You are very welcome! I'm glad to help out. I made these videos primarily with my own students in mind, but I very much like the fact that others around the world find them helpful as well. All the best on your exam.
Your videos are so well structured, they help me learn so much more than the videos my textbook supplies. Thank you for the great videos, I'll definitely recommend my friends who are taking stats next semester to your page!
I was looking over my notes and through my textbook trying to figure out this stuff for hours. I watched this video and your video on the Rejection Region and I understand everything. Thank you so much!
Thanks for the feedback. In that two-sided hypothesis I write that the p-value is 2 x P(Z >= |1.53|). This works in general for two-sided Z tests -- the p-value is double the area to the right of the absolute value of the test statistic. I don't feel that "P-value= Pl (left P-value) + Pr (right P-value)" would be clear at all. A p-value has a very specific meaning in statistics (not all areas are p-values). "P-value= Pl (left P-value) + Pr (right P-value)" doesn't really make sense. Cheers.
Great job!! One remark: in the last hypothesis z>= | 1.53 | must be | z | >=1.53 and it would be more clear if P-value= Pl (left P-value) + Pr (right P-value).
The way you explain these concepts is astonishing . You speak clearly with thoughtful words and simple yet informative demonstration I'm so very glad that I found you and will definitely recommend you to my friends who are struggling with statistics as well Thank you kindly good sir
4:04 , will wen not find probability of z being less than -1.53 in this case?, so like shade the far left of the graph instead of what we have done here?
A good video, but please do correct the typo about the absolute value mentioned by several people earlier: writing |1.53| is nonsensical, since that's just 1.53. The point is that in a two-tailed situation we want to consider |z| -- the absolute value of **Z**, of the statistic, and want that absolute value to be large enough to reject Ho.
It's not a typo, it's not a mistake, and there is nothing to correct. For a z test, the p-value is, in general, double the area to the right of the absolute value of the test statistic under the standard normal curve. Sure, we can write that in different ways if we want but this way is reasonable and compact. What was the value of the test statistic in that example? 1.53. What is the p-value? Double the area to the right of |1.53|. |1.53| is of course 1.53, as we obviously both know, but it's hardly "nonsensical" to write the absolute value of a quantity that happens to be positive. We're interested in that quantity's absolute value. That quantity happens to be positive in this particular instance. "we want to consider |z| -- the absolute value of **Z**, of the statistic," And what, pray tell, was the value of z in that example?
thank you JB statistics professionally I am pursuing engineering and we were introduced to statistics we were not familiar with but because of you cleared my concept and all went good. thank you 😊
Thanks for all your help :) I've been struggling a little with my AP Statistics class but now thanks to your videos I'm getting better at it! If I were to have a suggestion to you, I would suggest that you also include a calculator portion for your videos, it will be very helpful! Thanks, and have a Merry Christmas :D
I spent like 5 hours trying to understand this chapter from the prof notes and it was useless. Finally I found those videos that made everything clear.. thank you for saving our asses
Hi! I loved this video and it was very concise! I was just wondering for the last example at around 9:05 , why didnt we divide the significance level by 2? Isn't alpha basically the same thing as the confidence level, so if we do a two tailed test, wouldn't alpha be split amongst the two tails so it would be 0.025? Im just a bit confused, thanks!
+HerdingDogRescuer There are different table formats. Your version of the table (apparently) gives you the area between 0 and the z value that you look up. So if you look up 1.53, your table tells you that the area between 0 and 1.53 is 0.4370. Since the area to the right of 0 is 0.5, the area to the right of 1.53 must be 0.5 - 0.4370 = 0.063.
@@jbstatistics Thanks sir. From this lecture, I wrote the definition of P-value as: The area under the standard normal PDF curve (probability) corresponding to calculated z-value. Is this right?
around from 3:30, the z value is 1.53, and you said we will REJECT the NULL HYPOTHESIS if the p-value is behind 1.53, i.e., the bigger area, you shaded..how is it possible, as you already said that if we are precisely at 0, we will not reject the Null Hypothesis as it will be a standard Normal Distribution, and 0 is the subset of Z
I'm having trouble following your comment. I definitely didn't say anything like "you said we will REJECT the NULL HYPOTHESIS if the p-value is behind 1.53". I explain the reason we double the tail area in two-sided Z tests, to the best of my abilities, starting at 5:10 or so.
jbstatistics my second doubt was just a question on the mathematical notation you used, I got what you did there. I'm still feeling problem for the first doubt I had.. I'm not able to explain it properly, but till where I understood your videos, if we accept the area behind 1.53, we don't reject the null hypothesis, because it's in the region of the standard normal distribution, (0
Great video, nicely explained but just one question. Why did you prefer p-value over the rejection region approach? Isn't it the same (but doing it differently)? Because the p-value could still be really close to the critical values?
Yes, the p-value can be just a little over the cut-off or a little less than the cut-off. This means that two completely different results can be obtained with a slight variation in the p-value. I'm sure he has his reasons to prefer this approach, I wish he'd explained it to us :(
When z = 1.53, Ha: u < u0, and the p-value = 0.937 in the video. But z = 1.53 means sample u is bigger than u0. If the Ha establishes, the u is smaller than u0. It looks impossible. With Ha: u < u0, something wrong?
I do have many videos in which I work through examples, including for this topic (ruclips.net/video/Xi33dGcZCA0/видео.html). I'll get back to video production soon, and many of the videos will have examples included.
How is this different from the rejection region approach exactly? In rejection region, we basically calculate cutoff value of Z from the significance probability alpha, and then check if our obtained Xbar is outside that cutoff or not. P value is just calculating probability of the obtained Xbar, and checking if that is less than the significant probability. So the exact same process, just the other way around.
If you’re carrying out a test at a fixed level of significance, and completing ignoring the p-value other than the binary less than or equal to / not less than or equal to, then the methods are exactly the same. Many argue, as I do, that that’s a silly way to carry out a test in the vast majority of practical situations. In most situations it’s far better to report the p-value and let the reader make up their own mind.
@@jbstatistics Yup got it. The P value gives more information to the reader of the research instead of taking the researcher's decision as gospel. Your preferred approach makes a lot of sense.
You mentioned something about a text, perhaps textbook in your videos, where can I find it? In case you have no lecture notes accompanying the videos, can you recommend some textbook? And now concerning the video, this p-value stuff was quite a hot topic due to the Higgs experiments at CERN. Back then 5 sigma was reported, so it should be something like, measuring the mass many times and comparing it to the theoretical value, thereby computing the z score and the p value. In general how would you get your mean \mu in a real experiment. Perhaps you always assume some value, after all we are testing the null hypothesis.
The text that I refer to is the free pdf text that I supply to my students. I may very well make it available at some point. I have no interest in trying to sell yet another $100+ stats text. When I get a few more details completed, I may make it more widely available. (Possibly having the relevant sections posted with the videos, or something to that effect.) I have only a passing familiarity with CERN and the Higgs boson, etc., so I may possibly be a bit off on this next bit. But I imagine that they have some theoretical value based on the assumption that it did not exist, then the resulting data was 5 sigmas out (5+ standard deviations away from the theoretical mean, assuming the Higgs boson did not exist). This would be a highly unlikely event if the Higgs boson did not exist, thereby giving strong evidence of its existence. As to how they figure out the theoretical value assuming it does not exist, that's far beyond my physics competence level. Cheers.
jbstatistics Well the propbability for producing Higgs boson is calculated from a QM amplitude. QM is a superset of probability theory, where the probability for a certain event to happen is given by the mod-square of a complex quantity. But how this is exactly done requires knowledge in QFT. Setting up the experiment itself is a multi billion euro initiative. Unfortunately (actually thank god) I am not an experimentalist so I can't comment on this topic.
JB, how can say I thank you for this video!!!. You are indeed a TEACHER I've always struggled with how to compute this you made this so simple and explicit I could do this with E-A-S-E! I have simply made your video my webpage.....it's so explicit.....thank you! But do you happen to have videos on interpreting regression data using Stata?
Hi Ngozi. You are very welcome, and thank you for the compliments! I'm glad to be of help. I don't currently have any videos using Stata. I do have some videos on simple linear regression, but none on multiple regression (yet). All the best!
pnorm(x) yields the area to the left of x under the standard normal curve. So, in the example in this video, where the test statistic is z = 1.53: For a left tailed test (H_a: mu < mu_0): pnorm(1.53) yields the p-value. For a right tailed test (H_a: mu > mu_0): 1-pnorm(1.53) yields the p-value. For a two-tailed test (H_a: mu != mu_0): (1-pnorm(1.53))*2 yields the p-value.
Hi Can you tell me what is the interpretation of a two sided test as you did in this video? Does it mean that if we reject H0 of mu=10 it means we will not expect 10 to be within the CI for alpha=0.05 in a 2 sided test?
I watched three minutes and it suddenly clicked, thank you! Also If you're thinking about doing another revised version for any reason, get rid of the Comic Sans xox
now exactly how did you get that value for Z of 1.53? would it be something that is a given in a test question or problem? or is it something that needs to be calculated.....
I just pulled that number out of thin air for the example. The value of Z might be given in a problem, or you might have to calculate it with the formula.
Just imagine he used sample mean (X bar) - hypothesized mean value (Pop mean naught) / (true Standard deviation/square root of the sample number n) to arrive at the Z stat.
you are right. i don't get JB's responses to this same question asked by several people above. |1.53| is just 1.53, which is nonsensical. the whole point is that we want to look at the absolute value of Z, and want **THAT** to be large enough before we can reject Ho.
I could not find a video about 2 tail hypothesis testing so I will post my question here :) what standard deviation should I use when doing a hypothesis test ? the standard deviation of my population or my sample ?! I am really confused Thanks a lot
If you wish to carry out a hypothesis test on the population mean, and you (somehow) had access to the population standard deviation, you would use that in the test statistic. But the population standard deviation is almost never known, so we almost always use the sample standard deviation.
The alpha value is the error rate of making the wrong decision. If we changed the alpha value in the video to be 0.01, p would not be less than alpha and we would accept the null hypothesis, but we still have strong evidence against it and a more stringent error rate (i.e. 0.01).
It's the same conclusion if we are carrying out a test at a fixed alpha level, yes. But we're not always carrying out a test at a fixed alpha level, for reasons I discuss elsewhere (e.g. reaching the exact same conclusions for a p-value of 0.04999 and 0.000000000000000000000000000000002 is silly). Reporting the p-value is informative.
This didnt answer my question. When questions asking us to construct one-sided hypo testing, we are never given z, we are given the level of significance. I wanted to know how to find z given the the level of significance e.g 5 percent for a one-sided hypo testing.
It is so nicely explained that my dying words to my grandchildren is to learn stats from your channel.
I hope that, wherever you are, your life is going great. You have no idea how helpful your videos are. Thank you so much for making them!
You are very welcome! I'm glad to help out. I made these videos primarily with my own students in mind, but I very much like the fact that others around the world find them helpful as well. All the best on your exam.
Thank you so much my friend. Your lectures have been of a great help to me. Love and Regards from India :)
I love the way you structure your video sequences. Very well thought out. Cheers, man.
Thanks Gabriel, I very much appreciate the compliment and feedback. Cheers.
Your videos are so well structured, they help me learn so much more than the videos my textbook supplies. Thank you for the great videos, I'll definitely recommend my friends who are taking stats next semester to your page!
+LSUfan4life97 You're very welcome, and thanks for the compliments! Go Tigers!
Thanks, Professor for making these concepts understandable. This most certainly helped.
you are the best! I love the format, I love how clear you explain everything, I also love your voice!
I was looking over my notes and through my textbook trying to figure out this stuff for hours. I watched this video and your video on the Rejection Region and I understand everything. Thank you so much!
Thanks for the feedback. In that two-sided hypothesis I write that the p-value is 2 x P(Z >= |1.53|). This works in general for two-sided Z tests -- the p-value is double the area to the right of the absolute value of the test statistic.
I don't feel that "P-value= Pl (left P-value) + Pr (right P-value)" would be clear at all. A p-value has a very specific meaning in statistics (not all areas are p-values). "P-value= Pl (left P-value) + Pr (right P-value)" doesn't really make sense. Cheers.
fair enough.
You explained all what I didn't understand. Thank you!! It was the best video I've ever found in youtube about that subject.
Great job!! One remark: in the last hypothesis z>= | 1.53 | must be | z | >=1.53 and it would be more clear if P-value= Pl (left P-value) + Pr (right P-value).
The way you explain these concepts is astonishing . You speak clearly with thoughtful words and simple yet informative demonstration
I'm so very glad that I found you and will definitely recommend you to my friends who are struggling with statistics as well
Thank you kindly good sir
Thank you so much for the very kind words!
4:04 , will wen not find probability of z being less than -1.53 in this case?, so like shade the far left of the graph instead of what we have done here?
I have the same question too
You're welcome! I'm glad you found it useful.
Thanks oumawi, I'm glad you found this helpful.
i had doubt in this lessons and now i'm ok with your very good explanation.
I'm glad to be of help!
A good video, but please do correct the typo about the absolute value mentioned by several people earlier: writing |1.53| is nonsensical, since that's just 1.53. The point is that in a two-tailed situation we want to consider |z| -- the absolute value of **Z**, of the statistic, and want that absolute value to be large enough to reject Ho.
It's not a typo, it's not a mistake, and there is nothing to correct. For a z test, the p-value is, in general, double the area to the right of the absolute value of the test statistic under the standard normal curve. Sure, we can write that in different ways if we want but this way is reasonable and compact. What was the value of the test statistic in that example? 1.53. What is the p-value? Double the area to the right of |1.53|. |1.53| is of course 1.53, as we obviously both know, but it's hardly "nonsensical" to write the absolute value of a quantity that happens to be positive. We're interested in that quantity's absolute value. That quantity happens to be positive in this particular instance.
"we want to consider |z| -- the absolute value of **Z**, of the statistic,"
And what, pray tell, was the value of z in that example?
thank you JB statistics professionally I am pursuing engineering and we were introduced to statistics we were not familiar with but because of you cleared my concept and all went good. thank you 😊
You are very welcome. I'm glad to be of help!
Thanks for all your help :) I've been struggling a little with my AP Statistics class but now thanks to your videos I'm getting better at it! If I were to have a suggestion to you, I would suggest that you also include a calculator portion for your videos, it will be very helpful! Thanks, and have a Merry Christmas :D
I spent like 5 hours trying to understand this chapter from the prof notes and it was useless. Finally I found those videos that made everything clear.. thank you for saving our asses
Hi! I loved this video and it was very concise!
I was just wondering for the last example at around 9:05 , why didnt we divide the significance level by 2? Isn't alpha basically the same thing as the confidence level, so if we do a two tailed test, wouldn't alpha be split amongst the two tails so it would be 0.025? Im just a bit confused, thanks!
very very helpful...was so stressed about my online summer stats course and this video helped me so much... thank you!!
JB You lost me when you said 0.063 is on a table. I looked on my z table for 1.53 and got 0.4370. What table are you speaking of?
+HerdingDogRescuer There are different table formats. Your version of the table (apparently) gives you the area between 0 and the z value that you look up. So if you look up 1.53, your table tells you that the area between 0 and 1.53 is 0.4370. Since the area to the right of 0 is 0.5, the area to the right of 1.53 must be 0.5 - 0.4370 = 0.063.
jbstatistics Thank you!
Dude, I love your videos. You're a life saver!
3:27 This is a case of left tailed test. So critical value should be negative,shouldn't?
There is no critical value given there. The value of the test statistic is 1.53. The value of the z test statistic can be anything.
@@jbstatistics Thanks sir. From this lecture, I wrote the definition of P-value as: The area under the standard normal PDF curve (probability) corresponding to calculated z-value.
Is this right?
You're welcome! I'm glad to be of help.
around from 3:30, the z value is 1.53, and you said we will REJECT the NULL HYPOTHESIS if the p-value is behind 1.53, i.e., the bigger area, you shaded..how is it possible, as you already said that if we are precisely at 0, we will not reject the Null Hypothesis as it will be a standard Normal Distribution, and 0 is the subset of Z
I'm having trouble following your comment. I definitely didn't say anything like "you said we will REJECT the NULL HYPOTHESIS if the p-value is behind 1.53".
I explain the reason we double the tail area in two-sided Z tests, to the best of my abilities, starting at 5:10 or so.
jbstatistics my second doubt was just a question on the mathematical notation you used, I got what you did there.
I'm still feeling problem for the first doubt I had.. I'm not able to explain it properly, but till where I understood your videos, if we accept the area behind 1.53, we don't reject the null hypothesis, because it's in the region of the standard normal distribution, (0
Great video, nicely explained but just one question.
Why did you prefer p-value over the rejection region approach? Isn't it the same (but doing it differently)?
Because the p-value could still be really close to the critical values?
Yes, the p-value can be just a little over the cut-off or a little less than the cut-off. This means that two completely different results can be obtained with a slight variation in the p-value. I'm sure he has his reasons to prefer this approach, I wish he'd explained it to us :(
Can you use any standard deviation? Population or sample? In certain other lecture videos, they use sample standard deviation the same way.
P(|z| >= 1.53) seems more natural since z= < -1.53 -> -z >= 1.53.
That won't work if the value of the test statistic is negative.
When z = 1.53, Ha: u < u0, and the p-value = 0.937 in the video. But z = 1.53 means sample u is bigger than u0. If the Ha establishes, the u is smaller than u0. It looks impossible. With Ha: u < u0, something wrong?
Your videos are great. Thank you so much for explaining so well. Would it be possible to add more examples and applications ?
I do have many videos in which I work through examples, including for this topic (ruclips.net/video/Xi33dGcZCA0/видео.html). I'll get back to video production soon, and many of the videos will have examples included.
Hi there, thank you for the great video. What do I do if my z= 8.94??
JB YOU'RE A BEAST!! SO GOOD
Thanks again!
Thanks, it was a very helpful explanation of what a p-value actually is!
You mention getting the P-value from a standard z table, or from software. Do you know the excel formula to obtain that number?
How is this different from the rejection region approach exactly? In rejection region, we basically calculate cutoff value of Z from the significance probability alpha, and then check if our obtained Xbar is outside that cutoff or not. P value is just calculating probability of the obtained Xbar, and checking if that is less than the significant probability. So the exact same process, just the other way around.
If you’re carrying out a test at a fixed level of significance, and completing ignoring the p-value other than the binary less than or equal to / not less than or equal to, then the methods are exactly the same. Many argue, as I do, that that’s a silly way to carry out a test in the vast majority of practical situations. In most situations it’s far better to report the p-value and let the reader make up their own mind.
@@jbstatistics Yup got it. The P value gives more information to the reader of the research instead of taking the researcher's decision as gospel. Your preferred approach makes a lot of sense.
Your videos are the best!
Thanks!
You mentioned something about a text, perhaps textbook in your videos, where can I find it? In case you have no lecture notes accompanying the videos, can you recommend some textbook? And now concerning the video, this p-value stuff was quite a hot topic due to the Higgs experiments at CERN. Back then 5 sigma was reported, so it should be something like, measuring the mass many times and comparing it to the theoretical value, thereby computing the z score and the p value. In general how would you get your mean \mu in a real experiment. Perhaps you always assume some value, after all we are testing the null hypothesis.
The text that I refer to is the free pdf text that I supply to my students. I may very well make it available at some point. I have no interest in trying to sell yet another $100+ stats text. When I get a few more details completed, I may make it more widely available. (Possibly having the relevant sections posted with the videos, or something to that effect.)
I have only a passing familiarity with CERN and the Higgs boson, etc., so I may possibly be a bit off on this next bit. But I imagine that they have some theoretical value based on the assumption that it did not exist, then the resulting data was 5 sigmas out (5+ standard deviations away from the theoretical mean, assuming the Higgs boson did not exist). This would be a highly unlikely event if the Higgs boson did not exist, thereby giving strong evidence of its existence. As to how they figure out the theoretical value assuming it does not exist, that's far beyond my physics competence level. Cheers.
jbstatistics
Well the propbability for producing Higgs boson is calculated from a QM amplitude. QM is a superset of probability theory, where the probability for a certain event to happen is given by the mod-square of a complex quantity. But how this is exactly done requires knowledge in QFT. Setting up the experiment itself is a multi billion euro initiative. Unfortunately (actually thank god) I am not an experimentalist so I can't comment on this topic.
JB, how can say I thank you for this video!!!. You are indeed a TEACHER I've always struggled with how to compute this you made this so simple and explicit I could do this with E-A-S-E! I have simply made your video my webpage.....it's so explicit.....thank you! But do you happen to have videos on interpreting regression data using Stata?
Hi Ngozi. You are very welcome, and thank you for the compliments! I'm glad to be of help. I don't currently have any videos using Stata. I do have some videos on simple linear regression, but none on multiple regression (yet). All the best!
Could you please tell me what function do you type in R in order to calculate the p-value in the examples?
Thank you!
pnorm(x) yields the area to the left of x under the standard normal curve. So, in the example in this video, where the test statistic is z = 1.53:
For a left tailed test (H_a: mu < mu_0): pnorm(1.53) yields the p-value.
For a right tailed test (H_a: mu > mu_0): 1-pnorm(1.53) yields the p-value.
For a two-tailed test (H_a: mu != mu_0): (1-pnorm(1.53))*2 yields the p-value.
@@jbstatistics Thanks!
shouldn't we divide alpha by 2 in last example because it is two sided?
Hi Can you tell me what is the interpretation of a two sided test as you did in this video? Does it mean that if we reject H0 of mu=10 it means we will not expect 10 to be within the CI for alpha=0.05 in a 2 sided test?
I watched three minutes and it suddenly clicked, thank you! Also If you're thinking about doing another revised version for any reason, get rid of the Comic Sans xox
now exactly how did you get that value for Z of 1.53? would it be something that is a given in a test question or problem? or is it something that needs to be calculated.....
I just pulled that number out of thin air for the example. The value of Z might be given in a problem, or you might have to calculate it with the formula.
Thanx Sir, awesome and so clear and easy to grab explanation, I just wanted to ask from where the value of Z=-2.12 came at 8.36 timing???
That was just an example of a possible value of the Z test statistic.
jbstatistics : oo thanx sir 👍
Just imagine he used sample mean (X bar) - hypothesized mean value (Pop mean naught) / (true Standard deviation/square root of the sample number n) to arrive at the Z stat.
|1.53| is always 1.53. This makes no sense. Did you mean P(|z| >= 1.53)?
you are right. i don't get JB's responses to this same question asked by several people above. |1.53| is just 1.53, which is nonsensical. the whole point is that we want to look at the absolute value of Z, and want **THAT** to be large enough before we can reject Ho.
I could not find a video about 2 tail hypothesis testing so I will post my question here :)
what standard deviation should I use when doing a hypothesis test ? the standard deviation of my population or my sample ?! I am really confused
Thanks a lot
If you wish to carry out a hypothesis test on the population mean, and you (somehow) had access to the population standard deviation, you would use that in the test statistic. But the population standard deviation is almost never known, so we almost always use the sample standard deviation.
I'm too dumb for this
lmaooo
I didn't understand how to find the p-value?
The alpha value is the error rate of making the wrong decision. If we changed the alpha value in the video to be 0.01, p would not be less than alpha and we would accept the null hypothesis, but we still have strong evidence against it and a more stringent error rate (i.e. 0.01).
Isn't it same as rejection region approach?
It's the same conclusion if we are carrying out a test at a fixed alpha level, yes. But we're not always carrying out a test at a fixed alpha level, for reasons I discuss elsewhere (e.g. reaching the exact same conclusions for a p-value of 0.04999 and 0.000000000000000000000000000000002 is silly). Reporting the p-value is informative.
You're welcome!
This didnt answer my question. When questions asking us to construct one-sided hypo testing, we are never given z, we are given the level of significance. I wanted to know how to find z given the the level of significance e.g 5 percent for a one-sided hypo testing.
I'm a bit stuck at the a-level of significance part. I don't understand why p-value must be smaller than a.
Its in the rejection area
thank you so much this is very helpfull
Can I have those slides of your video,It would be very helpful :)
Thanks for the suggestion. I'll make them available at some point, but it may take me some time to get to it.
Ok ,Thanks man :)
EXCELLENT SIR
Thanks!
Thank u JB