Statistics 101: Confidence Intervals, Estimating Sample Size Needed

[@mayani71]

Hi Brandon, you are God sent and have been a blessing during my stats course, Its a shame that I am paying $4 500 for my stats course and I have not gotten anything, everything I have learnt, I have done from your videos. Thank you for feeling in the gap. Kudos for a job well done and keep being a blessing. Cheers

[@BrandonFoltz]

You are VERY welcome my friend. This is a labor of love for me, so it never really feels like work. The real kudos goes to YOU, for committing to learning wherever that may be. Keep up the good work and never stop learning! - BF

[@GoodDreamsImagination]

This video saved my life. Well, at least my GPA. Thank you so much. I looked at so many videos before yours. But you helped me see the math.

[@ybeholla45]

I have just started to listen to your videos for the first time and already, I am sold. First off, your intonation is nowhere near as monotonous and lifeless as my stat professors. You do a good job of briefly reviewing topics which are at the base of the new topics you mention. Thank you for your videos. I do have a question though. I will put the question in another post.

[@riakumar3914]

Hi Brandon! I am from India. I love the way you explain all the concepts from scratch. Keep making such amazing videos on statistics. Thank you very much.

[@atulhadap2176]

Hi Brandon, I am very fortunate that I stumbled on your video 'Statistics' while searching to estimate a sample size. You made it interesting and simple. Wish you were my instructor in the class. Now I find it interesting.

[@RicksterBerlin]

If only I'd seen this before I took my Open University Data Analysis exam! The interpretation and case-study format of these videos brings the subject to life. That's what makes it stick. Highly recommended if you want bite sized nuggets of Stats know-how. Rickster

[@BrandonFoltz]

Hallo. When finding confidence intervals we are usually given the sample size and that determines that margin of error. In this case we are reversing it. We are given a margin of error and then we are solving for the sample size that will produce the margin of error we chose at the beginning. For example a rectangle, we know that Area = L x W. If we know 2 of these, we can solve for the other. Same thing here. We are just solving for a different unknown.

[@kassondrahickey2468]

Love your introduction to this video! So positive and healthy for students to hear. Thanks for helping calm down anyone who is struggling and encouraging them that they are capable and can get through it.

[@changisimo23]

These have been an excellent supplement to my course. You explain concepts logically and clearly, which increases my understanding of these concepts. I haven't taken stat almost 20 years so these have been a life saver!

[@BrandonFoltz]

Thanks so much! Glad you find them helpful. Keep on learning!

[@dr.abhijeetsafai7333]

Thanks a for for these videos. My teacher, Mr. Sanjay Sane recommended this video so I was watching it and it is a wonderful way of teaching I must mention. Your teaching is really wonderful. Many good wishes. :)

[@antoinettenelson4315]

I don't really comment on youtube much but I just watched two of your videos and they were extreeemeellyy helpful! I'm a PhD student and I needed to refresh myself on some statistics quickly for experimental design. Thanks a lot!

[@indaytorres2302]

brandon, thank you for discussing the basics in detail. i just realized how amazing stats could be. i really appreciate your teaching skills. you are so dedicated and patient . thanks and more power.godbless

[@ashagreaves106]

I am sorry I didn't see your sessions earlier. I was so lost. It made things so much clearer. Well done. Thanks

[@KPAVideoful]

Brandon, again great job! This video answer most of the question I have with regard to how to select the sample size with 95% ci and specified MoE. You explanation is really more of self explanation, which is a great way for this kind of distance/online leaning. It's Really really really helpful. I can't stop sharing your video with my friends. Thank you so much Brandon.

[@androy001]

Thank you for this, labored over my notes ( online masters course) for days, spent one day with these videos and I am now comfortable with these topics. Thanks again

[@jamesslipszenko203]

Absolutely perfect explanation for a question that has been taunting me for weeks, thank you very much.

[@cynthiarojas4199]

Nobel Prize for Best Educator!!!!

[@monkyjamz894]

Just wanted to let you know you literally saved my life today. :)

[@supergenkilife]

I've been using your lectures by topic as supplemental lectures and instruction for my Stats I class. You've helped so much, in particular with linear correlation. Thanks so much! I really appreciated your playlists by topic and hope you will continue to expand these and maybe also add some more application problems. You're a gifted lecturer and teacher. Thank you for your contribution to higher education and equitable access to high-quality educational resources.

[@muhammadsyukri746]

You explain with simple way. Loved it

[@YoginiKrysten]

' just started watching your vids. They are super helpful in expaiining what''s going on. Thanks and keep up the great work!

[@bloomingtonvolleyball639]

Excellent explanation focusing on the concept and with enough of examples to support it. Thank you so much for the effort.

[@zorbasg1001]

Brandon, you are god! I think you have done a PROFESSIONAL work and it is a jewel for education purposes. I just wanted to ask something though. In 15:08 you interpret what is our conclusion. Is it also correct to say, interpretation: to have 95% of samples contain μ (miou) in the interval of plusminus 8 from Xbar of the sample, 78 must be our sample size? i try to grasp statistical philosophy and you help tremendously with your videos! Thank you.

[@BrandonFoltz]

Confidence intervals for variances are much more involved and that is actually the next topic I will cover. You do not need to know how to find those to do any of the problems up to this video in the playlists. :)

[@kipseremjacob9690]

Thank You Brandon, So informative, slow in explanation and super easy to follow. good work, God bless.

[@krishnashrestha8380]

Excellent video. I wish I had this instructor in my graduate class.

[@jmmac14]

Thank you very much! You just helped me through my Operations Management presentation. More power bro!

[@dianelindsay8422]

Wow, can't believe I took so long to find you. You make it all sound so easy! Thank you!

[@sujeewapanditha6062]

Gives a good understanding of factors interplay with sample size.

[@kayumanis1313]

wow! this is the very similar question out in ASQ CQE exam practice paper and I was always wondering why only a portion of the equation used to get the sample size, n. Many thx for this vid!

[@elsieakwara3823]

Hi Carolyn, you can use fisher’s formula [Z2 (1-p)p/d2], where Z= alpha (or 1.96 at the 95% CI), p= probability, d= margin of error) or Cochran’s formula [Z2pq/e2] where Z alpha (or 1.96 at the 95% CI), p= probability, e= margin of error). So in your case, you want a 95% CI (Z= 1.96), p=.20 (20% of participants volunteer in such studies), thus q= 1-p, which is .80. You did not specify your margin of error (let’s say a tolerable margin of error is at 5%, thus we will use .05 in our calculation). Using Cochran’s formula= 1.962*.20*.80/.052 = 245 Your sample size is very small Carolyn :-/ Alternatively, if you want to stick to that sample of 14, you can do the reverse to find your margin of error, which I presume would be large and you will have a weak sampling design, you would not be able to generalize your results. So, let’s take Cochran’s formula again= Z2pq/e2 So, 14 (your sample size)= 1.962 *.20*.80/e2. Square root both sides to get e= 1.962 *.20*.80/3.74= 0.16 (margin of error)

[@iheartthemisiheartthemis6551]

Brandon. Thank you so much for your video, which is very clear and informative. I have two questions for you: 1. How should I go about choosing a margin of error to calculate the sample size? 2. If I plan to eventually do a regression analysis on my data and will be analyzing two variables, which variable's standard deviation should I use to calculate sample size? The larger of the two? Thanks.

[@Tomizzle10Gaming]

I was already getting so mad I wasn't understanding this, this video saved me lol

[@gauravpadalia7983]

In the gas problem example no. 2, we are given sample S.D (s) not population S.D(sigma), so why you have used it as population S.D. Also when 'sigma' is not known we use t distribution (i.e t score) so why you used z score (upper and lower boundary) in the formula at 20:07.

[@osnn8156]

Gaurav Padalia since the t distribution is dependent on the degrees of freedom =n-1,we'll have to use the normal distribution to find n. He could have said 'population S. D' but he did use the word 'appropriate'

[@EpicByte91]

I actually had the same question after watching this and found myself in a circular argument. I was wondering why you wouldn't use the t statistic here if we don't know sigma. Then I realized you need n for the df. so you would be going in a circle lol!!

[@sadiqurrahman2]

At first I also thought like you. When 'sigma' is not known and sample size is small i.e. 30 we use z distribution (i.e z score). And in this type of z distribution instead of population S.D. 'sigma' we use sample standard deviation 's' or estimated standard deviation using sample standard deviation. So t distribution is one kind of z or normal distribution considering both unknown 'sigma' and sample size .If sample size increase gradually it converts to z distribution. As we don't know exactly whether it is t distribution or z distribution , it is wise to use z distribution.

[@MRkhanhftu]

has your question been answered yet ? thank you in advance

[@MRkhanhftu]

for the 1st margin of error (a. +- $0.05), i used the t-distribution and found that n is 7.

[@alirezabasiri3541]

Hi Brandon. You are awesome! How lucky are your student to have a such a wonderful instructor! Would you please add some i depth videos for different statistical models, as well? like mixed and random models.

[@PhoenixGraz]

Great Videos and a lot of motivation throughout a very fascinating topic. Thanks for that!

[@lilprotakeit]

thanks a lot .. you are god to me ! Love from India

[@woodchuk1]

Hi SouthpawGrammar, For your problem, If we can assume normally distributed data, I get an answer of 420 specimens. We don't know sigma in your population, so we have to estimate it from the range of 53 to 680, which is 627. Divide this by 6 (since 99.7% of normally distributed data falls within 3 standard deviations of either side of the mean) to get an estimate for sigma of 104.5. Our z score for 95% is 1.96, so the answer for a 10 PPB margin of error is ([(1.96)(104.5)]/10)^2, or 420 specimens rounded up.

[@DrAamirAbbas]

Thanks for adding such an amazing presentation really liked it

[@BrandonFoltz]

Hello! First and foremost there is no "easy button" for this. It will take hours of doing practice problems in your book and/or notes; preferably in a study group if that is possible. Secondly, I have not covered a few of those topics...yet. The goal of my videos has been for people like yourself to recognize the basic pattern and method for working these and then apply them in your classwork. Practice, study groups, note cards, reviewing examples in your book. Just a few ideas. You can do it!

[@marcosdearruda77]

Beautiful video, Brandon. Thanks for posting it.

[@vannanuon6077]

You are really good. I can understand it easily. Many thanks

[@simplerajagopal]

came across your video today... good one!

[@christinesimmons6916]

Thanks Brandon, very helpful! Wondering if you can help guide me to an answer on this one. I want a 95% C.I. for the difference between the means of two populations (normal distributions) to within one standard deviation, and these populations also have the same standard deviation. Taking equal-size samples from each population, what is the minimum number of samples I would need to take from each sample? I'm not sure if there is enough information here, I'm thinking since I don't have the margin of error requested that I can't solve for n. Thanks!!

[@v-chuelee3050]

Thank you very much for your videos. God absolutely blesses you! Vangchue Lee, from Kobe University, Japan.

[@rinfal]

Great job, topic was presented clearly, concisely, and logically. Thank you.

[@abhijeetparihar3349]

Hello Brandon, you teach really well

[@rskulkarni]

Excellent video. It was very helpful. Thank you very much.

[@tristenbrown7099]

God bless you, Brandon.

[@TheHorizons10]

thnkxx u started with imparting some motivation...

[@iLoveTurtlesHaha]

I purposely listen to the intro because I want Brandon to tell me I'm smart even though I'm not. :(

[@BlackBNimble]

@Brandon Foltz In correlation work, when the sample size decreases, does the size of the correlation that is needed to reach statistical significance; increase, decrease or stay the same?

[@mauroandreu5290]

Hi. How can I explain results statistically significant but not reach the magnitude pre established at the sample size calculation?

[@edwardlopez5930]

I think it would be great if at minute 31:27 you explain how you got the numbers that are in red.

[@BrandonFoltz]

Hello! I do that at the 28:00 mark where we have the three confidence intervals listed and we walk trough each one. Hope that helps!

[@wayneC7]

Professor do you have a cd kit with all your videos in order of learning?

[@lamecknatangwe3109]

this is a super presentation. it help me a lot believe me.

[@brendacarter2483]

Brandon, which one of your videos uses the following formula: p +/- 1.96* sqrt p(1-p)/n?

[@plantastica4622]

Brandon. Little confused with this video. Do you have a video for confidence intervals for variances and standard deviations.

[@golfedanhanem]

i really thank u so much but i dont know how to calculate a sample when i know the population number?

[@AJ-et3vf]

Awesome video! Thank you!

[@robboyko3712]

Can you do a couple of videos pertaining the sample size calculations using Gy Pierre's sampling theory. I have browsed the entire youtube site and more and no one discusses, Ingamell's, Gy's, and Vismans sampling theorems.

[@ybeholla45]

A problem I am working on mentions. The types of widgets used typically fall into the second classification on the company’s pricing scale. This classification places an upper limit of 850 pounds on the mean. There is no mention of a lower limit. In determining E am I to assume 2 classifications above the mean and 2 below for a total of 4? Or am I to work with the upper limit value?

[@SetiaBudiBoedyBios]

I am totally amaze with your videos :) Help me a lot in order to understand some fundamental stuff about statistics :) I am just hoping that you might also be able to make some videos related to time series analysis. It would be great :)

[@nurawario1235]

Thankyou for the video,its absolutely clear

[@johnschearer8924]

Brandon. When calculating the 'desired' sample size, why do you not substitute the t-values into the equation to solve for n, when you don't know the population standard deviation. I understand that CI with same sample size will have same MOE for given population standard deviation. And, that when you aren't given the population standard deviation and have to estimate using sample standard deviation (s) that samples of same size DO NOT have same MOE. Is this the reason that you have to use Z-values when estimating n (not given population standard deviation)?

[@srivatsgopalan4308]

Hi thanks a lot for the videos, you are a lifesaver. I have a doubt in question 2, if it says the sample standard deviation is 0.05, then doesn't it mean s and not sigma? so wouldn't that involve using t values and not z ? how to know the difference?

[@radheygupta697]

Hi ! Thanks for the video..I could understand the difference between the margin of error and confidence interval. I can infer that the sample size doesn't depend on the size of population size i.e. for 2 desks - a and b producing 5000 policies and 2000 policies the sample size would be same for a given margin of error and confidence interval ?

[@plantastica4622]

Brandon I desperately need your advice. I am being tested this coming Saturday for Confidence Intervals sigma known, sigma unknown, sample size, confidence intervals for proportions and finding confidence interval for a variance and standard deviation. What do you suggest I do in terms of studying for these with your videos? Thank you.

[@HehersonAngel]

Hi. May I know the author of the formula of the sample calculation that you used? I find it more researcher friendly. Thank you.

[@vamsimohanramineedi7630]

In Gas example problem, why was the sample standard deviation used as population standard deviation?

[@purelynumpay1660]

Hi, Sir Brandon! Can you help me with this? If I will be solving for the required sample size where the population standard deviation is unknown and I will be using my best guess for sigma with a 99% level of confidence, can I still estimate the population standard deviation as one-fourth of the range? Because I've read a book that says if the confidence level is 99%, the range is divided by 6. Thank you in advance for your help. Stay safe!

[@8fold_path]

Hey Brandon. I am a student doing my thesis. As a part of my thesis, i need to test electrical componants. How can i decide number of those Componants(samples) needed to test to get a confidence level of 95%? Thank you.

[@darkside2326]

Excellent video!! One question, what should I do to select a number (sample size) of surveys when qualitative data is involved? They are made to know customer perception in 6 different topics.

[@ricardofranco-duarte346]

Hi Brandon. One quick question. In all your examples (until this point I´ve watched all videos in order) you are "assuming" that all your data are normally distributed, right? Otherwise the analysis were not possible. Shouldn´t you start by doing normality tests, before applying these analysis? Thanks

[@BrandonFoltz]

In theory yes, but my content is geared towards students who are learning the content and need a little help. In those environments normality is something that is assumed. Very few undergrad (or equivalent) courses go into that much detail.

[@edwinnjagi9058]

Hi Brandon. Example 4: Confident retirement: Why are the n =153, n = 217, n = 374 Instead of n = 152, n = 216, n = 373 ? df?

[@ArijitBiswasdotcom]

In example 1, you took mu + 8 and mu - 8 and mu in the center of the 95% CI. So is that saying that we're 95% confident that the population mean lies within this interval?

[@ahmedalalaq2288]

Dear, my research is applying questionnaire then take biological sample from patients so i do not know what sample size will be

[@pratikshajhawar1629]

Brandon thank you so much for these wonderful video of yours.. I wanted to know if you have any video for confidence interval for population proportion ?

[@mididoddi]

Brandon, quick question. When I am estimating sample size, I am using Standard Deviation from a data set. Should this data set be normally distributed? What if the data in not normally distributed. Thank you!

[@bakaemoitlhobogi1860]

i learnt a lot from this video

[@nomattermhosira3840]

thanks a lot Brandon ,so helpful

[@shanice4315]

Thank you for the video! May I know how you got 4 in the denominator of the planning value? :)

[@helen4805]

Yes please, I was wondering that. Why range/4?

[@libertarianPinoy]

Can you derive this formula with finite population correction factor?

[@emceededon803]

Bless u Brandon. U've made my day

[@nehalmedh623]

In Example 2, should E be a % of the average ($3.55)? Thus, if we are looking for an margin of error of $0.03, then should E = 0.03/3.55 =0.845?

[@adtgrh]

Hey, Thanks a ton for the video. You explained how to calculate sample size where pop std dev is known. I also see people using the below formula for sample calculation. Why is it different and what is the significance? n = [(z^2 * stddev^2)/E^2] / [1 + (z^2 * stddev^2)/E^2*N] (N = Population size)

[@OriginalJoseyWales]

I see the formula for the margin of error involving the standard deviation (SD). So why does this website say that the margin of error = 1 divided by the square root of the number of people in the sample -does not include the SD. www.robertniles.com/stats/margin.shtml

[@Dsurvivor21stCentury]

Hi Brandon. Thank you so much for the video, it was very helpful! I was just wondering it the formula used in example one can also be used if the margin of error and standard deviations are percentages rather than set values? Would you convert them to decimals? So if the the question said the margin of error was 8% and the standard deviation was 36%, would we then use 0.8 and 0.36 instead?

[@mattsamelson4975]

Brandon, Thank you again for your videos. Others have expressed the valve better than I ever could. Question. In. this video we are estimating the population SD (especially when using the range formula). If estimating or unsure of the population SD, shouldn't we use the t value instead of the z value in the respective calculations? Thank you in advance.

[@greenstrokesart]

I'm trying to solve this problem, and just couldn't get the right answer. The Bureau of Alcohol, Tobacco, and Firearms (BATF) has been concerned about lead levels in California wines. In a previous testing of wine specimens, lead levels ranging from 53 to 680 parts per billion were recorded. How many wine specimens should be tested if the BATF wishes to estimate the true mean lead level for California wines to within 10 parts per billion with 95% confidence? Thanks

[@remyohajinwa229]

thanks, what is planning value

[@arahmanabdelrahman6661]

Verbally: a thumb up Thanks a lot You have paved the way thro to a tasty stat. I have a question:- from does this confidence level come? On what base do I decide my confidence level?

[@BrandonFoltz]

Choosing a confidence level is a tradeoff between Type I and Type II error. That is why 95% is used most often since it offers a balance between the two error types. I have videos on Type I and Type II error if you need more help. Thanks!

[@najibabdullah9328]

Hi Brandon I love your video, I have question on sample size. If I have 3 parts measured 5 times each by 2 operator, what is my sample size then. is it 3 or 30? and for dof what will be the figure 2 or 29? Thanks in advance

[@tamergomaa5494]

fantastic discussion

[@ajt5021]

Thank you so much, your video was great. How can I see all the videos that you have posted?

[@salmaatiya6330]

Hello, for Example 4, using the Z distribution table, I am really confused as to why you chose, a Z score of 2.576 for 99% instead of 2.33 and 1.645 for 90% instead of 1.289? By the way, your videos are a blessing! Thank you!

[@wilfredosalinas4876]

Thank you for your videos!!!

[@LearnerCB246]

Sir can I use the above formula to calculate the population size to determine my sample size. 95% (1.96) and ME = 5% n= ?, population size = 300 lets say I am doing a school survey how many students would I need to survey in the 300 to get 95% and be within my margin of error of 5%.

[@renayachan5714]

sir, does m also means the width of the confidence interval?

[@denniswest4132]

Why aren’t we using t distribution since we are estimating the pop standard deviation?