I've been watching Khan Academy since I was high school back in 2012. I'm now in my master's program in 2024 at Columbia for epidemiology and Khan Academy is still out here saving my life during finals week. Thank you so much for being the best educational resource over the years.
Except the Gaussian confidence intervals are wrong to use for binomial distributions (like the A vs. B candidates here). You need a binomial proportion confidence interval (like the Wilson score interval or such). Differences are much more apparent near 0 and 1 (so, when one of the candidates has a near-certain win or loss).
I'm in a T30 MBA program and referencing khan academy videos because the material in these videos is easier to digest (better taught). So please, keep up the good work! And donate to this awesome organization!
I can't begin to tell you how much I appreciate the effort and simplicity you put into this video. Thank you for all the hard work!!!! I'm currently passing my class with an A and it's all because of this channel.
Thank you so much! This last week of stats kicked my butt and I thought this was going to do the same. You really simplified this in a manner that was easy to understand.
Phenomenal video. I appreciate so much your detail and logic. I haven't taken Statistics in over 20 years and was struggling with this principle in my refresher. Your explanation really made this concept simple. I look forward to learning more
The margin of Error is 2* SE which then is 2*0.05 = 0.1 so 0.54 + 0.1, 0.54 - 0.1 = 0.44 to 0.64 The margin of Error = (ME) is the amount added/subtracted in a confident interval - and it depends on the sample size; and you, at times, can decide which margin of error you desire for your project, let say.- i.e. 1%, 5%.. Standard Error = (SE) is the standard deviation of the sample if we could take many of the same samples of the same size and combine the results to get one value p. Standard Deviation = (s) of the sample (not population) is the standard deviation of the individual values in the sample, instead a bunch of sample like bootstrap or randomization mentioned above for the SE.
Thank you so much for this channel. You are doing fundamental work for equality; knowledge available for everyone. It's priceless. Trying to donate as soon as possible! Thank you for your hard work!
It would be nice if you state the Z critical value used in the 95% confidence, then it wouldn't be as confusing as for where you're getting the Confidence interval from.
The issue that I have with this video is, after thoroughly over explaining population, sample, sample proportion, sample deviation of sample proportion and sampling distribution, he didn't have enough space to do a written explanation on how he got his Confidence Intervals and Margin of Error; which is ironic, being a part of the videos title and the only reason I clicked play ;)
@@danielinostroza7122 every course is different but one piece of advice that works across the board is pay attention and ask questions. i fell behind for part of the semester because i didn’t pay attention for two classes and spent the rest of the time playing catch up
@@joshbux99 Would you say the course requires self-motivation and self-accountability? Interestingly, this semester went really well for me because I held myself accountable to do my work, which was something in-person school didn't require me to do. I've found that online school has had me make myself accountable for the schoolwork I need to do more than any previous school year
6:12, thank you a lot! now if you sample the whole population or have huge samples the whole distribution could look totally different. not standard distributed
Hi @Khan Academy, heads up: my text book actually explicitly guards against interpreting CI's with the statement "There's is a 95% probability that the population parameter is within the interval".
Yeah, this is a clear mistake. The confidence interval must be treated as itself a random variable. 95% confidence level means only that 95 confidence intervals out of 100 generated from repeated experiments will contain the population parameter. Once a confidence interval of a specific experiment is generated, the population parameter either exists within it or it doesn't. Probabilistic thinking at that point is no longer valid.
the same came to my mind, while watching it. Isn't this statement: "There's is a 95% probability that the population parameter is within the interval" the interpretation of bayesian inference (which we do not have here)? In terms of frequentists we would say: "the ensemble of all confidence intervals (calculated based on samples) would capture population parameter in 95% # of cases" which is not the same. We in fact do not know this "interval" that would cover population parameter with 95% probability.
I believe there is an inaccuracy @5:30 where it says that "there is a 95% probability that the population proportion p is within two standard deviations of p-hat". This is a common misconception about confidence intervals.
I love using elections for confidence interval examples. I just put my own video up about how to interpret CI's after talking with friends and family over the 2020 election.
I came to conclusion by wathing this vidoe is that "the standard deviation of entire population is analogous to standard error of sample populuation" , meaning standard error is nothing but a standard deviation of sample population
The assumptions: Each person being asked to is independent, true proportion not too close to 0 or 1. How and Why are these assumptions essential in concluding that the sample proportion follows a normal distribution?
Why the population standard deviation equation in this video is quite different than the one you showed in other videos? It doesn’t make sense. Why std=square root of p*(1-p)/n? Never see this std equation in any text book as well. Can anyone please tell me where it comes from?
The health of the bear population in a park is monitored by periodic measurements taken from anesthetized bears. A sample of the weights of such bears is available below. Use a single value to estimate the mean weight of all such bears. Find a 95% confidence interval estimate of the mean of the population of all such bear weights.
asdFRap yeah it’s annoying that they have video mixed up. You can find this on the app but can’t play it there. You have to go to the browser app and then open it in youtube.
I think it is wrong to say "There is a 95% probability that p is within 2 sd of p^". This is because p is not bound under probability, it's a fact. P is P with probability 1.
Because he was using a confidence level (CL) of 95% and the population is assumed to be normally distributed. Though confidence levels & confidence intervals are two different thing, I find it easiest to think of them together by reminding myself of what concluding statement I'm making using my sample finding. In the video's, I, the sampler, am saying : "I randomly selected (aka, sampled) 100 people from a population of 100,000 and I found that 54 of them (0.54 of the whole sample or 54% of the people sampled) prefer Candidate A. Based on that sample finding, I am 95% sure that were I to have asked the same question of every member of the population, I would have found that 54%, plus or minus 0.10, of the population preferred the same candidate as did the 100 people whom I surveyed." So, with that in mind, let's look at the math. Step 1: I got 0.54 in favor of Candidate A, so I will put 0.54 in the center of my normal distribution curve and call it the "sample mean" or "sample proportion." Step 2: Ask myself, "How many std deviations away from my sample mean - i.e., how wrong can I be - can the actual population mean be and still have my above stated conclusion still be true?" The answer to that, for a 95% confidence level, is 2 std deviations. For a 99% confidence level, it would be 3 std deviations. Step 3: Ask myself , "How far numerically is 2 std deviations from my sample mean?" To determine that, I need to know how far one std deviation is from my sample mean, and then I will multiply it by 2. Step 4: Calculate the std error. The std error that Sal calculated is the distance you must go (left or right) to get to one std deviation from your sample mean. In the video's sample, Sal calculated the std error as 0.05. Tip -> Do yourself a favor and calculate the std error assuming Sal's sample size was 55, 85, 150, & 350. That will allow you to see how the std error will increase or decrease. Step 5: Multiply the std error by 2. Why by 2? Because 2 std deviations (aka, std error's worth of distance) is how far the 95% confidence level is from the sample mean for a normally distributed population. (Can one have a not normally distributed population? Yes, but that's a different lesson & a whole new "ballgame.") Since the std error was 0.05, twice that is 0.10. Step 6: Determine Confidence Interval The confidence interval is the distance from (point A) 2 std deviations below (left of) of the sample mean to (point B) 2 std deviations above (right of) the sample mean. -> Since std error = 1 std deviation, twice the std error subtracted from the sample mean gives us "point A," which is the lower limit of the confidence interval. -> Doubling the std error and adding it to the sample mean gives US the upper limit of the confidence interval. What's 0.54 - 0.10? 0.44. What's 0.54 + 0.10? 0.64. And, voila. The confidence interval is 0.44 to 0.64. Now that you see how we calculated the confidence interval, do you know what it means, what it tells you? The confidence interval tells you how wrong the value you got as the sample mean - i.e., the percentage of people in the sample who preferred Candidate A - could possibly be. In other words, for the sample in the video, the confidence interval says: "Because I know that my sample merely estimates, rather than actually counts or measures, what share of the population actually prefers Candidate A, I know that my estimate could be off by a bit. How off? Well, by as much as 0.10, or 10 percentage points in either direction. That is to say, it's possible that anywhere from 44% to 64% of the population prefers Candidate A." Realizing that's what the confidence interval is telling you, you should also be aware of one very important thing: samples indicate what was so at the time the poll was taken. They do not indicate what will be so in the future. Thus context is critical to interpreting a poll's findings and the germanity of them given the confidence interval. For example, if Sal's poll were of the percentage of quartz found in bituminous coal deposits, the 20 point wide confidence interval may not be too big of a deal because the composition of coal deposits doesn't change much. But Sal sampled people's opinion, and people's minds change a lot. So you have to ask yourself: "Given the confidence interval is 20 points wide, does it make sense to rely on the poll's finding as a predictor of who will win the election that will occur at some time in the future? I hope the preceding discussion, long though it is, helps you understand how the confidence interval was determined and, more importantly, what a confidence interval tells you and the types of things you should think about upon seeing it and the thing that was sampled.
@@anthonybell6156 God bless you Sir! You should make school textbooks. I did my homework just by following your 6 steps and your notes at the end. I cannot thank you enough! (_)(_):::::::::::::::::::::::::::D~~~~~~~~~~
Watch some guy on the internet teach this better in 11 minutes than my stats teacher did all unit. A true hero
All stat teachers are 😢😢😢
It is easy to get distracted in a long lesson, shorter compact videos are easier to understand Dante general picture of a subject
And maybe you already had some intuition from your stats class which made this easier to get 🤭
watching a khan academy video for something you dont get crying before the assessment is due is another kind of pain
yeah..
exam in 9 hours... wish me luck
@@jackwaterman8185 lo.l
@@jackwaterman8185 Did the luck work?
watching a khan academy video DURING an online exam is a whole new level of pain Covid 19 has invented
I've been watching Khan Academy since I was high school back in 2012. I'm now in my master's program in 2024 at Columbia for epidemiology and Khan Academy is still out here saving my life during finals week. Thank you so much for being the best educational resource over the years.
Watching this just helped me pass a quiz that required a pass in order to not fail the entire unit. Thanks heaps, you're a legend!
The handwriting in this video is phenomenal
lol
bahaha! I kept thinking the same thing while watching it! lol!!
That straight line at 2:12 tho
@@andreathompson7136 Omg me too!
@@KPheeze he didn't draw that it's a tool
I love how I needed this during election season, thank you RUclips algorithm
right? same here! what a coincidence!
Except the Gaussian confidence intervals are wrong to use for binomial distributions (like the A vs. B candidates here). You need a binomial proportion confidence interval (like the Wilson score interval or such). Differences are much more apparent near 0 and 1 (so, when one of the candidates has a near-certain win or loss).
I'm in a T30 MBA program and referencing khan academy videos because the material in these videos is easier to digest (better taught). So please, keep up the good work! And donate to this awesome organization!
I can't begin to tell you how much I appreciate the effort and simplicity you put into this video. Thank you for all the hard work!!!! I'm currently passing my class with an A and it's all because of this channel.
Wow ive been doing stats for a month and you put this better than anyone I have watched.
I bet 50% of this channel's success is due to this beautifully balanced handwriting
Its insane how much better this is than my actual professor
Thank you so much! This last week of stats kicked my butt and I thought this was going to do the same. You really simplified this in a manner that was easy to understand.
Phenomenal video. I appreciate so much your detail and logic. I haven't taken Statistics in over 20 years and was struggling with this principle in my refresher. Your explanation really made this concept simple. I look forward to learning more
The margin of Error is 2* SE which then is 2*0.05 = 0.1 so 0.54 + 0.1, 0.54 - 0.1 = 0.44 to 0.64
The margin of Error = (ME) is the amount added/subtracted in a confident interval - and it depends on the sample size; and you, at times, can decide which margin of error you desire for your project, let say.- i.e. 1%, 5%..
Standard Error = (SE) is the standard deviation of the sample if we could take many of the same samples of the same size and combine the results to get one value p.
Standard Deviation = (s) of the sample (not population) is the standard deviation of the individual values in the sample, instead a bunch of sample like bootstrap or randomization mentioned above for the SE.
Thank you so much for this channel. You are doing fundamental work for equality; knowledge available for everyone. It's priceless. Trying to donate as soon as possible! Thank you for your hard work!
It would be nice if you state the Z critical value used in the 95% confidence, then it wouldn't be as confusing as for where you're getting the Confidence interval from.
The issue that I have with this video is, after thoroughly over explaining population, sample, sample proportion, sample deviation of sample proportion and sampling distribution, he didn't have enough space to do a written explanation on how he got his Confidence Intervals and Margin of Error; which is ironic, being a part of the videos title and the only reason I clicked play ;)
@Finn You do realize each segment has like 5-6 videos that explains the general concept then goes into more specific problems.. lol
@Finn What other source?
@Finn DON'T LEAVE US HANGING LIKE THAT BROTHER, GIVE LINKS TO THE PEOPLE xD xD
One year later and @Finn still hasn't given us the alternate source. The internet is still such a cruel place...
i thought i was the only one, he lost me... didnt know how he got 0.44 and 0.64, made this video pointless to me
I think we all owe our career to you Khan♥
i have my stat final tomorrow morning. i hope this video helps me pass, will update after the test
Good luck!
i passed
@@joshbux99 NICE! I may take AP Statistics next year for 2021-2022 as a Senior in High School. Any tips?
@@danielinostroza7122 every course is different but one piece of advice that works across the board is pay attention and ask questions. i fell behind for part of the semester because i didn’t pay attention for two classes and spent the rest of the time playing catch up
@@joshbux99 Would you say the course requires self-motivation and self-accountability? Interestingly, this semester went really well for me because I held myself accountable to do my work, which was something in-person school didn't require me to do. I've found that online school has had me make myself accountable for the schoolwork I need to do more than any previous school year
6:12, thank you a lot! now if you sample the whole population or have huge samples the whole distribution could look totally different. not standard distributed
Hi @Khan Academy, heads up: my text book actually explicitly guards against interpreting CI's with the statement "There's is a 95% probability that the population parameter is within the interval".
Jad Sayegh yeah, it's an interesting mistake Sal made here.
Yeah, this is a clear mistake. The confidence interval must be treated as itself a random variable. 95% confidence level means only that 95 confidence intervals out of 100 generated from repeated experiments will contain the population parameter. Once a confidence interval of a specific experiment is generated, the population parameter either exists within it or it doesn't. Probabilistic thinking at that point is no longer valid.
the same came to my mind, while watching it. Isn't this statement: "There's is a 95% probability that the population parameter is within the interval" the interpretation of bayesian inference (which we do not have here)? In terms of frequentists we would say: "the ensemble of all confidence intervals (calculated based on samples) would capture population parameter in 95% # of cases" which is not the same. We in fact do not know this "interval" that would cover population parameter with 95% probability.
Hi, I know I'm late but I have a statistics exam in a week and I don't fully understand why the statement is wrong? Could you maybe explain it?
@@evertbronstring5219 how did you do
i love your enthusiasm for maths! it keeps me interested and willing to learn more!
I want to ask why you don't need to times 1.96 which is the Z(a/2) to the margin of error?
I believe there is an inaccuracy @5:30 where it says that "there is a 95% probability that the population proportion p is within two standard deviations of p-hat". This is a common misconception about confidence intervals.
Thank you as always Khan Academy!💛
This guy is a true hero
Many are saying this is too complicated for an intro, and maybe so. With that said, I found this to be an excellent example. Great job!
Clearer than all other explanations I've watched on this. Thank you
very well simplified this basic and foundational concept, thank you!
Got all my doubts cleared about confidence interval. Thanks a ton
you a literal LIFE SAVER
I add one thing for clarification that for me personally was useful: area here is equivalent to proabability.
This is incredibly well explained!
You saved me and my career. Thanks
that helped a lot with explaing margin of errors
Such a life saver. Thank you so much
Appreciate this video and others on statistics and charts, provides a clear understanding
I love using elections for confidence interval examples. I just put my own video up about how to interpret CI's after talking with friends and family over the 2020 election.
I came to conclusion by wathing this vidoe is that "the standard deviation of entire population is analogous to standard error of sample populuation" , meaning standard error is nothing but a standard deviation of sample population
Perfect explanation. i dont need to read boring books
No matter the topic...I know I will understand something if I come here......🥲
Great video and explanation! You are helping me very much! I´m a brazilian fan.
5:22 "starts to, f*ck, feel a little bit more
Great to the point explanation. Thanks.
Great video! One doubt: what p(-p) really means?
what is the difference between margin of error and 2*Standard deviation?
Thanks!.
Thank you sir!
A true legend
Having the word problem written out first would have been better for me, so I can see the problem
Going through it this way is lost me
Excellent teaching
This is very helpful, thank you!
I'm confused...but generally Stats is confusing to me
Jen _29 you’re not alone😂
Thank you, you are a saint
The assumptions: Each person being asked to is independent, true proportion not too close to 0 or 1. How and Why are these assumptions essential in concluding that the sample proportion follows a normal distribution?
Very helpful!
so the sample population probabilities in the abscissa, whats in the ordinate then?
I had fun while learning. Thanks!
Explan are good
Why the population standard deviation equation in this video is quite different than the one you showed in other videos? It doesn’t make sense. Why std=square root of p*(1-p)/n? Never see this std equation in any text book as well. Can anyone please tell me where it comes from?
I love how he is using the trial version of the TI calc haha
Who else watching this right before the test lol
thank you
thank u vrry helpful
why did you not multiply the critical vale of z with it??
Thank you again!
Perfect! Helped me a lot
thanks bud
I hate statistics 😂
This guy is all over the place I need to make a video that streamlines the information rather than throwing out all these what if's to confuse people.
Tag me on it when you do.
Good explaining once again. thanks!
Good explanation
brilliant
i got 5.5 out of 10 in my stat quiz all of my marks gained from this video
watching this more than once and still not understanding anything is an infuriating kind of pain
The health of the bear population in a park is monitored by periodic measurements taken from anesthetized bears. A sample of the weights of such bears is available below. Use a single value to estimate the mean weight of all such bears. Find a 95% confidence interval estimate of the mean of the population of all such bear weights.
You're best
I missed a day of class because of a social burnout, so here I am 💀
Edit: explaining better than my teacher lol ngl
Thank u
what course is this from? on the website it only has high school statistics and it doesn't go into confidence intervals
asdFRap yeah it’s annoying that they have video mixed up. You can find this on the app but can’t play it there. You have to go to the browser app and then open it in youtube.
Oh my! This is not easy!
why not n-1 on the sd? I thought n-1 is for samples like this one?
what would change if i wanted to change the confidence level from 95 to 99%?
Too complicated for someone trying to understand for the first time
bear beets, battlegalatica. 👌
@@potatonoodlebear8035 False.
Go watch the earlier videos
What app do they use to do the writing
at 9.14 , why did you calculate twice the standard error while adding and subracting from samlpe proportion ?
Can you plz upload lecture on Theory of Estimation
I think it is wrong to say "There is a 95% probability that p is within 2 sd of p^". This is because p is not bound under probability, it's a fact. P is P with probability 1.
so cool
Can someone tell me where he got a Standard deviation of 2 from?
Why is the margin of error two times the SE when applied to developing the CI?
Because he was using a confidence level (CL) of 95% and the population is assumed to be normally distributed.
Though confidence levels & confidence intervals are two different thing, I find it easiest to think of them together by reminding myself of what concluding statement I'm making using my sample finding.
In the video's, I, the sampler, am saying : "I randomly selected (aka, sampled) 100 people from a population of 100,000 and I found that 54 of them (0.54 of the whole sample or 54% of the people sampled) prefer Candidate A.
Based on that sample finding, I am 95% sure that were I to have asked the same question of every member of the population, I would have found that 54%, plus or minus 0.10, of the population preferred the same candidate as did the 100 people whom I surveyed."
So, with that in mind, let's look at the math.
Step 1:
I got 0.54 in favor of Candidate A, so I will put 0.54 in the center of my normal distribution curve and call it the "sample mean" or "sample proportion."
Step 2:
Ask myself, "How many std deviations away from my sample mean - i.e., how wrong can I be - can the actual population mean be and still have my above stated conclusion still be true?"
The answer to that, for a 95% confidence level, is 2 std deviations. For a 99% confidence level, it would be 3 std deviations.
Step 3:
Ask myself , "How far numerically is 2 std deviations from my sample mean?"
To determine that, I need to know how far one std deviation is from my sample mean, and then I will multiply it by 2.
Step 4:
Calculate the std error. The std error that Sal calculated is the distance you must go (left or right) to get to one std deviation from your sample mean.
In the video's sample, Sal calculated the std error as 0.05.
Tip -> Do yourself a favor and calculate the std error assuming Sal's sample size was 55, 85, 150, & 350. That will allow you to see how the std error will increase or decrease.
Step 5:
Multiply the std error by 2.
Why by 2? Because 2 std deviations (aka, std error's worth of distance) is how far the 95% confidence level is from the sample mean for a normally distributed population. (Can one have a not normally distributed population? Yes, but that's a different lesson & a whole new "ballgame.")
Since the std error was 0.05, twice that is 0.10.
Step 6: Determine Confidence Interval
The confidence interval is the distance from (point A) 2 std deviations below (left of) of the sample mean to (point B) 2 std deviations above (right of) the sample mean.
-> Since std error = 1 std deviation, twice the std error subtracted from the sample mean gives us "point A," which is the lower limit of the confidence interval.
-> Doubling the std error and adding it to the sample mean gives US the upper limit of the confidence interval.
What's 0.54 - 0.10? 0.44.
What's 0.54 + 0.10? 0.64.
And, voila. The confidence interval is 0.44 to 0.64.
Now that you see how we calculated the confidence interval, do you know what it means, what it tells you?
The confidence interval tells you how wrong the value you got as the sample mean - i.e., the percentage of people in the sample who preferred Candidate A - could possibly be.
In other words, for the sample in the video, the confidence interval says: "Because I know that my sample merely estimates, rather than actually counts or measures, what share of the population actually prefers Candidate A, I know that my estimate could be off by a bit. How off? Well, by as much as 0.10, or 10 percentage points in either direction. That is to say, it's possible that anywhere from 44% to 64% of the population prefers Candidate A."
Realizing that's what the confidence interval is telling you, you should also be aware of one very important thing: samples indicate what was so at the time the poll was taken. They do not indicate what will be so in the future.
Thus context is critical to interpreting a poll's findings and the germanity of them given the confidence interval.
For example, if Sal's poll were of the percentage of quartz found in bituminous coal deposits, the 20 point wide confidence interval may not be too big of a deal because the composition of coal deposits doesn't change much. But Sal sampled people's opinion, and people's minds change a lot.
So you have to ask yourself: "Given the confidence interval is 20 points wide, does it make sense to rely on the poll's finding as a predictor of who will win the election that will occur at some time in the future?
I hope the preceding discussion, long though it is, helps you understand how the confidence interval was determined and, more importantly, what a confidence interval tells you and the types of things you should think about upon seeing it and the thing that was sampled.
@@anthonybell6156 God bless you Sir! You should make school textbooks. I did my homework just by following your 6 steps and your notes at the end. I cannot thank you enough!
(_)(_):::::::::::::::::::::::::::D~~~~~~~~~~
Anyone has a video that explains why Sigma=sqrt(p*(p.1)/n)?
where did he get the .46 for the SE?
.46 = (1 - P' ) = (1 - 0.54)
where P' = 0.54 is the sample proportion
@@61percentodicarica thanks.
I am in love with Sal
thank you because my teacher confused the **** out of me
Praise Jesus for Khan Academy
Wait so it this only for n=100? Or can I use this also for one like n=961
Tbh I’m still very confused.
Honestly this doesn't help me at all. I'm so confused
i literally just finished stats yesterday. WHERE WAS THIS BE3EUFNDS
912sonic Exactly
I did not get it... how did you calculate 0.54 and 0.58????
54/100