explained so succinctly the difference between probability and p-value

[@statquest]

Thank you! :)

[@techandmoar1922]

Simply awesome! Basic concepts clarified, and on to more complex, tangential topics

[@statquest]

Glad you liked it!

[@mohammadzeinaghaji2499]

at 15:44 "when we are working with a distribution, we are interested in adding more extreme values to the p-value rather than the rarer values". Question: Values further 142 cm (i.e.< 142 cm) are considered more extreme in the example (height distribution)? and what values are considered rarer value in the example?

[@statquest]

In this case they are the same. But it is easier to talk about things in terms of them being "more extreme" and "further from the mean".

[@ellenpasternack9750]

Richard Feynman once said something that I think helps to conceptualise why we include things that are equally rare in the p-value: "You know, the most amazing thing happened to me tonight... I saw a car with the license plate ARW 357. Can you imagine? Of all the millions of license plates in the state, what was the chance that i would see that particular one tonight? Amazing!" In this example it is easy to see that, although the chance of seeing that particular numberplate is tiny, any other numberplate you could have seen would by definition have been exactly as rare. It would be impossible to have any observation less rare. Therefore the observation is not remarkable at all unless we have something else to say about it.

[@statquest]

That's great! :)

[@PraiseNnadi-w3v]

"This flower is equally as rare as all of these other flowers" got me rolling

[@statquest]

Bam!

[@PraiseNnadi-w3v]

@@statquest Yo. I'm a master's student, right? So I'm taking this data science module. But I don't have a strong background in statistics AT ALL. Had an assessment today but I binge watched a bunch of your videos yesterday. Guess what? I got 90%. And it's not like I crammed stuff. I got 90% AND actually understood what I was doing. When I take over the world, I'll make sure every one watches statquest. BAM!

[@MelodicOcelot]

I understand at 22:53 that the Two-Sided p-value still achieved the goal of detecting something unusual happened. Could there be a case though where you would need to use a One-Sided p-value here? For example, if the One-Sided p-value for 4.5 days was 0.03. Because if you included the other side as well then: p would = 0.03 + 0.03 = 0.06 therefore p > 0.05 therefore it would be incorrectly classed as 'usual'

[@statquest]

This is a good question. My next video in this series (on "p-hacking") addresses this sort of thing - where we plot the data first, and then, based on what we see, decide whether or not we will apply a statistical test to the data and if so, how we will apply it (i.e. will we use a one-sided or two-sided p-value). Doing this sort of thing introduces a bias and results in false positives (small p-values that result in the incorrect decision to reject the null hypothesis). So, in order to avoid this problem, we decide what test we want to use and how we use it before we collect the data and look at it. So, assuming you have no idea what the data will look like, choose which type of p-value you want you want to use. One-sided? or Two-sided? Although the two-sided p-value will miss a few things that the one-side one will get, it will not miss the times when the exact opposite of what we want to happen occur.

[@bankmaniac8377]

wooh !! was trying to understand this topic for last two days. finally only you could teach me that. thanx a lot...

[@statquest]

Happy to help!

[@racimeexe9868]

Top notch video , congrats for being so concise 🎉🎉

[@statquest]

Thanks!

[@marziehvaez3866]

Hello and thank you for your special videos. When the p-value is not smaller than 0.05 and we fail to reject the Null hypothesis (6:11), can we also fail to reject its opposite (6:20)? Thank you very much.

[@statquest]

If your hypothesis is that getting two tails in a row is special, then you will fail to reject that hypothesis as well.

[@marziehvaez3866]

@@statquest I think I understand now, thank you. You have also mentioned at 1:56 that if we reject H0, we conclude that the coin is special. So failing to reject H0 automatically fails to accept the coin is special. Thanks!

[@mangomilkshakelol]

You are a hero to the world.

[@statquest]

Thank you! :)

[@akashmanojchoudhary3290]

All your tutorials are just amazing!! 😍

[@statquest]

Thank you so much!

[@sanjaydokula5140]

hi josh, at roughly 4:04 you say why we don't care about the order of heads and tails, but counted head,tail and tail,head separately, if we don't care about the order then the sample size would be 3 right? or have i made some mistake?

[@thegreengrocer99]

At 18:52, what do you mean by "more extreme parts"? Are you basically referring to all values belonging to the lateral parts of our interval of interest? (155.4 ; 156 in this case)

[@statquest]

"More extreme" = "Further from the hypothesis"

[@phongapex3741]

Hello, at 12:13, I am still confused about the "did not convince us that our coin is special". we have the null hypothesis: our coin is normal, and the alternative hypothesis: our coin is special (is not normal) we have alpha = 0.05, p-value = 0.375. 0.375 > 0.05 ===> reject the null hypothesis ===> accept the alternative hypothesis ===> our coin is special or is not normal Why did you say that "did not convince us that our coin is special"?

[@statquest]

We only reject the null (that our coin is normal) when the p-value is less than the threshold. In this case, the p-values is 0.375 and the threshold for significance is 0.05. Thus, because 0.375 > 0.05, we fail to reject the null hypothesis that our coin is normal.

[@wtfJonKnowNothing]

The woh woh at 8:03 got me

[@statquest]

:)

[@henrmota]

Best explanation ever. Now I see why p value is so miss understood.

[@statquest]

BAM! :)

[@henrmota]

@@statquest I am a software engineer trying to go to data science to make data driven decisions. I would love to see a course on bayesian inference maybe with pymc :). Thanks for your videos.

[@suheyla655]

You make all topics so easy. Thank you so much !

[@statquest]

Glad you like them!

[@mitchynz]

Hi Josh, thank you kindly for the clear concepts - I had a question about the continuous example: @17:30 you look at a single sample for someone measuring less than 141cm to reject the null hypothesis... but the normal distribution could explain one off outliers, couldn't it?.. wouldn't it be important to compare the mean of a small sample for your test statistic with a minimum sample size (like ten people) and calculate that p-value before you reject the null hypothesis? .... sorry if I have this confused

[@statquest]

The normal distribution could also explain a group of outliers. So to keep things simple I just decided to use the smallest sample size possible to illustrate a concept.

[@jennifertrudeau8076]

This has been very helpful!! I still got lost in couple of places... about the .04 value at 18:37 -- where did that .04 number come from? I understand that it represents the probability of that part of the distribution. But how did you calculate it out? Where exactly does the .04 come from? And my next question is about one-sided p-values: why are you taking all of the 98% to the left of the extreme right? Why didn't you start with the mean here as well?

[@statquest]

Great questions! 1) To calculate the probability (0.04) we integrate the equation for the normal curve en.wikipedia.org/wiki/Normal_distribution with a mean of 155.7cm and a standard deviation of 6.6cm from 155.4 and 156. Doing this by hand is very tricky, but we can get a computer do it (there are functions in excel that will do it for you) and that's what I did. 2) We take all of those values to the left because all of them represent shorter recovery times.

[@alinouhi8626]

Your method of explaining things is unique, you make complex concepts so easy to grasp. Can you please mention some textbooks (preferably intermediate to advanced level) of probability and Statistics that you yourself have read?

[@statquest]

All of the statistics textbooks that I've used have been really bad. That's one reason why I created this channel to begin with.

[@slouma1998]

Damn such a well timed video, I was just watching the old p value video, and I was confused hahaha, great explanation, and thanks!

[@statquest]

Hooray! I'm glad this cleared things up.

[@ahfodder]

Bam

[@statquest]

@@ahfodder Yes! :)

[@ngochanvo6017]

I would like to send my thankful to you! Your explain is really clear and interesting! Hope you always are healthy and make more interesting lessons

[@statquest]

Thank you very much. :)

[@kristi739]

Thank you for the best explanation of p-values I have ever encountered. However, I still can not say with confidence that I have fully understand the true meaning of the p-value. Referring to the Null Hypothesis at 1:50 ; does it depend on the type of hypothesis (NULL, Alternative, or even the way we formulate the hypothesis) whether we reject it or not; or when p-value < 0.05 we always reject, no matter our hypothesis? As far as I understand it, p-value tells us the portion of random events is (or is not, depending on the value) effecting the outcome of the experiment.

[@statquest]

I talk about what a p-value means in this video: kzbin.info/www/bejne/rJbQi6d7gptmfbs

[@SarrouTube]

Again! Excellent information, crystal clear! Good instructor!!

[@statquest]

Thanks again!

[@annelisefree]

I am so struggling with this and love the videos. I just can't see at time 18:52 where the p value of 0.04 came from. How was it calculated?

[@statquest]

See 13:07. The area under the curve represents probability. For the probability of measuring someone between two specific points, we use calculus to compute the area under the curve between those two points. In practice, this can be done with a computer without us having to deal with the mathematical details.

[@oneminuteasmr6486]

Your videos are so clear and helpful! Keep it up!! You earned a new subscriber 😊👍

[@statquest]

Thank you! :)

[@shanxW16]

Great videos! @20:46 why would we calculate two sides P values if we're looking for recovery time below 4.5 days? I'm new to this... Thanks in advance

[@statquest]

See 21:26 and 22:57

[@ibanguniverse811]

Wow, my Best profesor is Back !

[@statquest]

Thanks! :)

[@tim40gabby25]

.. now time to get yourself an English Professor :) just kidding.

[@ibanguniverse811]

@@tim40gabby25 sorry for my poor english, please correct my words

[@tim40gabby25]

@@ibanguniverse811 hey, you're doing fine. regards from the UK.

[@dragonk4tz470]

Thank you so much for this! I am so confused on EVERYTHING stats but this made tons of sense. I'm gonna go watch the other ones now! Thank you!!!

[@statquest]

Glad it was helpful!

[@gauravmohan9271]

Thank you josh…love from India

[@statquest]

Thanks!

[@SNAKE1375]

I don't understand either why the data are inconclusive (16:59). What was the Ho hypothesis concerning the size distribution? What do you mean by "it's normal or not" to measure someone 141 cm tall? normal against what?

[@statquest]

Normal just means "is it commonly done". For more details about hypothesis testing, see: kzbin.info/www/bejne/ZqDGZWx6rqZmnrc

[@Patrick-ew3to]

This video helped me get through my first quiz in my regressions analysis class. One thing I did't see: How might we determine the likelihood that two sample means are part of the same population.

[@statquest]

I'm glad my video was helpful. From here you might want to learn about t-tests. I have a StatQuest on that, but I teach it in an unusual way - I teach it from the perspective of Linear Regression. It's all part of my Linear Regression playlist: kzbin.info/aero/PLblh5JKOoLUIzaEkCLIUxQFjPIlapw8nU

[@statquest]

ps. Thank you so much for supporting me! :)

[@Patrick-ew3to]

@@statquest Thank you! That's actually extremely relevant since my next module in school is linear regression :)

[@statquest]

@@Patrick-ew3to Awesome! :)

[@Jordan-vl8wm]

The flower example deserves a BAM!

[@statquest]

bam!

[@poohjj888]

Hi, thank you so much for the video! It has been so helpful. I just have some questions regarding 17:43. I see that you've picked an example, where you select one random person, and calculate a p-value based on their height. How do I know if this is a robust p-value? If I were to pick a random person 100 times, surely there will be more times that the p-value will be larger than 0.05, as the random person is more likely to fall nearer to the average than to the extremes.

[@statquest]

The p-value I calculated in the video is just for that one, specific person, so it doesn't really make sense to ask if it is robust or not - because it only applies to that one person and that one person's height is not going to change. This p-value does not, in any way, reflect what we might expect if we picked a bunch of random people. It only reflects what happens when we pick a person and their height is exactly 141 cm. Now, what would we expect if we picked 100 people at random from that population? Well, we'd expect about 95% of them to have p-values > 0.05. Now, what would we expect if we think we are picking 100 people at random from that population, but maybe we're wrong, and maybe they come from a different population? Well, in that case, it depends on if the other population really is different and how different, and this leads to to hypothesis testing. To learn more about hypothesis testing, see: kzbin.info/www/bejne/ZqDGZWx6rqZmnrc

[@patrickbigbigx5312]

After I watched this video twice, I finally understand why one tail is dangerous, because the null hypothesis is specific for “shorter “, and probably only expert would make a hypothesis for longer!!!

[@statquest]

bam!

[@yuan8947]

In 15:54 "all heights further than 142cm from the mean are considered more extreme". My question is: the criteria we decide the probability is based on the distance from the mean? Can't we set the median or other number rather than mean? Thank you so much!

[@statquest]

In theory you could use the median, but in practice it is rarely done because of technical issues (with a relatively small sample size we can infer a lot about a mean, but it is harder to infer much about the median.)

[@trotts1221]

Your a great teacher man

[@statquest]

Thank you!

[@tomas96lv98]

This is beyond gold

[@statquest]

Thanks!

[@anthony8977]

May I know how to get the probability 0.04 mentioned at 18:28 ? Is it the total number of people fall between 155.4 and 156cm divided by the total population ?

[@statquest]

If we were using a histogram, we would use your approach and it would work great. However, since we are using a continuous distribution, we use calculus to integrate the curve between the two points. At least, that is the theory. In practice we just get the information from a computer with a few commands.

[@anthony8977]

Thanks a lot. You are awesome.

[@vincentchong2647]

Hi @Josh Starmer, thanks for the useful video. At 18:50, may I know how to get 0.04 as the P-value? Thanks.

[@statquest]

We calculate the area under the curve. You can do this with calculus by integrating the curve between two points, or you can get a computer to do the work for you. I used a computer.

[@eyanagazi5093]

You are really WAAAW! everything becomes easy with you♥ thank you for this great job you helped me a lot to understand many difficult concepts with your funny method BAAAAM!

[@statquest]

Hooray and Bam!!!! :)