great video and very informative! would love my AP Stats students to be able to see this too. any timeline on when it will be added to https://www.khanacademy.org/math/ap-statistics ? Thanks!

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.

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.

Khan is good, but the idea of a significance level is being phased out of statistics. Many stats classes no longer teach that concept and some teachers will mark you incorrect if you use a significance level.

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

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??

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.

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!

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.

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.

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.

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

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

Thank u

Excellent, very clear and informative, can you cover confidence intervals (CI) pls, thanks!

Thank you

Cool

First!!

don't understand still

okay

What if your new sample mean is < 20?

Surely the alternate hypothesis is Ha: u =/= 20 minutes.

if 1+1=2 and 2+2=4. but why 2+2=3.didn't 3.I think I try to understand my word.PLZ GIVE ME AMSWER

Lol

Thank you sir you have changed my life

Sal (or anyone viewing these comments), what would your steps be if you made an important math discovery?

Will the Khan Academy app have a whole section dedicated to English, and Grammmar

.

What website do they use to make their videos?

xD

great video and very informative! would love my AP Stats students to be able to see this too. any timeline on when it will be added to https://www.khanacademy.org/math/ap-statistics ? Thanks!

Dude sounds like djvlad

Sal can you please cover the topics of modular arithmetic and matrices more thoroughly? Thanks

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.

can't believe that I finally got it! A huge thank you! This made my day 😀

82

Stat finally in 2018! Now please do real analysis next!

And how to use the value of sample size ? He did not use it!

What if u < 20? Is that an alternative hypothesis to the alternative hypothesis? I think there's something wrong here…

great. thanks

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.

Great Job!

if p value is low ==> the null must go!

if p value is high ==> the null's your guy!

Khan is good, but the idea of a significance level is being phased out of statistics. Many stats classes no longer teach that concept and some teachers will mark you incorrect if you use a significance level.

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

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??

In other words p value shows the similarity of means between a sample and the whole population??

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.

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!

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.

so how do we get p values-

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?

how do we find p value

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.

U sounds like bane in dark Knight Rises

Does H_0 include all the Normality assumptions on the data?

Why Ha is u>20?

Can Ha be u is not equal to 20

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.

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

If you’re given an illustration and the sample mean is not given what do you do ?

is it always 0.05?

Thank you

so say if p value is 0.001 does that mean rejecting a true null hypothesis is 0.001%?

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