P-values and significance tests | AP Statistics | Khan Academy
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Learn how to compare a P-value to a significance level to make a conclusion in a significance test.
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AP Statistics on Khan Academy: Meet one of our writers for AP¨_ Statistics, Jeff. A former high school teacher for 10 years in Kalamazoo, Michigan, Jeff taught Algebra 1, Geometry, Algebra 2, Introductory Statistics, and AP¨_ Statistics. Today he's hard at work creating new exercises and articles for AP¨_ Statistics.
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Ahh, even at university, Khan to the rescue!
Even at work, Khan to the recues!
Same lol
Even at retirement, Khan to the rescue!
This is better than most other articles and videos that I found about P-values. Huge thanks!
Think this is the essence of the video: If we assume H0 were true, what is the probability that we got the result we did for our sample. So if below alpha (our treshold) then reject H0.
This comment just saved me so much time. Thank youuu!
Joshua Kölzer u are the best, thank u, saved so much time.
Yes . thanks for the comment this provides more understanding on p value.
I donate to you and will do so every year because you sir truly care about education in its most fundamental form. My daughter uses your free services and our family does and we dont have to hear about any politics or underlying agenda. Sal Khan you are a scholar and a gentleman comparable to Ghandi himself!
read a number of posts on quora..watched few videos on youtube..got nothing..
Watch the first 3 minutes of Khan's video and in no time could understand the intended meaning of p-value. God level.
I wish he actually calculated the p value
take a look at Z stat and T stat videos. its easy
Here is the link @metogema mentioned.
@@metogema thanks!
@@samcohen3647 sure:)
@@ekbastu great
Your explanation blew my mind! Definitely would recommend for anyone having problems with understanding this test!
Let me explain with an example considering the same scenario as in the video:
Let's say we have a total of 4 samples - s1, s2, s3, s4.
t - represents sample mean >= 20
f - represents sample mean = 20
Below are the possible combinations of means of each sample.
s1, s2, s3, s4
1. f f f f
2. f f f t
3. f f t f
4. f f t t
5. f t f f
6. f t f t
7. f t t f
8. f t t t
9. t f f f
10. t f f t
11. t f t f
12. t f t t
13. t t f f
14. t t f t
15. t t t f
16. t t t t
Basically, Null hypothesis represents Null(No) effect. So, in this case, we take Null hypothesis as 'There is no change in average time people stay on the website after changing the background to yellow'.
Probability of seeing zero t out of all samples available = 1/16 = 0.06
Probability of seeing one t = 4/16 = 0.25
Probability of seeing two t's = 6/16 = 0.375
Probability of seeing three t's = 4/16 = 0.25
seeing four t's = 1/16 = 0.06
So, let's pick 4 samples and they all turn out to be 't'. Would you believe that Null is true? In other words, would you believe there was no change in average time people stayed on the website even though all samples you picked up showed otherwise? No!! You wouldn't believe it. You would say, no probably the average time has increased and that is why all the samples showed 't'. In other words, you would not believe that Null is true when such a weird scenario happens. You would reject Null effect hypothesis.
p-value basically says, if you assume Null effect hypothesis to be true, how likely the result supporting the alternative hypothesis is a random result. If p-value is low, result supporting alternative hypothesis is not random. Hence you reject Null Hypothesis. If p-value is high, result supporting alternative hypothesis is random, hence you stick to Null Hypothesis.
Thank you very much!!!
So there are two context to be taken into account i.e. population and sample.
P-values lets us decide whether the sample that we have taken concur with the population attributes, answering the question whether our sample is random.
Also, when the p-value goes below the significance level, it states that the sample that we have taken agrees with the alternative hypothesis.
I don't agree with "the sample that we have taken agrees with the alternative hypothesis" when the p-value goes below the significance level. As you said in our 2nd sentence, p value indicates how likely it is for you to get such sample from your null hypothesis population. If the p value is high, it means it is very likely for you to get such sample from the null hypothesis population, meaning your observed sample contributes very little to prove that your null hypothesis is wrong, because your observed sample can happen by chance very often: it doesn't tell you that your observed sample might come from a different population than your null hypothesis population. On the other hand, if the p value is very small, it means that it is extremely unlikely for you to get this sample that you have now from the population of the null hypothesis. However, it doesn't necessarily tell you that the alternative hypothesis is correct: It only tells you that your sample is not from your null hypothesis.
@@mint.f2060 why we are rejecting the null hypothesis when the p-value is less than the significance value?
@@jayanthperneti9213 Because it is extremely rare for your observed sample to come from this null hypothesis' population. Therefore, the actual population that your sample is from is not the null hypothesis, so we reject it.
From my understanding, the p value represents the propability that the sample mean behaves as H1 if H0 is true. For example, if alpha is 0.05 and p value is 0.005. The alpha means i do not reject H0 if at least 5 % of the time the sample mean behave as H1. However if p is larger than alpha which for instance as 0.06 the probability the sample mean to behave as H1 increases. So we do not reject H0 but doesnt meant we accept it. This is because the sample mean do behave as H1 6 percent of the time if H0 is true. In a nutshell, we want to see whether the sample mean behave as H1 how many percent of the time if H1 is true. The higher the p the higher the probability that sample behaves as H1 and we do not have sufficient evidence to reject H0. Very counterintuitive for me actually. Correct me if I'm wrong.
I can't verify this but I'm supporting this logic. 4 years later and it still helps, thanks man.
It would've been helpful if you guys completed the whole example and added a visual element like drawing it out on the teardrop graph/ binomial function to emphasise each aspect 👍
I've been trying to get this idea in my head for 2 hours now and I just can't. I don't understand how you would reject H0 if p value is low but you would accept it if it is high. It makes ZERO sense to me. And I usually understand your videos. If I have a higher probability of getting a value higher than 25, why wouldn't I reject H0??
We assume the H0 is true - that is the key. If the p-value is high, then the null hypothesis is still acceptable because of high probability, then we can not reject it.
alpha, or the threshold, is the probability of getting a type I error (rejecting a true Ho, or false positive). p-value is the probability that you got the result given the Ho being true. therefore, it is reasonable to state that we must reject Ho if the probability of getting our results is low assuming it is true. however, how low? well, this is where the threshold comes in. as long as it is lower than the probability that we reject a true Ho, it is safe to say that we can reject Ho. i hope this helps
@@zackm5693 Zack Manesiotis
Back to the example in this video, In this example the mean is 20 minutes for H0. So if H0 were true then the Probablity to get mean >= 25 should be small Then We should not reject H0. But if this is big then H0 should be rejected.
@germanottass
Think of p value as probability of new data conforming or adhering to null hypothesis.
If p is low...the new data doesn't conform or adhere well to null hypothesis..and hence reject it(the null hypothesis)
If p is high..the new data conforms or adheres well to null hypothesis..and hence it cannot be rejected.
What is low or high p value: the threshold or alpha or significance level decides it
@@SrikanthReddy-uu4kg hold on but isn't p-value the probability of getting "extreme values for new data", so relative to the null hypothesis it would be the probability of new data NOT conforming or adhering to the null hypothesis right? Then if p-value is low there is a low probability of getting new data that is extreme so there is little deviation between groups, which supports the null. And if p-value is high there is a high probability of getting new data that is extreme so there is lots of deviation between groups, which does not support the null.
It just doesn't feel right logically the way it is and I'm tryna make my brain make sense of it but I can't spot errors in my logic and claims so if someone else can explain that would be amazing.
To those saying the Ho and Ha are not properly formulated, it depends on the statistical test we run. We can run a statistical test on Ha as shown, or on Ha where mu != 20, but its irrelevant for explaining the p-value that we get from such a test. He mentions running a t-test, which only tests for equivalence of means (not for Ha as shown), but since that was just an example of a type of statistical test, it doesn't invalidate his explaintion what a p-value is or how to interpret one.
THIS IS GOLD I STUDIED P VALUE FOR THE WHOLE DAY ALL OVER THE INTERNET AND FINALLY I CAME TO UNDERTSTAND IT HERE !joining medicine really makes your brain sluggish at stats haha
Pls how do we calculate the p-value
Great video!
For those who may still be struggling, here's how i learned it in simple terms. Feel free to correct me if I've misspoken.
You want to compare A to B. Can be anything. Like a straight line of points points to a semi-straight line of points.
Question, are they the same?
nuLL: has two 'L' s at the end of nuLL. They're the same letter L. Thus, null means they're the same. (A is the same as B).
p-value: in it's simplest form, p is the probability the null is true.
If p =1. Then nuLL is true.
If p = 0. Then nuLL is not true.
The threshold value is 0.05, usually.
If p is less than 0.05, then nuLL is not true. Meaning A and B are not the same.
If p was, for example 0.80, then obv it's way higher than 0.05 (the threshold). And if p is the probability that the nuLL is true, then A=B in this case.
I thought I understood it and this is how I understood it as well, until what he said at 07:15 - 07:36😢
Thanks! Admittedly, I didn't get to the end when I first watched this video. I think I see what's going on with p.
To further clarify, it is not exactly the probability that the null is true. Instead, it seems to follows Bayesian statistics, where something is true or false given something has occurred.
If this is the case, then there's four conditions where two will always be p=0:
p (A=B given means are the same)
p (A=\=B given means are the same), may never occur
p (A=B given means are not the same) , may never occur
p (A=\=B given means are not the same)
It is rather confusing. 😑
i spend the whole day trying to understand p value concept and it took you 8 minutes to explain it.thanks
if p value is low that means null should be avoided cause we assumed it is true while calculating p. As probability of p is less when null is considered true so we can let it go. But when probability is high that means we cant ignore it cause we assumed and our assumption is high.
thanks, very clear.
can't believe that I finally got it! A huge thank you! This made my day :D
Omg, after 2:20, you explained it perfectly and in the right order. The light bulb came on.
I was looking at other youtube videos they had more views, in the comments, people were saying they understand. However, I was not getting it. But, your explanation is what I needed! Ty
Everybody has different level of understanding
I am still very, very confused. If the null hypothesis is true (no difference occurs), then if the probability that we get the recorded statistics is high, it should mean that our experiment did produce a difference and hence we should accept H1? Can someone clarify this up for me?
Just think about it this way maybe: null hypothesis stand if p-value is between 5-100%, meaning there is no difference between the samples, the are basically the same. If the p-value is lower than 5%, then you reject the null and accept the alternative, which means the two hypotheses are not the same. Confusingly the alternative hypothesis is what you are really interested in proving. You can you reject the null hypothesis because the p value is statistically significant
I cant believe Im here again, I first saw your videos while preparing for igcse 10 years ago, now Im back since I'm doing my masters degree, Cant't thank you enough
I don't get it. If the p-value = the probability of getting sample mean >= 25mins | H0 = true,
and if the p-value were say 0.5, then wouldn't that mean that there are many instances where sample mean >= 25mins; which would mean that there is evidence to reject the H0, that population mean still = 20mins?
I dont really get it on intuitive level. If P(mean(x) >= 25 | H_0 is true) = 90 % means that probability that the mean value is greater than in H_0 given H_0 is 90 %. Isnt it more logical to reject H_0? why is it vice versa?
Wouldn't the alternative hypothesis be =/= 20. Not >20? I'm pretty sure you're just disproving the null hypothesis, not affirming another hypothesis
The way I understand this is: in a world where no difference is the truth, then, if a difference does INDEED OCCUR, that means the occurrence is completely by chance. And if the p-value is high, it would mean that the probability that the recorded statistics happen BY CHANCE is high, therefore we cannot reject the null hypothesis.
What if for that particular sample alone we got p-value of 0.03 by accident? Wouldn't it be an error to reject to null hypothesis just on this basis? Shouldn't we be repeating for more samples...if yes then how do we then find a way to accept or reject the null hypothesis?
highest quality education video in the entire world as of 2024 for explaining p value. Again and again, Khan academy teachers are the best!!!!!!!!!!!!!!!!!!!!!
i think there should be one more hypothesis. that is u
Hi Khan Academy, thank you for your video! It is helping me to prepare my exams. I have a question, why did you use 25 minutes instead of 20 minutes? I thought that if you want to reject your null hypothesis you have to take the mean of the sample like it is and then calculate the p-value, because when the p-value is to small then we can reject the null hypothesis.
I would appreciate an answer.
Thank you for you time!
True I had the same doubt.
Let me know if you have found out why?
@@ranjithsekar9537 because 25 minutes was the sample mean from the new samplw
same doubt
we want "the probablity that the obersevation (25) would happen given that our null hypothesis (20) is true"
Thank you Khan Academy for helping me out with my online courses!
Can anyone help me? I do understand how to reject the null based on the p-Value (the number). The thing is...if the "P-value is the probability of obtaining an effect at least as extreme as the one in your sample data, assuming the truth of the null hypothesis" then it sounds like we should reject it when the P-values is high, cz we have a high probability of getting something that extreme. :(
I thought the same way. Everywhere, this video of Khan included provides the same explanation, which really makes me confused.
The key is in understanding that if u get a high p value that means there is high probability that u will get the results as extreme as the one in your sample data just by chance which basically means the difference is not significant and u can accept the null hypotheis in this case. And reverse the scenerio for rejecting ho: .
2:06 "What is the probability of getting the statistics that we get." What!? The probably of 'getting' the statistics that we 'get' is 100%. How can you get any other statistics than the ones that you get!? Why is this so confusing!?
yeah that was confusing to me too
Think he means: what is the probability of getting the statistics you just got if you were to repeat this with different samples
Because essentially you want to know whether the result you just got in the sample you researched reflects an actual effect of your intervention, or is due to coincidence
Trying to wrap my head around this - shouldn’t we reject null if p-value is higher than alpha? Since it would mean that in a world where null is true, the chance of that result (p-value) would be higher than my threshold?
same thing has me confused lmao. Anyways, did you figure it out now?
Thank you so much and God bless you.
Thanks for explaining Sal, although I'd like to call out a logic error in the explanation.
In probability, and while assuming the scenarios for null hypothesis and alternative hypothesis, H(0) & H(A) need to be mutually exclusive and exhaustive (i.e. they capture all potential events).
However, in the explanation, H(0) is "20 minutes after changing colour" and H(A) is "greater than 20 minutes after changing colour".
This doesn't account for the scenario when the time dropped below 20 minutes after colour change. So when we reject the null hypothesis H(0), we basically assume that if the time (after change) spent by visitors on the website is not equal to 20, then it was a success (which is incorrect).
“If we assume the null hypothesis is true, then what is the probability we got the result we did for our sample” - this last line is the perfect summary
What do you mean by "then what is the probability we got the result we did for our sample". Does it consider more than one sample?
@@krishnagattani8182 it's comparing the null hypothesis, to the probability that the sample changed due to the experiment.
understand the significance level as the the meaning of "randomness" will help you to understand the meaning
This was fantastic and almost brought tears to my eyes. After two days of constant confusion and chaotic searching, I finally understand p-values. Thank you Sal Khan. Thankn you Khan Academy. 🥹
Wow. I always just memorized the workings and solved without understandings. Now I kind of understand why we reject or not reject the null hypothesis.
Thank you sir you have changed my life
So ur life's still changed😆
Amazing didatics, finally understood the intuition behind it, thanks!
P for (player) so you are the P-value, to win the game we must reject the Ho(hoe) we lose if P-value gets eaten , the hoe must get eaten so it goes like this
P-value > alpha we fail to reject Ho
P-value < alpha we reject Ho
Why he takes a random number 0.05 and then uses it to make calculations for a critical decision? Where is this alpha should be coming from?
I watched like 20 different videos on p-values for weeks and none of them made sense to me. I felt stupid. Then I watched this and it made perfect sense.....
His videos never disappoint! No matter how many times I read my course's textbook I couldn't get it.....
This has helped me a lot !! Thank you 😊
Khan Academy pulling me through yet another exam
Not understood even after many videos, still confusing...
How we can reject null hypothesis if it getting p value below threshold value...that is the point confusing a lot
the p value is the probability of your statistics on the sample when you assume that the null hypothesis is true. It means that even when you are inclined to believe that the new feature in your website has no effect, yet you observe and see something extremely unlikely (it strays very far off the standard deviation), so your hypothesis must be wrong.
Think of your situation right now: you don't believe that this video makes any sense. You think that this video doesn't help people understand p-values. Yet when you look at the comments and see a lot of people found the video helpful (the feedback is so overwhelmingly positive that it can't be said to happen by chance), you will have reason to believe that your initial hypothesis is wrong, and the video does help people.
The question being addressed here is: What are the chances of increasing time spend from 20 to 25 without changing anything in the website (null hypothesis)? Logically, it should be very small, right? In this case if it is less than 5% of chances, then we are confident that something happened, possibly the change in the background (2nd hypothesis).
Think of p value as probability of new data conforming or adhering to null hypothesis.
If p is low...the new data doesn't conform or adhere well to null hypothesis..and hence reject it(the null hypothesis)
If p is high..the new data conforms or adheres well to null hypothesis..and hence it cannot be rejected.
What is low or high p value: the threshold or alpha or significance level decides it
p-value gives us the probability of our sample statistic being true when our H0 is also true. now if p value > alpha then we say that "hey h0 , you are right. The probability of you being true is a possibility because you have surpassed the significance threshold. But remember that alon with the assumption that you would be true, I also assumed that my sample stat is true. So you kind of won but not entirely"
if p value
If the null hypothesis is mean = 20, shouldn't the alternative hypothesis be mean != 20, instead of mean > 20? As per my understanding the null Hypothesis and the alternative hypothesis should be opposites.
it can be not equal to, depending on what you're trying to test. if you're solely trying to find out if the minutes haven't changed you would use not equal to.
H1 can be greater than, less than, or not equal to, depending on what you are trying to test
look u are ignoring one thing that it is a fact that we took sample and then perform statics on it and we got 25 as sample mean
no it is a fact u cant change it
now again u took sample and it came out 25 or greater
again u took sample and it came out 25 or more
again
and
again
so total 4 times your sample mean came out 25 or greater now u are confused and every time you took sample it came out greater than 25 or more
so you will say i assumed it wrong that H0 is true so i reject it
now in math form
u got 4 times 25 or greater and its a fact now your boss can see results that people are spending more time on yellow website and boss is angry with you and he said you assumed it wrong that H0 is true
------------------
but being math guy you did not believe in you boss and said let me check through math if i am wrong or right
so you use p-value (x>=25| H0 true) and it showed u 0.003
this piece of math tell me that------- if u have assumed H0 to be true then probability of getting 25 should be 0.003
now u are shocked that probability of getting 25 was 0.003 and i assumed H0 to be true
calculations are assumptions and it get checked by reality fact and fact was that 25 or greater smaple mean of many samples 4 or 5 samples
and there u made a mistake things don't happen by assuming things happen by fact
and fact is that all your values are above 25 or equal to it
so u slap your face and say oooo GOD i assumed it wrong and i reject it
having probabilty of 25 or greater with h0 was low
but in
reality
h0 was not low due to which we got 25 sample mean time after time
---------------------------------------------------
for non mathematics explanation more
suppose CIA and MI6 told u that if you go to Afghanistan your portability of coming back is 0.003 given that there are Taliban in Afghanistan so you decided to send your wife to Afghanistan and she came back and then you send her again and she again came back after 10 times she again came back
so u rejected that CIA MI6 report because reality is different then what MI6 CIA assumed
you've done it again. Thank you for the clarification!
how do you arrive at a significance value , is it arbitrary , is it based on experience ?
Make it make sense
So we have a sample whose probability of occuring is 0.03 given that Ho is true.
It can't be usual getting a case with such a low probability but we are having that case...thats why we reject Ho.
Is this what you are trying to say?
That’s exactly it
how many time that case happen????
Super clear explanation
how do we find p value
Holy crap, you're still doing this?
Props
I wish that yellow dot was a Pac-Man... I feel like it would help me learn good
I have no clue what you said, but I appreciate the attempt.
Excellent, very clear and informative, can you cover confidence intervals (CI) pls, thanks!
so touching for an excellent video
Thank you very much, that's super helpful 👌
Great video, explanantion is super clear
Amazing, thanks !
How do you determine the significance level?
Very grateful! Thank you!
Really, big thanks
Will the Khan Academy app have a whole section dedicated to English, and Grammmar
Claymagic 101 they do have a section dedicated to Grammar
Thanks for the awesome video! Just wondering which tools did you use to draw and record this?
I suppose that in order to let the people have a better understanding of the video, you should say the p value explanation at the beginning of the video, saying that the p value means that assuming the H0 is true, what is the probability of mean.
Thanks ❤
Why do we change the standard deviation if it’s already given to us
In other words p value shows the similarity of means between a sample and the whole population??
If the alternative hypothesis was changed to u
You would still reject null hypothesis, if your sample sample mean is 25. Rejecting null doesn't mean you are accepting alternative hypothesis,
And how to use the value of sample size ? He did not use it!
I am wrecking my brain but still cant get why cannot we just compare mean values before and after the change o0
Great explanation!
Thank you!
@ 2:07 "hey if we assume that the null hypothesis is true .... if that probability is < 5% then we reject the Ho"
I simply don't get the language : i.e., how would that statement enhance, or explain anything more than, let's say if we said : "if the probably is
Reject the Nullos!!
It helped me a lot🙏🏽
What if theres an oppisite effect, in this case the yellow background backfired and less people visited the site? would that be the null or postive hypothosis?
After many, many videos talking about statistics and p-value I still don't get it. I simply cannot visualize it in my head (yet). Robotics is waaaay easier than this.
Well explained. Thank you.
Thanks
check the null hypothesis again
Sal (or anyone viewing these comments), what would your steps be if you made an important math discovery?
Stat finally in 2018! Now please do real analysis next!
Thanks a lot
how do you set up the p value step when the alt hypothesis is "does not equal" instead of greater than/less than?
Defination of p value read it
Are u sure the formation of Ho and Ha were corrected ? The statement should be Ho = 20 ，Ha not equal to 20. Or Ho equal and greater 20, Ha is 20.
Thanks sir
If you’re given an illustration and the sample mean is not given what do you do ?
How the pointer writes, what's the input device? Please guide
Is P value the number that a program gives you after running a two tailed test?
Great, I can always count on you ;)
Thanks so much!
Sal can you please cover the topics of modular arithmetic and matrices more thoroughly? Thanks
good teacher 👍🏻
Thank you
Hello sir !
Im trying to write the report of my data analysis. If there is a difference in weight gain between two groups (male and female) but the difference is not significant. Is it still worth mentioning it in this way " there is a difference in the weight gain between males and females but the result is not statistically significant "
It’s a type one or two error
It’s a type one or two error
So basically in order to prove your hypothesis (alternative hypothesis), you have to disprove the null hypothesis (the opposite hypothesis).