# P-values and significance tests | AP Statistics | Khan Academy ## 50 thoughts on “P-values and significance tests | AP Statistics | Khan Academy”

1. Pishoy Gobran says:

Thank u

2. David says:

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

3. Marwan El-sangary says:

Thank you

4. KingNabilion says:

Cool

5. KingNabilion says:

First!!

6. CHRISTABEL ASHUN says:

don't understand still

7. CHRISTABEL ASHUN says:

okay

8. Daniel Wardak says:

What if your new sample mean is < 20?
Surely the alternate hypothesis is Ha: u =/= 20 minutes.

9. Zk'es Videos says:

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

10. Nitecore Dj says:

Lol

11. Vedant Sahu says:

Thank you sir you have changed my life

12. Elizabeth GR says:

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

13. Claymagic 101 says:

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

14. Claymagic 101 says:

.

15. Diamond Laser says:

What website do they use to make their videos?

16. Irzan Khan says:

xD

17. steamroller82 says:

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!

18. DunnyDunDidIt says:

19. Arnav Negi says:

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

20. Allan Pui says:

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.

21. Ara Aboolian says:

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

22. Huyền Trường says:

82

23. Ankur Chaulagain says:

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

24. Pavel Koryakin says:

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

25. Rafael Pontes says:

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

26. Nirman Kodithuwakku says:

great. thanks

27. TheTvkkk says:

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.

28. Jussien Fleurinor says:

Great Job!

29. Sara T says:

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

30. Jeremiah Farr says:

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.

31. Harishbabu K.S says:

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

32. germanottass says:

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??

33. THEODOROPOULOS DIMITRIS says:

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

34. Krishna Kumar says:

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.

35. Muffinduchocolate says:

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.

Thank you for you time!

36. Lakshay Chhabra says:

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.

37. trish says:

so how do we get p values-

38. Devanshu Sachdev says:

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?

39. Hanna Beverly says:

how do we find p value

40. Vamsi Mohan Ramineedi says:

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.

41. Mohit Singh says:

U sounds like bane in dark Knight Rises

42. 8932 yoi4j24 says:

Does H_0 include all the Normality assumptions on the data?

43. Romil Mishra says:

Why Ha is u>20?
Can Ha be u is not equal to 20

44. Joshua Kölzer says:

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.

45. Faith Barbie says:

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

46. Krysten Awuradwoa says:

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

47. mario mariousz says:

is it always 0.05?

48. João Araújo says:

Thank you

49. natalie says:

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

50. Julio Santiago says:

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