Statistics 101: Standard Error of the Mean

[@raymondst.6792]

This guy is my GPA saver! Spending 1.5h in class I get nothing, but with this man for 30mins, I can solve homework questions.

[@1Dispretty2me]

the whole inspirational intro actally hit me in m feels. Enter: supportive mathematical father figure

[@denissedeo895]

AMEN!

[@JayZigZag]

this guy deserves way more likes, comparable to khanacademy

[@mollypete4270]

This guy puts Khanacademy's sporadic nonsense to bed.

[@paultrayers494]

I love khanacademy but Brandon has been my goto channel for Stats class. Such a great and detailed explanation of Standard Error compared with khanacademy, brilliant job in picking apart all the elements.

[@Scoogies3]

I am taking online classes and the one I am taking now is Statistics. I have been struggling a lot with this class, the book doesn't make a lot of sense and my teacher doesn't explain things very well. I found your videos randomly one day and you have been a life saver! You explain this stuff so amazing, you break it down so there is no question about what your doing. You use great examples that I an relate to and really understand. I just want to say THANK YOU for making these videos, you do a great job!

[@BrandonFoltz]

Oh thank you Frank for your generous words. And thank you for inspiring me to keep making these for viewers like yourself. All the very best, B.

[@tonynicholas1695]

You made statistics easy. I should have found your videos 15 years ago when i was taking undergraduate stats. Your videos are awesome and you have made these freely available as well. Thanks alot..

[@thembekiletaaibosch960]

ola

[@littlecanvases]

Thank you so much for taking the time to help us out here!! There are so many poor instructors out there! Since you asked I will suggest one thing (and maybe it's here somewhere and I missed it) - it would be great if your videos were either linked (for proper order) or if there was an "order sheet" somewhere so that we could figure out the proper sequence for learning. I am struggling with sample size - margin of error etc and am bouncing around :-) Thanks!!!

[@foxman3374]

I second this idea strongly. It would help is go through this awesome material way easier

[@Qornv]

you are a master of education literally and figuratively. I can't believe how good your lectures are.

[@labyrinthine8546]

I'd like to express my gratitude. Regrettably, I can be quite slow of comprehension, especially with statistics. Despite several statistics courses (which I miraculously passed somehow), I clearly had some fundamental gaps in my understanding of many statistical topics including the SEM. Now, I finally understand it. Again, thank you very much!

[@yassineelhouari3085]

This is amazing, all my questions are answered in these videos. I couldn't be more thankful for the very appreciated effort you've done here. Thank you so much for everything!

[@danasmycoach]

These tutorial videos are the best ever. I like how they are so thorough and methodical and detailed in the explanations. Most stats tutorial videos go way to fast and make all kinds of assumptions about what i already know. Love these videos!!...more, please!

[@shannonpennington8559]

Dr. Foltz, THANK YOU! I have watched your Statistics 101 videos for each chapter of my online Statistics class that I am completing for my MBA! They are so clear, organized, and simple. You're the best!

[@vijaysripuram5374]

Hi Brandon, Although I am not a beginner to stats, it is the most neglected subject through out 13 years of my academic and professional life. Now I am a research student in pharmacometrics where stats is the back bone of any work I do. Your video is as simple as I watch an interesting movie in terms of understanding. Thanks is a small word to express my opinion on this video but I would encourage my friends to watch your tutorial. It would be very helpful for people like me if you can add even more tutorials such as concepts of Random effects, fixed effects or Mixed effects modeling.

[@jk23233]

It is a bad idea, at 26:51, to throw standard error of the mean (SEM) 38.7 on each of the 9 graphs. SEM is the standard deviation of the sampling distribution of the sample mean, not to be confused with the standard deviation of each sample. Any one of the 9 graphs represents a sample of the population. The shape of the graph should resemble the population distribution, therefore, their standard deviation should be approximately equal to that of the population, not the SEM. A better example would be to draw 9 samples from a not-normally-distributed population, to avoid this confusion. Other than that, this video series is excellent. Thank you very much!

[@lifecat8452]

I completely agree with your point of view. Calculating the SEM for individual samples is indeed confusing.

[@MANDINGLOST00]

Terrific video. You were born to teach. Thank you for the effort you put in.

[@sathishraghuraman8567]

I think this video was a bit hard to follow. Individually each slide made sense, but it is difficult to kind of appreciate what the standard error of the mean actually is. Here's where it gets particularly confusing: Understood Concept 1: Standard error of the mean is the standard deviation of the sampling distribution. Understood Concept 2: Standard error of the mean = (Population standard deviation)/sqrt(sample size) Where it gets confusing is when you extrapolate standard error of the mean to individual samples (like sample 1, sample 2, etc). If it is something related to the sampling distribution of a whole, it kind of doesn't make sense to me how we can extend it to sample 1, sample 2, etc. I went through the comments and saw that others had similar issues. From what I understand, "Suppose you want to estimate the population mean and you know the population variance, you take a sample of size 15. You can get a sample mean for this sample, and the value (population variance / sqrt (15)) is something that you use to come up with confidence intervals around the sample mean to estimate the population mean. I hope I am right! :P

[@BrandonFoltz]

@saladbrain Oh thank you so much my friend! Those are very encouraging words from people like yourself who inspire me. And yes! My stats videos are organized into playlists on my channel home page. There should be a playlist option in the upper left. The playlists are in order and internally they sequenced. All the best and keep on learning! - B

[@liranzaidman1610]

Hello all, I see that many of you asked why does Brandon takes 9 or 15 speciman of 15 samples instead of taking 1 sample of 135, thus leading into a much smaller standard error of the mean. Well, this is where Stats comes in rather than Math; technically you will get much smaller number when dividing by a large number, however when you are a researcher than you are not always capeable of doing that, or it's not logical of doing so. Let's take the exanple of that pavement; if you are a company which produces it, you would want to examine this in a large number of cities around the US, so you can cover many other parameters that can have an effect on the viscosity like heat, freeze, # of cars going over that material each day, rainy days per year, type of land beneath this pavement and other stuff. In that case, if you take a sample of 135 from New-York and it shows a good viscosity, does that tell you something about the viscosity in Vegas? or in Taxes? Always rememebr, Stats is the interpatation of Math. Your own thinking and added value is the difference which counts here.

[@lilprotakeit]

my goodness me !! you make things so clear .. god bless you .. you have made an old man live again

[@BrandonFoltz]

Same. 😊

[@funnyvideobymonster2795]

god bless you! i just understood my concepts very well. In roughly a half hour, all my confusion is gone! thank you!

[@laurafarkas2007]

Thank you so much! It is obvious that you are a master teacher. You taught me more in half an hour than I learned in a week of struggling through an online class. I think I can do this because of your efforts. I shared your videos with the entire class.

[@pastormaparura4228]

Well explained I was having problem in getting the difference between Standard error and Standard deviation. I can smile on my way to examination I will be watching your confidence interval vedio hope to get the best thank you God Bless you well motivated with your introduction. 56 years have a diploma but will one day will be lecturing at a university.

[@temiadebiyi5005]

thank you for making the scary stuff easy. I am definitely a fan!

[@saifulhoque5883]

Again kudos for your great effort. The best video so far I found regarding SE of the mean. Thanks again Foltz

[@AetheriusLamia]

Beginning is a little awkward: You comment, "If you are watching this as a student, ..." implying you will address the rest of the audience who isn't a student after addressing those who are -- and then you don't. lol ("If you are watching this as a student, great job, hang in there! If you're not, meh, whatever." ;) ...) Watching at 1.5x speed -- love this youtube feature ... Your teaching is clear. Good job! It is inspiring me to record my own presentations and put them on youtube (though I am tempted to cower at the time needed to rehearse comments, and create subtitles for English learners)... But good presentations /should/ be so prepared, not off-the-cuff remarks, so thanks for the 'iron sharpening iron' ...

[@ntwede]

Your videos are like the cumulative sum of all knowledge of statistics, 1 lesson at a time. Your 1st vid is just itself. The 2nd vid has 1 and 2. And the 3rd has 1,2, and 3 in it.

[@ntwede]

Because of how the playlists work.

[@amitjadhav5765]

Brandon, I like your content so much!! Specifically the videos on statistical inference are really wel structured and help light the right areas of your brain and grasp the concepts very quickly!! However there is one error which I would like to point out to alter your understanding, and to preferrably help others out there!! between 26:00 to 27:00 you constantly are iterating that the standard errors or the standard deviations of individual samples of same sample size are same. That is not at all the case. Each sample even though of a same size, will have its own mean, and own std deviation. The mean of all these means of all samples drawn will however have the standard error of Sigma / Sqrt(Sample Size). So the graph shown around 26:55 is also inaccurate. Hope this helps!! All good intentions man! Thank you for all the content.. Really appreciate the effort!

[@MsAstrona]

absolutely wonderful how you break things down so that the information is attainable.

[@npt0112]

I am clearly understand anything which you teach, thank a lots.

[@stevegyro1]

Brandon, You are the only instructor (IMHO) that uses the Central Limit Theorem correctly! So many people just take one sample, and then apply that value for n in the sort. Q- Why not use 9 instead of 15 for n? Nine samples of (15) are taken. Just wondering! Thank you.

[@pastormaparura4228]

I felt that there is a point on sample you wanted to correct what you wrote was correct, so you were cnfusing yourself good video with excellent introduction well done continue to help man kind thank you God bless you.

[@DGerharts]

Thank you Brandon! I love you how you place focus on creating the right train of thought and understanding the processes associated with the subject.

[@NixuOfTheNorth]

Thank you! These are the kind of videos I need to understand statistics. Apparently my mind was not made for math, so understanding this stuff is more difficult than it should be. The way you explain things helps understanding WHY things happen, so my brain has something to "anchor" all the information to.

[@B1nary0]

+Nixu88 Statistics/Math can be challenging subjects, but I don't think you are approaching learning with the right attitude! You are quite capable of mastering almost any topic, but it is a matter of practice, growth, and patience! At some point in your life you were probably struggling with learning to read, learning to multiply and divide, even subtract,... Practice and perseverance truly the key! If Euclid or Capernicus were presented with calculus, they would surely have felt the same way!

[@KevinNguyenSESE]

Thank you I think your video series are very helpful and provide more intuitive understanding if the concepts. My suggestion for this specific video is as follow. I think the first 15 minutes is repeat of your other video on sampling distribution. I would suggest you shorten this down to the last 15 minute and make it a part II of that video.

[@MrGhostiemon]

Thank you Brandon, loads of info in a 30 min class.if i would have watched this on my first go around in statistic i would have nailed it. (that was about 10 years ago) great video. thank you for sharing your wisdom.

[@miteseminar7134]

A humanistic amazing instructional video! Thank you so much! Admiration from India!

[@siddhantbajpai5889]

Here, you have taken 9 samples of size 15 each. So when we talk about sample size, does is it refer to "number of samples" or "the size of each sample"?? I am really confused about this.

[@odojoachim]

Oh bless you:)) I've found the channel on KZbin just on time In January I will have my mock exam from stats. I do revision with you, and I am really glad about it:)) Thank you.

[@mayuragrawal4352]

beautifully explained this very difficult topic. This was almost never explained anywhere why do we use population SD to get sample distribution standard error. This is beautifully explained here by telling that sample would not tell us SE but population SD will tell us SE and samples would gives us different means but they will all have same standard error if they are of same size.

[@oscarbanuelos7041]

Thanks Professor for keeping us confident. Great Teacher.

[@amirhosseinyazdavar]

I enjoyed every seconds of your explanations. Thanks a lot for this amount of effort.

[@anushrimore5820]

Thanks, Brandon. Your video lectures are helping me to learn Statistics in an easy way.

[@drsagozo8860]

Awwww, that introductory encouragement is REALLLLY GREAT! THANKS

[@siddh89]

Hey Brandon, First off, thanks a bunch for the time and effort you have spent in creating these extremely useful videos! I'm just having a hard time visualizing the concept of standard error - in this video at 29:00 you say that the standard error is the same as the standard deviation of the sampling distribution, but having watched another of your videos Statistics 101: Confidence Intervals, Population Deviation Unknown - Part 1 at 22:00, the explanation seems contradictory. In that video, the variable s is assumed to be the std dev of the sample, which differs from s subscript x, which is the standard error. I guess it would help if you could clarify the difference between the standard deviation of a sample vs standard deviation of a sampling distribution. A second question I have is regarding the standard error formula itself - specifically the division by the square root of n. Just as an academic exercise, lets say we were to take a sample that is the same size as the population - I would assume that the standard error of this "sample" mean should be zero, as it is always the same as the population mean? However, you can see that if we blindly apply the (sigma/sqrt(n)) formula, we would end up with a non-zero standard error, which doesn't make sense to me, as the sample and the population are one and the same in this case. Is there an exception to this formula or is there something I'm missing here?

[@swastiksanmay2315]

Give this guy a medal

[@dr.juliesamaru548]

I was just about to drop this class, but after listening to your words of encouragement I am motivated to give the course a chance

[@BrandonFoltz]

Great! Follow along with my videos during the course and you should be just fine. I may not cover everything but I do cover the bulk of almost all intro stat courses. Hang in there!

[@saladbrain]

Excellent videos. I really enjoyed watching them, and will continue to go through them to improve my understanding of stats. One thing ... have you produced a 'road map' that gives a suggested order of viewing? I would find that beneficial. Please keep on producing these videos, Brandon. They are very clear and I have found them very helpful in clarifying many of the fundamentals of stats, which many texts either gloss over or provide vague explanations. Great stuff!

[@dkwteacher]

Thank you so much - I would just add a link to future videos to facilitate finding what we should do when the standard deviation is not known. Your video was very clear and I know it will help.

[@melisavines4548]

Oh my goodness! Your kind words and encouragement are awesome!!! Thank you so much!

[@fouziasubhani9138]

U have done MARVELOUS work. I never thought, STATAISTIC is interesting Subject.

[@downtownmafia123]

Cheers for this video Brandon. Concisely explaining (what can be) a difficult topic to a mass audience can be challenging but you have done just that. The words of encouragement were the icing on the cake; subscribed!

[@arundhotishome8824]

your teaching technique is just awesome ...

[@trevorpope1913]

Your teachings are brilliant

[@zia8950]

all your vids are fire and i dont know where to start

[@BrandonFoltz]

Hi Zia! Thanks for watching! kzbin.infoplaylists

[@yazzerarafat4551]

THANK"S A LOT Mr. Brandon Foltz, give me enlargement, knowing how to important take differentiation concept about sampling population in order to calculate standard error of mean and the result for take final of ratio Variable.

[@sufalmanorath]

Excellent 👌 , after a long time I have watched a quality education video.

[@robertreid64]

Excellent work, Brandon. Extremely helpful and informative.

[@lifecat8452]

when we say "as n gets larger," does n refer to the sample size or the number of samples? at time 13:02

[@oosakful]

Thank you so much! Great teaching style ... take the anxiety out of learning stats. :)

[@jenndematteis1466]

You seem like a real sweet heart! Thank you for your videos, they're clear, concise, and very appreciated. Nikki in Alaska

[@bailamos2]

Probably I am a bit confused, but what I understand is that you are taking the mean of the means of samples (grand mean), then taking standard deviation of each sample separately; hence, refer to it as the standard error of the 'grand mean'! which is confusing. What I suggest is: set n=9 then calculate s.d. of the sampling distribution. Then take the grand mean with the 'grand' standard error to make your inference. (I could be just confused).

[@thomasjostaufderstroth684]

I´d like to add a different answer to the question of why the SEM is so much smaller than the population standard deviation: When your sample size is larger than 1 you don´t use individual scores for a comparison distribution, you use the mean of many scores, and high and low scores tend to even each other out - this effect is what causes the SEM to decrease when sample size increase.

[@xoawolf6343]

Thought this was very helpful. I have not been doing poorly but I have to work hard to understand. Thanks for making it understandable

[@TheHeycalmdownfella]

What a fantastic explanation of this concept. Thank you.

[@latasharose-harrison4599]

You are amazing. Great teaching. Way to reach your student!!!!

[@AhsanAli-fg1fv]

i don't understand why negative ppl exist he is explaining so well despite all of that some ppl have disliked the video

[@prabhudaskamath1353]

Thank you Brandon. You are the best..

[@abigailperrino2868]

Thank you so much for the encouragement!! It is so needed, at any stage!

[@pjgdba306]

Great vid. I would add watching the following vid before watching this one - it tee's Dr. Foltz's video up nicely - sets the stage. 28:10 Critical Piece of Info, at least for me...

[@fakeburrito5404]

Thanks again for another great video. It's very helpful!

[@missyogakris]

Thank you for such a thorough video! I found it extremely helpful

[@darthglowball]

Thanks a lot! I like the details. What I don't understand though is: if you have a dataset, say with 20 measurements, and you split it into 10 samples, depending on how many samples I choose, while keeping the samples of such size (n) that they fit into the dataset when layd out consecutively, I get a different SDOM for every sample amount! What is the point of SDOM as the precision of your samples if I can arbitrarily change it by declaring where the splits are?? Who determines where the best split locations are? Here's what I mean: dataset = [23,325,21,677,46,3,84,34,225,62,1,43,28,964,4,625,233,1,4,85] sample_count = 10 samples = [[ 23, 325], [ 21, 677], [46, 3], [84, 34], [225, 62], [ 1, 43], [ 28, 964], [ 4, 625], [233, 1], [ 4, 85]] OR: sample_count = 2 samples = [[ 23, 325, 21, 677, 46, 3, 84, 34, 225, 62], [ 1, 43, 28, 964, 4, 625, 233, 1, 4, 85]] SDOM changes for every different sample_count! I calculated it by taking the averages of the samples and calculating the SD (with n-1 in denominator).

[@changhoonjun4413]

Hi, In your explanation the number of sample batches (here :9 ) will not affect? Only 15 (number of samples per batch) will affect? Then, we do not do sampling 9 batches of 15, rather 1 batch of 135 samples. Our effort to sample is same (135 samples: One case is 9*15, another is 135*1) Can you answer to my question? Thank you!

[@CatchTheTrade-ig4ld]

Phenomenally explained.

[@BrandonFoltz]

Thank you! Phenomenally watched!

[@capressley]

Very helpful. Thanks for sharing your time and expertise.

[@saladbrain]

Excellent! Got it. Thanks so much for the prompt reply.

[@satyapalsingh7935]

you have made it very easy to understand. thanks.

[@VioletBird]

thank you! these stats videos are super well put together and very helpful. :)

[@HaiLeQuang]

One question. If we already have the data point, the mean and the number of data point (which is 9) in that sampling distribution. Why cant we calculate the std error of the mean directly like any usual distribution?

[@shahnazmalik6553]

Brilliant 5 Stars. May i please know how could I take my statistics skills upto highest level and I aim to use it in Data Scientist field. May I know what is the best road map you could advise me. i am ready to put 200% efforts in it. I Promise! and i look forward to you precious advise and thanks once again for such a brilliant explanation . i give you 5/5

[@stevencampasjr.2840]

This is a great video and I thank you. How did you determine the range of 100 in determining the frequency?

[@elijahd.spragueph.d8905]

I am confused, maybe he meant to say almost 500?

[@swarajkadu3681]

thak you sir i think i have find the perfect statstics playlist

[@vaibhavdhote1304]

Hey Brandon, I have a question around the ' n ' that you stated @12:43. Does it refer to many 'n - unit' samples taken or to number of the total samples taken of same size?

[@SivakamiPLFL]

Great Video. Just one small quibble. Sigma X bar is the standard error of the Sampling distribution of the Sample Mean. Its not the Standard deviation of the Sample. So can we really say that the standard deviation for all samples of size n is the same? The standard error is the standard deviation of the sampling distribution, not of each sample.

[@Wifeofmassinstruct]

Hi Brandon. I was just a bit confused when you said that the sample size is 15. I thought the "sample" size was 9? There are 9 samples with 15 values in each. Could you help me to understand this? Thanks so much!! By the way, your videos are FANTASTIC!! I like them better than Khan Academy, although Sal is also fabulous.

[@AlvaStrong]

Brandon, please explain. In the beginning you mentioned you did not like to use the term "sample" to represent the 15 "specimens" because there were actually 9 "samples". I am wondering if you were confused and did the whole calculation on n=15 specimens instead of n=9 samples.

[@javedmohib9736]

What is the point of taking 9 different samples of 15 observations. Why not only 1 sample of 135? In the latter case standard error of mean would be lesser.

[@caseyjonas352]

In this case it might be 9 samples over a batch prepared or stored over a period of time. In that case 9 samples would be more accurate if it was made to order and the asphalt was kept heated for say 8-10 hours before being delivered. If you took one sample of 135 at 8am it wouldn't be as good of a reflection as say 9 samples from 8am-5pm, even if n is smaller.

[@10083607]

Clear and to the point. Very didactic

[@snehasandapu2784]

Brilliant content, very neatly explained. Thank you :)

[@sajjadhaydar]

Wonderful tutorial. I learned a lot. Thanks

[@eziola]

Brandon, Great video, but I have a question that I just can't get my head around. You said that "Standard Error of the Mean is the Standard Deviation of the Sampling Distribution" and then proceed to give us the formula for Standard Error of the Mean (StdDevPopulation / SQRT of Sample Size). =150 / SQRT(15) = 38.7 I don't think that statement is literally true. Let me explain in "Excel Language". . . Wouldn't the Standard Deviation of the Sample Means simply be =STDDEV( {list of all sample means} ) = STDDEV( {3210.73, 3150.13, 3345.54, 3190.67, 3217.9, 3301.45, 3100.72, 3413.01, 3023.59} ) = 121.56? 38.7 and 121.56 are very different numbers, but 121.56 is literally the standard deviation directly calculated from the sample means. Can you please help me clear up my understanding? Statistical verbiage is so different video to video and textbook to textbook. It makes my head spin.

[@abdirizakadawe9042]

Very helpful indeed. Thanks. Keep it up.

[@dominikb12]

A great video! Still, a question remains. When you say a standard error of the sample... do you mean the standard error of the sampling distribution or the sample of size n(where n is the number of observances within one sample)?

[@AlvaStrong]

Is there a link to that future video where we get to learn what to do if you do not know the standard deviation of the population?

[@michabouts3454]

Hi Brandon, thanks for the great video material. I do stay stuck do with one fundamental question which I don't see answerd in your video and in any text book. In your example you take 9 specimen of 15 samples. I understand the sample error goes down when the sample size increases. But, why do you consider the sample size to be 15, rather than 9 x 15 = 135, while calculating the standard error? I could have considered taking 9 specimen of 15 samples each in fact the same as taking 1 specimen of sample size 135. In the latter case though the standard error will drop significantly. Therefore my question, which size to choose (15 or 135) and why? Thanks for taking time to answer.

[@pawekopytek7596]

I have a question: why square root of n? I get what it does (it decreases the overall number) but I don't know why it's there. The standard error of the mean is supposed to be the standard deviation of sample means - how does sample size (or its square root) find itself in the formula for that?

[@nelisafreitas739]

HI Brandon I am struggling with setting up hypotheses. I am not sure if I need to turn research questions into hypotheses or whether I need to have claims and omit the research questions.

[@MrPerfectlogic]

Brandon your videos are very good and clear. Though have a constructive comment on a fundamental statement you make time and time again ( you are consistent) in relation to the central limit theorem which I think is incorrect. In this video ( and your other ones) you state that the standard error of the mean FOR ALL SAMPLES of the same size and from the same population is the same. To the best of my understanding the central limit refers to the standard error of the distribution of samples averages. That's not the same as saying all samples have the same standard error.

[@biswashgauchan5644]

Hi Brandon, you are superb and your tutorials are great. I agree with the above observation that the standard error is the square root of the variance between the sample mean and the mean of sample mean divided by the sample size (uniform) and therefore, the standard deviation of each sample is not necessarily equal to the standard deviation of another sample.... Hence, in your example, the standard deviation (or error as you have mentioned) of each of the nine different samples need not be same. However, if we take another 9 samples with the same sample size of 15 and then calculate the standard error of this distribution, it will be more or less equal to the standard error of the first sampling distribution... Hope I am right...

[@wh33l6r]

OK. This is probably a picky point, but it occurs to me than the "mean of the sampling distribution" is NOT the population mean. That really threw me the first couple of times you said it because I was taking you literally since you've made a lengthy point that the entire case for taking samples is that you can never really know with certainty the population mean. Actually, as you state later, the "mean of the sampling distribution" is an ESTIMATE or APPROXIMATION of the population mean, hence the ~ over the = sign. Right?

[@shreyachawla988]

Hi Brandon, amazing video! I had a doubt, we also refer to standard error as a means to gauge Population SD from Sample SD i.e. SE= s/√ n. Dividing by √ n brings us closer to population SD. But then SE is also the SD of sampling distribution of means which is clearly σ/√ n. Are both these interpretations same? Am I missing something?

[@v-chuelee3050]

God always blesses you, Brandon Foltz.