Statistics 101: To z or to t, That is the Question 

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.

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.

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

I love you Brandon!!! Thanks for believing in me! :D :D

I'm taking an online Stats class and you just did my professors job. Thanks!

+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.

Thank you Brandon! Your explanations are clear and thorough. I also greatly appreciate your sincere motivational touch to the videos-very inspiring!

Awesome video. You are helping a lot of students. So keep up the good work!!

Your Statistic videos are the clearest, and, most effective! Thank you Brandon! :) You are helping me understand everything. You are awesome!

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.

your videos are truly awesome! you consistently do a great work! thank you so much for posting them!

A guy with zero stats knowledge can also picl this up. It's so amazingly described. Thanks Brandon. Love from India.

Your videos are really helpful. I wish my stat professor could explain some basic concepts as clearly as you do.

The best way one can explain Z and T distributions for non-statistics major. Thanks.

thank you for spending your time doing these videos, trying to help the wife with her degree and needed a good explanation.

My all appreciations for your quality teaching !! Keep it up. World need perhaps lie you many many teacher with passion as you have.

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

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 :)

Thank you very much Brandon; the video helped me refresh some of the basics; really enjoyed watching it!

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.

amazing, learnt the whole concept because of this video and was able to ace through the questions! thank you so much!

We, student of statistics really thankful to you, sir 😊 please keep helping us doing more tutorial on statistics ☺

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.

great lesson. linking with examples is really an effective way to help understand the concept. thanks so much!

I wish you were my professor! You explained it so clearly. Good job Brandon!!

Thanks Brandon. You are my new superhero :)

Thank you for adding clarity in your explanations of z or to distributions.

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!

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.

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.

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.

Sweet nugget of wisdom! This was a missing chunk of logic in my brain. Thank you :)

Wow! This is the best explanation since I've tried to learn stat!

I love your videos!!!! thank you so much for making them you have helped me so much!

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.

@brandon Many thanks from India, you have been such an amazing teacher. You made a complex subject like stats-a cakewalk for the students.

I would like to say, Thank you for making this video, I really appreciate it

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

Love Dr. Foltz! He simplifies the most complex material.

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.

You are the best. Thank you Brandon for making these videos.

Thank you so much. I just love your wonderful videos simplifying the complex topics. Thanks a lot.

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.

I love your explanation. Excellent video. Thank you

Hi Wei Chen! Thank you. :) But YOU are the great person for committing to learning, growing, and improving. All the best! - B

Thank you very much for taking the time to make these videos, your explanations are always very short, clear and simple.

great explanations! thank you!

thank you... i am a distance student with an exam in 3 days. you explain slowly and clearly!

The best stats videos.

Great explanation! This benefited my learning in my statistics course

Great video Brandon, keep them coming!

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, Brandon!

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.

Thank you for this video. Well explained in simple language.

thanks a lot. i was very much confused about the differentiation. now i am very clear.

This was simply awesome!! Thank you so much. Tee

Mr, Foltz excellent explanation, as a Regulatory and Manufacturing Process and Project Manager I would like to thanks for such extraordinary lesson!

Thank you so much! Keep making videos :D

Really Great Effort; Thank you, Brandon, ☺ Thank you

Thank you for giving such detailed information.

This was so helpful. Thank you

I have really been enjoying your videos. They have helped tremendously. Thanks!

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.

Thank you for doing this.

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

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.

You are doing undoubtedly GREAT, sir ✌ Thanks for helping us 😊 (From Bangladesh)

A very good clarification! Thank you!

Really outstanding youtube videos on statistic. Thank you. I hope you keep doing them as it has helped me a lot.

Another awesome video:) Thank you so much!

Great Video--very helpful to the typical layman as myself.

Just amazing . Thank you very much !

Awesome video! Thank you!

As always Brandon, great stuff.

thank you Brandon this was really helpful

thank you for the explanation and motivation words..

Brandon! You are a gift on RU-vid.💕 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.

Thanks,it help me a lot, you are the great man

Very helpful! Thank you so much!

Superb tutorials!

Way better than my instructor. Thank you!

Amazing video! I was really able to understand z and t distribution and degrees of freedom.

Good Work!

This was great stuff

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) :)

thanks..i was drowning in the ocean of stats..your video gave me the lifeline..!!!!

Brandon you the best teacher ever

Thank you, Brando.

Great video.

Awesome Video Sir..keep up the good work :)

very good video- understand material fully

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 🙏

Great video thanks

Thank you. 👍👍👍

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 Brandon :)

Fantastic!