Statistics 101: To z or to t, That is the Question
Vložit
- čas přidán 11. 09. 2024
- Statistics 101: To z or to t, That is the Question.
In this video, we explore the difference between the z- and t-distributions. Many formulas in stats look exactly the same, except one has a z-term and the other has a t-term. Why? We also talk about sampling and sample size since they are related to the t-distribution concept.
My playlist table of contents, Video Companion Guide PDF documents, and file downloads can be found on my website: www.bcfoltz.com
In a nut shell: Use the z statistic (normal distribution) when the population variance is known - PERIOD. The only reason to use the t distribution is when the population variance is not known. In that case you have to estimate the population variance by substituting the sample variance which introduces error into the calculation. So, to repeat, use the z statistic if the population variance is known. If the population variance is NOT KNOWN, then use the t distribution if your sample size is less than 30 - PERIOD. If the sample size is 30 or greater then you can use either the z or t distribution (whichever your teacher prefers). The differences will be so small as to not have any real practical significance.
If population variance is not known and we have a sample size say ex. n = 50, should we use T or Z distribution?
@@AbhishekSingh-uq6ux Since population variance is unknown most people would say to use t-distribution. But the difference between z and t will be insignificant. Therefore either one works. Use the one your professor prefers.
@@randallblake1213 thanks a lot.
What if the sample is smaller than 30, but the population std. dev. is known?
@@kufreibanga7980 use the T distribution ( calculate the sample's standard deviation)... because the sample size is less than 30 ... so the standard error of the T and Z distribution will be different....
Always keep in mind that the T and Z distribution is a continuous probability distribution of test statistic of a sample and not the data point of the sample...
so sample size matters.
I'm taking statistics by distance education, and your videos have been instrumental in helping me when I get stuck. Your positive uplifting statements have made me cry a few times when I have been really frustrated and have no fellow students or a professor to bolster my spirits. Thanks for your efforts!
Thanks for the comment! I have divided more recent videos into parts. Viewers can watch these longer ones in segments using the stop button. However I am trying to fill the niche of full length tutorials / lessons for people who may have missed...(cough...skipped) a class. :) The length may turn away some viewers, but the deeper understanding I seek takes time. It is still shorter than a 50 minute class and you can carry it with you :P All the best, B.
To z or t, seems like thats the same as always t, however is there a performance reason since the z hasn't been discarded as obsolete or legazy? Would you please consider to explain the degrees of freedom, as its probably quite intuitive if one understands it. The problem with stat/prob is that its complex and seems not like math, but magic. Not having an understanding of DOF just adds unhealthy carbs to that feast.
You are simply awesome, I wish my college professor had explained things in such an intuitive manner. Seen many of your videos, I liked each and every one of them.
Great video but if you are specifically looking for when to use z or t, you can TOTALLY SKIP and start watching until minute 16:30
Thank you Barbara!!
Thank you so much lol
Thank you otherwise that would have been waste of 16:30 minutes as I have paper and short of time. Thanks and regards
Wish I would have read your comment sooner. I waited 17 minutes to get to the "meat". Looooong intro.
Actually thats the most important part, namely the understanding of why and not just how to do it. This is actually also what Brandon says in the beginning :-) Great video!
I love you Brandon!!! Thanks for believing in me! :D :D
+Brandon Foltz I have been trying to find the right channel that can break down these "seemingly" complicated statistical ideas for quite some time. Your videos place a great amount of emphasis on the "why", which is something that my university professor fails to acknowledge. Furthermore, I am the kind of student that likes to question newly learned information and have trouble with teachers saying "that's just the way it is", without any other clarification. I believe that this explains why most students resent math-based topics, as they never really understand why they are conducting certain operations (memorization of formulas doesn't inspire long-term retention or interest). In most business programs, it is often the stats courses that are branded as being the "most difficult", but the teaching methods are never addressed. Thank you very much for taking the time to make these videos, as well as your encouraging words.
I'm taking an online Stats class and you just did my professors job. Thanks!
The best way one can explain Z and T distributions for non-statistics major. Thanks.
Prem Anand Thanks so much! :)
In short, we use t- test if the SD/variance is unknown and the sample size is less than 30. Thus, we use Z-test if SD/variance is known and the sample size is more than 30. Yet, one twist- you can also use t-test with a sample size more than 30 because both almost overlap in the bell-curve or what you can call as the law of diminishing return.
A guy with zero stats knowledge can also picl this up. It's so amazingly described.
Thanks Brandon. Love from India.
I missed two months of my Applied Statistics course because I found it just too hard to learn and so many x's going around. I scraped thru my exams without the slightest clue of when to use Z, t and chi. Thank you so much for making things so easy to understand. I am actually enjoying Statistics throughout this playlist and I am able to complete some of your thoughts correctly, which means I really am getting Statistics this time. You are a wonderful teacher.
We, student of statistics really thankful to you, sir 😊 please keep helping us doing more tutorial on statistics ☺
thank you for spending your time doing these videos, trying to help the wife with her degree and needed a good explanation.
Hi Wei Chen! Thank you. :) But YOU are the great person for committing to learning, growing, and improving. All the best! - B
You sound exactly like Seth Rogan. At 4 am and 8 hours into course work you're voice is really keeping me going. Thanks for breaking down this material that the TWO University of Phoenix texts skim over.
Thank You for saving my education from a crash, you can explain it so I can understand!! Please make a Statistics 102, with non parametric tests!
Your videos are really helpful. I wish my stat professor could explain some basic concepts as clearly as you do.
I was loosing my sleep that why xls is giving me different confidence internal as compared to manual calculation (which was taught in a course) and now I understand that formula was using z score, while xls was using t score. My sample size was quite small (just 10) and there was considerable difference coming in two. Thank you so much Brandon for such a detailed explanation here
I enjoyed watching all the videos that I have watched so far, the explanations are very clear and you give us confidence to understand statistics, which appears difficult some times, but it is necessary and by the way, interesting to know about. I am teaching a course design of experiments, and it has helped me to set my mind straight on the statistics I need to know about. Thank you so much Brandon, keep up the good work.
Mr, Foltz excellent explanation, as a Regulatory and Manufacturing Process and Project Manager I would like to thanks for such extraordinary lesson!
my final is in 1 day and i have been crying for a week because I never understood the concepts but this video really helped me and your positivity really helped with my confidence, i feel ready for my exam
+Madeline Johnston You can do it. Keep digging. I am pulling for you. It's hard. Push through. Let me know how everything goes.
Hoping for the best! Thank you!
Just an update: your videos have made me feel so comfortable with concepts that I aced the practice exams! Totally prepared for my final!! I recommended these videos to my classmates as well, thank you so much!
We would only use Z if we know sigma or our sample size is greater than 30 (I prefer 100 or greater). The non-normal population distribution shapes can influence small sample sizes. So that is why it is best to take a sample between 30 and 100. The sampling distribution moves towards normality the larger the sample size. (basically that is the case) :)
Everytime I get stuck on a concept, I check your youtube account to see if you have covered. It is nice when I find you have. Thanks
I enjoyed this video. Doing a crash course in statistics to help a friend. For having taken a class ever - Your videos have helped me a lot.
Thank you so much Brandon. You have answered my queries yet again. Finally, it's all making sense. To add comment to the above, I don't believe your videos are too long. I am studying via distance learning and your videos give me the opportunity to attend virtual lectures and make sense of the theory. Keep up the brilliant work.
Thank you for adding clarity in your explanations of z or to distributions.
Awesome video. You are helping a lot of students. So keep up the good work!!
I wish you were my professor! You explained it so clearly. Good job Brandon!!
I just have to comment to thank you for all your great work. You couldn't explain thing more clearly. Watching via VLC with increased playback speed allows me quite quickly to get through topics that my entrance exam book does a lousy job of explaining.
Great video/lesson, Brandon! Keep it coming for people like me who just have a hard time getting their head around these topics! I found the presentation clear, succinct and informative. Above all, it was a pleasure to listen to as often times these topics can be quite tiresome (if not tiring). I even referred your site to my sister who will be taking a course for which she needs to brush up on her stats. Many thanks for an excellent learning resource.
Great video, mate! I'm going to check out some of your others now. I'm struggling in an online EdD stats class. Your encouragement is nice too.
Brandon, I just love your videos and I must say that I hated math but started watching your videos, I kind of have started loving it and also have recommended a lot of friends and guess what, all of them liked your videos so much. Please make more videos on Unsupervised learning as well. Just a request. You are the best tutor I have come across. A big thanks from New York :)
Your Statistic videos are the clearest, and, most effective! Thank you Brandon! :) You are helping me understand everything. You are awesome!
The video is due to be 10 years old this year, but bro Thank You!
Loved your videos, your explanations are amazing and they've built my confidence in completing my access course module for my first practical experiment. Thanks to you I'm able to build and submit my work with the most confidence I've had all year.
Your videos make me feel so much better about myself. Thank you for giving me hope in what I'm learning!
Thank you very much for taking the time to make these videos, your explanations are always very short, clear and simple.
@brandon Many thanks from India, you have been such an amazing teacher. You made a complex subject like stats-a cakewalk for the students.
Love Dr. Foltz! He simplifies the most complex material.
You mentioned that we use the t distribution if we have a sample size less than 30 OR if we do not know our standard deviation. However, if we do not know our population's standard deviation, but our sample size is large enough, the sample standard deviation is a good enough approximation of the population's standard deviation since we can assume normality, thus a z test is sufficient.
Thank You So Much. Now I know why I am using t and z distributions. I have watched you videos on youtube for other math subjects and they too were great. I have subscribed. Keep up the great work.
Epeeñyptp
Manuel Silva Glad to be of help. Keep up the great work.
My all appreciations for your quality teaching !! Keep it up. World need perhaps lie you many many teacher with passion as you have.
thank you... i am a distance student with an exam in 3 days. you explain slowly and clearly!
Thank you Brandon! Your explanations are clear and thorough. I also greatly appreciate your sincere motivational touch to the videos-very inspiring!
Sweet nugget of wisdom! This was a missing chunk of logic in my brain. Thank you :)
You are the best. Thank you Brandon for making these videos.
your videos are truly awesome! you consistently do a great work! thank you so much for posting them!
Thank you Brandon for excellent videos! One comment reg degrees of freedom (df); when I got df explained through a chi-square test it made the concept of df clearer to me (if you have 10 values including the total values the "last" value can only be one value, hence it has no degree of freedom, but all others have it, ie 9 df). I'm not sure if it help others but it certainly helped me.
Hello! Yes I have heard df explained that way (the last value can only be one number).. 4+2+5+x = 15, for the expression to be true x can only be 4, and I have also heard it explained as the number of parameters being estimated in the test / model. It confuses a lot of people so I just kind of present it as a given. Thanks!
thanks..i was drowning in the ocean of stats..your video gave me the lifeline..!!!!
Thanks Brandon. You are my new superhero :)
A very important point that is missed in this video is that z- and t-distributions are not applicable to the original random variable of interest; they are applicable to the estimated mean of that random variable (Note: the estimated mean is itself a random variable). By the central limit theorem, if the mean is calculated using an large number of points then the distribution of the estimated mean is a normal distribution (if infinite points are used, then it is a normal distribution of 0 variance, that is, a Dirac delta function, located at the true population mean). However if a small number of points is used to calculate the mean, then the estimated mean has a t-distribution. In practice, when N=30 or more, the t-distribution is practically the same as the z-distribution, i.e., 30 is "large enough" for most people (for some like Brandon, 30 is not "large enough", 100 is)
Hi and thanks! I cover these topics in the Sampling Distribution video(s). When talking about true t- and z- convergence, n=100 is the sweet spot but in in practical terms using t- with n >= 30 is fine. 😀
The best stats videos.
You are doing undoubtedly GREAT, sir ✌
Thanks for helping us 😊
(From Bangladesh)
great lesson. linking with examples is really an effective way to help understand the concept. thanks so much!
Brandon you the best teacher ever
I have really been enjoying your videos. They have helped tremendously. Thanks!
Brandon! You are a gift on CZcams.💕
One question please? What does it mean there are different t-distributions on every sample size and the role of degree of freedom in it? Please clarify.
This video was helpful. A review of the formulas at the end would have more helpful. I am still asking myself the difference in formula, or is there one? I will check out other postings thank you!
Wow! This is the best explanation since I've tried to learn stat!
Way better than my instructor. Thank you!
This is a wonderful series... I do have one question, why is the threshold of n30 not dependent on population size? I would think that number would change relative to total population? Just curious.
Wow great video ...your explanations is the best I have heard in statistics lessons. You have blessed with a soothing voice and simple way of explaining complex statistics.Many thanks,if there is a God ..may u be blessed :)
Just one question....why did the 't' chose 30 as a cut off why not 29 or 9?
amazing, learnt the whole concept because of this video and was able to ace through the questions! thank you so much!
Really outstanding youtube videos on statistic. Thank you. I hope you keep doing them as it has helped me a lot.
Thank you very much Brandon; the video helped me refresh some of the basics; really enjoyed watching it!
thanks a lot. i was very much confused about the differentiation. now i am very clear.
Great explanation! This benefited my learning in my statistics course
Really Great Effort; Thank you, Brandon, ☺ Thank you
This was so helpful. Thank you
Hey I am sorry to be off topic. I've watched all videos till this point...that's 6 playlists. All the songs that you play at the start of the videos sound good. Could you please share the list of songs that you've used in all your videos 😁 And yes of course your videos are extremely helpful for me to achieve my goals 🙏
Thank you so much. I just love your wonderful videos simplifying the complex topics. Thanks a lot.
Somewhat unrelated but what's that guitar riff in the beginning of this video?
Love the videos! Very useful! Keep it up!
It was a really great video , but it would be even better if you could increase the pace a bit , or maybe create a few new videos for exam preps.
Fear and confusion abating. Thank you for that.
32:00, In other words, the df increases the 'fiddle factor' in the t-distribution.
Hi Prof
can you give us examples of where you might use Z as we in real life would never know the rtue mean of the population and if we did Iam assuming you have the data to make error free predictions . why even look at Z . also even if you sample us 400 you and you still not know the men of population , would we not be using T in any case. You are great in your videos
As always Brandon, great stuff.
Amazing video! I was really able to understand z and t distribution and degrees of freedom.
Glad it was helpful! Thank you for taking the time to watch.
Thank you very much, Brandon!
Thank you very much for making the things simpler.... Concepts are taught very clear and most importantly, it is interesting.... Helping millions to learn and implement....
Great video Brandon, keep them coming!
Superb tutorials!
GOD BLESS. BEST TEACHING
I would like to say, Thank you for making this video, I really appreciate it
I love your explanation. Excellent video. Thank you
Thanks for a great video, Brandon. I'd like to share something I found confusing: you say "the sample size
Aditya, Think of it as
- first pass: If population standard deviation is unknown - we use the t distribution
- If the sample size is greater than 30 (or 100 in some studies) - then using Z distribution and T distribution is almost the same. because at that time the values converge.
- your specific question - if sample size=20 and variance is known - if you know population variance/ standard deviation then you use Z distribution.
Hope that helps
@@funny_tiger11 hey, thanks for clarifying it out :)
Great Video--very helpful to the typical layman as myself.
Awesome! Do you teach Econometrics too ?
Very helpful! Thank you so much!
Thank you for this video. Well explained in simple language.
Are we supposed to already know how to calculate the t-distribution, or have been introduced to it? I understand the concept of using a different calculation to determine probabilities when we're using samples versus the entire population, and that the results of the two different calculations would "converge" as our sample sizes get smaller, but I have no idea how to actually calculate the t-distribution, or to graph it.
Thank you so much! Keep making videos :D
Brandon, is your guitar intro by any chance based on "Animal instinct" by The Cranberries?
On topic: I am gung ho about your videos ;-) thank you very much!
I noticed in each to the graphs comparing the z- and t-distributions for various standard deviations, I am assuming, all the curves seem to at -2 and +2- why?
Awesome video! Thank you!
Thanks,it help me a lot, you are the great man
Thank you for giving such detailed information.
Thank you..
I love your videos!!!! thank you so much for making them you have helped me so much!
My family is from western Pennsylvania, that is to say, the greater Pittsburgh area. I'm writing to draw your attention to the correct spelling.