Hypothesis testing and p-values | Inferential statistics | Probability and Statistics | Khan Academy
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Hypothesis Testing and P-values
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Probability and statistics on Khan Academy: We dare you to go through a day in which you never consider or use probability. Did you check the weather forecast? Busted! Did you decide to go through the drive through lane vs walk in? Busted again! We are constantly creating hypotheses, making predictions, testing, and analyzing. Our lives are full of probabilities! Statistics is related to probability because much of the data we use when determining probable outcomes comes from our understanding of statistics. In these tutorials, we will cover a range of topics, some which include: independent events, dependent probability, combinatorics, hypothesis testing, descriptive statistics, random variables, probability distributions, regression, and inferential statistics. So buckle up and hop on for a wild ride. We bet you're going to be challenged AND love it!
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I feel like you deserve my quarterly tuition more than the professors at my University. Your videos always seem to explain these topics in a fraction of the time it takes my professors, yet you still somehow manage to also explain them more thoroughly. Thanks for your help!
fr
yeah I was thinking the same thing!
- student from hopkins here
If you guys got it, how do we know when to use which formula?
I'm a new grad student who hasn't taken a stats class in about 4 years. I'm currently in a stats class (also for learning r and spss) and was feeling lost when it came to the basics. These videos explained everything I was missing in such a digestible and understandable way! Now I'm caught up theoretically with my class and I'm getting more out of the lectures! This is fantastic content. Thanks Khan Academy!
I learned more in 12 minutes online than I did for 3 90 minute university lectures lol
tell me about it...
Bro, I feel that. I've given up watching my lectures and come straight to Khan Academy now.
Thank you Khan!
Absolutely. I don't even think that my university teachers knew that "p-value" stands for "probability value".
Me too!
Literally
Look at it this way, the null is saying that "there is no way on earth that the average is any value but 1.2 seconds." Then, assuming that is true, we do some math and figure out that if the drug indeed did have no effect, and we randomly sampled mice 100 times, it there would be a 0.3% chance that some of those mice had response times of 1.05 seconds. So it would be super improbable to get a value of 1.05 seconds. Now....rewind back to the problem. We were told that the scientist not only had mice with a response time of 1.05, but even better, that was his average response time! This means that it is crazy to think that the drug had no effect, because if it didn't there would only be a 0.3% chance we got a value of 1.05 seconds.
But that the mean of the sample would be 1.05 seems different (even less) than 0.3%, right?
eteoklos man, you should make your own set of videos. Thanks for that explanation :D
Thanks alot man!!!
It totally cleared my doubt.
Saviour u r!!!
I m ur fan nw.
Thank you so much it cleared everything.
That makes total sense. Thanks
This is amazing! Having heard about Khan Academy a million times, this is my first time watching it. This is too good and I want my tuition back
5:18 it's not the standard "deviation" of the sample distribution but standard "error" of the sample distribution. se=s/sqrt(n)
@Nimbus : some books call it standard error of the sample mean. So in C.I, you see the sample mean +|_ z score*S.E, you do that for adjusting the error in the sample mean which gives an interval containing the pop mean with some level of confidence.
I have been searching for this comment. Thank you m8 for clarifying
old comment but THANK YOU ! I was so confused...
Was around for your original videos in undergrad many many years ago, and now that I’m back for my Masters, you’re still coming in clutch as ever. Owe you a ton.
So in 2 more hours i'm having mathematics exam. The hypothesis says i'll fail it and will come back after 2 months to watch this video again for a resit paper. Thanks anyway.
i will reject the null hypothesis which means that your hypothesis is statistically significant and is applicable on population which include me which means that i will also fail the exam and come beck here 2 months later XD
spy 009 haha.. You'll pass don't worry.
Call your teacher instead of waiting till the last minute before the exam to learn the material
You shouldn't skip class, js.
@@ellaiyarasankalidass5699 what happened
i still don't get it... damn exam is screwed
i feel u.
+Toby chua yep... and is actually a retake and im still screwed
I'm done too.
+Leo R.
This was the ONLY thing that I could not understand when I took probability and statistics. I'm just all duuurrr when it comes to this concept.
Toby Cai y
Dear Khan,
So im switching between 3 statistics textbooks trying to understand the p-value, and it takes me hours and hours. Then I come here and you explain it in 11:26 minutes.
You are really kicking ass with this khan academy, or as charlie sheen would put it, you are winning.
LukSkajwokerrr
Same here 😅
@@bagiromer8587 bhai hypothesis testing nhi kr skte mujhe stats mein kuch nhi aata h
OMG the following clarification just made starting my homework a WHOLE lot more fun!
The probability (P-Value) of getting a sample (H1) being 3%, assuming that the null hypothesis (H0) is true, suggests that we should reject the null hypothesis (H0).
So, if (P-Value) is > 5%, then we will accept H0, b/c the chances of getting (H1) are high enough.
Thanks Khan!
Ok, I think I figured something out. There are actually three standard deviations at work here: SD1: the SD for the 100 individual drugged rats (the SD of the sample, .5 seconds), SD2: the SD for all could-be drugged rats (the SD of the population, we don't know), and SD3: the SD for AVERAGES taken of 100 drugged rats (the sampling distribution, which here is estimated to be .05 seconds) . SD3 represents the SD you get if you take averages of 100 drugged rats, many times. The fact that you're averaging 100 at a time makes the distribution tighter, and in that light, a difference here of .15 between the null and the test result is significant. In effect, it's bigger than the distance you'd normally see between an average of 100 rats and the true average. He said SD3 is supposed to use SD2 but you can use SD1 if it's a reasonable size like 100.
Thank you I was so lost
you single-handedly got me through a-level maths alive god bless you and all of your descendants
THANK YOU!!!!
I was struggling to grasp this concept in a practical sense, and your video helped me connect the dots.
This...makes so much more sense. You just saved me from my stats final, thank you
I still don't get it.. fuck..
You and 72 others. The narrator neglected to define many terms, and he used lots of jargon.
kimaegaii I'm with you bro
Yue Zhang
thank you man, i thought i was the only one for a minute lol
*****
Thank you Rafsan!
What is the sample standard deviation?
Why don't we use it as a standard deviation for the sampling distribution but as a standard deviation for the whole population?
Very nicely explained! It's one of the most important concept in Data Science and Machine Learning! Thanks team! :)
Khan, you seriously rock. Never understood p-values from my professor, but I definitely do now!
You do not understand how grateful I am to you.
Thank you so much.
Wish I had found these sooner, I struggled so bad with econometrics. You make things so easy to understand.
There is a mistake : The t-statistic would be much more accurate since we know nothing about real s.d. (population s.d.).
Edit : For n > 30 CLT kicks in and Z-score can be used instead of t-score even tho we don't know population sd
I'm so glad I found this channel & wished I knew about it during my undergrad yrs. I am currently preparing for a quiz & I think I can say I got this.
Thank you Khan!! You're the best. So much explained under 15 min - incredible!
You taught me more about this concept than my professor and a tutor were able to. Thank you!
Many Thanks! Sal. I really appreciate your educational videos. Keep up with good work Sal and Khan Academy. You guys Rock!
Great video, in general hours of study in pure elegant 11 mins! Bravo!
I wish I had found them when I was working and studyng together...
p-value for Z score of negative 3 (-3) is 0.0013, which is less than alpha (significance level = 0.05 for 95% confidence), hence we Reject H0 null hypothesis. Another way is that the probability that the observed sample mean 1.05s being -3 Z scores away is less than 0.05 (5%) .13% here, hence Reject Null hypothesis.
Do you have to consider the fact that it is a two-tailed test and therefore use .26% instead of .13%? ( I know it doesn't affect the rejection of H0 but still useful to know)
ps: exam on Monday I beg you, answer me fast lol ^^
Thanks a lot! This video really explains hypothesis testing in a very simple way.
In just 11 mns, all the picture is really astonishingly clear enough to understand this part of inferential statistics. Thanks.
Thank you for the video- quite helpful and comprehensive!
Ur Z test inverts the position of x-u by u-x It suposed to be Sample mean 1.05 minus Population mean 1.2 and u put Population mean 1.2 minus Sample mean 1.05.
Yess, he did. I got so confused
I love Khan Academy and think Sal Khan is a hero. If only more teachers could explain concepts the way he can! Maybe he should do a series on 'how to be a better teacher' :-)
Very detailed and interesting lesson. I got it at the end of the video.
Thanks so much.
0:38 This made me kind of smile.
excellent illustration! thank you so much! i will take those statistics courses again! i understood the concept of p-value for the first time!
Thanks so much, your videos are a huge help. Keep up the good work!
Thank you thank you thank you! I finally understand it now. Or almost. I will probably have to watch it again.
Perfectly explained...hatsoff!!
Yay! I get it now! My instructor made is SO confusing. This was beautifully simple. Thank you, thank you, thank you!
great viedo guys! I love the way you explain things intuitive. Keep up the good work!
Omg this makes sooooo much more sense now
Gonna go to sleep now and give it a try tomorrow with homework questions
that blue color is so cool
+Stan Land LMFAO XD
THANK YOU. i didn't get this in class just today. Pro. gave the formula without the details behind those simple formulas as z-score. Now it's very intuitive to have the x subtracted from mean and then divided by the sample standard deviation. so make sense now.
There are three standard deviations he is talking about: the std of sampling distribution (of the mean) "\simga_{\bar{x}}" , the std of entire population distribution "\sigma" and sample std "s". (1) When the number of examples in a sample is large, "s" will be very close to "\sigma". This is pretty easy to understand, more sampling, closer to the true distribution. (2) "\simga_{\bar{x}}" means another thing, 100 examples as a sample, we compute the mean of these 100 examples; then we take another 100 examples and compute the mean; we do a lot of times; we compute the std of these means, this will be the std of sampling distribution of the mean. This is what he wants to compute and his computation is correct. (3) why computing "\simga_{\bar{x}}"? because all from beginning, all he compute is the mean. 1.2 is the mean, 1.05 is the mean. He tries to determinate how 1.05 is from 1.2. And the distribution of the mean is also a Gaussian distribution but with a smaller std, which we didn't at first but we can compute it by the formula given in the video, so it's 0.5 / sqrt(100) = 0.05. (4) why 0.03 not 0.015? I think it's because the hypothesis here is u != 1.2, not u < 1.2. So the extreme situation like getting 1.05 has the same probability as getting 1.35. Hope this helps.
You guys are awesome...even for this middle aged professional...education never ends 😀
Thanks alot. I was stuck on my stats homework as to what a Ho and Halternative hypothesis were. Thanks!
thank you so much this really helped in grasping the basic concept !
I've spent whole day to understand this and this video my concepts clear within 10 minutes. You're awsome Sal.
Sal, I am in love with your lessons. So clear and concise.
explained very well thank you for clearing my doubt
this the best method of evaluating a null hypothesis, no need to refer to any table, amazing.
first channel I ever followed on TH-cam (since 2011, I think). Sal has never disappointed me.
This is so helpful. Thank you!
Do not stop the good work Mr Salman it has made things a lot easier for people please go to some unattended topics and make videos of them..:) love ya
Hi, mr khan. Thank you so much for posting all of these learning resources here. They have been "Everest-ly" helpful, especially to a "lost mountain swan" like me. I will definitely recommend your precious teaching materials to everyone I know, also in hope that they would pass them on to yet more curious and knowledge-thirsty individuals. After all, imparting and sharing knowledge is a great way to foster friendships around the world. Your willingness to help others learn is a heartwarming act of philanthropy. I for one am sure it feels like arriving at the mountain-top to find an inexhaustible spring that bursts with the waters of knowledge.
ur the best teacher ive ever had! Thank you Thank you Thank you
I know that drug. He is right, it does have a lot of effect. Yeah.
hahaha
Why do hypothesis testing when you can do drug testing 😂
machine learnig on its way ...lol
looll
with just two words you helped immensely, thank you
thank you very much, first time i Understand the utility uf the p value. Love you khan
I liked this lecture and it was easy to understood. Thank you.
why does statistics exist.huhuhu
After 5 years, i will ask the same queation, why?????!!!
@@raulecreuset4558 After 3 months, I will ask the same question, why?????!!!
so that people like you can get video recommendations like this one and others that you enjoy.
So we can have plandemics
:(
This lecture definitely helped me a lot.
this can't be explained better then this... spot on..
I appreciate this video and your existence you saved my life xo
But why 0.5 is considered population standard deviation in the calculation? I though 0.5 is the sample deviation????
I don't get that too, he says since sample size is large enough, we can assume population standard deviation is almost equal to sample standard deviation.
Because if the sample size is greater than 30 we assume them to be equal
@@iansequeira3352 Then why is he recalculating the standard deviation when we can assume it to be 0.5?
@@zhen3356 0.5 is the standard deviation of samples, and we are calculating standard error of the mean
Thanks Sal, as always, this is great
Thanks Sal!! This is what we need.
thank you soooo much!!!! where have you been all my life.
Thanks for the great teaching on the concept, p value
Yes! Thank you!
Why did you divide the sample standard deviation by 10 instead of multiplying it by 10 to obtain the population standard deviation just as the reverse of the formula says?
I am confused too. I thought .5 was the sample std dev and the pop std dev would be .5*10 = 5
He was calculating the standard error not the standard deviation..
@@femidaelettil1002 It still doesn't make any sense, the formula for the standard error is the same. se=s/sqrt(n), it should be .5*10 = 5. Plus, if you take the "approximated standard deviation of the population" that he got it's not equal to the sample standard deviation. Se = 0.05/sqrt(100) -> 0.005. Can someone explain it to me?
Late but 0.5 is not the standard deviation of the sampling distribution, it is just a standard deviation for sample with sample size of 100.
@@yuzhe6054 thank you
these videos are really helpful. thanks a lot
Super clear explanation!!! Thanksss
Z = (Xbar - Mu) / [SDV / sq.rt(n)]
He made the error of subtracting Xbar FROM Mu. He needs to reverse the two numbers for the correct formula. Z = (1.05 - 1.02) / [ 0.05 / sqrt(100)]
It doesn't make a difference. A z score of -3 would give the same probability of three standard deviations in either direction from the mean.
No he did 1.2 - 1.05 which is correct
@@BurgoYT no, its incorrect because the formula is (sample mean-population). it should be 1.05-1.2
Thank you! It's very helpful.
This was helpful - thanks!
Very nice explanation! It was very comprehendable,Thank you
Thanks man this really helped a lot
Thanks dude, clear and easy to follow
Neat explanation, thank you for your effort and time.
You know you will always learn something here. Thank you.
Amazing my god,u explain with damm clearity which I can't get in any video/class lecture
Oh man ... you've made my day !!!!
thank you
you helped me a lot
in fact, you save me
you are a very great teacher
I can easily understand what those mean only from your explanation. Thanks.
Very concise, thank you.
I have a final on this in 5 hours. It's 2 AM right now. Shout outs.
Yup in the same situation
Khan you provide a legendary service. Thank you.
This channel helps me not fail!
literally every video is so helpful
GREAT video. Very well explained.
man , he explained so clear!!!
for those who dont understand , go improve ur basic in probability
This always helps me: "If the p is low, the null must go". which means, if the p-val is less the significance level(alpha), then you reject the null hypothesis.
Thank you sir for this 😂 slogan. I am taking my Ap stats exam today 😊1
The man just has a talent for explaining things.
Wait, (1.2 - 1.05)/0.05 is NOT the z-score. It is the t-statistic because the we have estimated the standard error using the sample SD in place of sigma (the population SD), which is not given.
onthe verge The sample is large enough hence you use a Z-stat
he had something like >30 samples so the two is same at this piont
this is prob the best explanation so far
At 3:30, when you're talking about the sampling distribution, do you actually mean the distribution of the sample mean? By LLN and CLT?
The assumptions of using z test are that first population is normally distributed and second the population standard deviation is known(not the sample standard deviation).
For the first time in years I really understood the meaning of p-value hahahaha