Why are degrees of freedom (n-1) used in Variance and Standard Deviation

Tutorial on how to understand degrees of freedom and why n-1 is used instead of just n for sample variance. Includes the reason why n-1 is use for a sample, but for the population variance. Video includes a visual and numerical example. The n-1 is used to adjusted the variance because of the error between the sample mean and the population mean.

Video on How to Calculate Standard Deviation

Created by David Longstreet, Professor of the Universe, MyBookSucks

[statisticsfun]

The reason for n-1, is in standard deviation (or variance), we are estimating only 1 variable. In a linear regression equation degrees of freedom are n-2 because we are estimating two variables (y intercept and slope of the line).

[statisticsfun]

Thank you for you compliments and feedback. This idea of degrees of freedom keep coming up, so I am working on another video that discusses degrees of freedom across statistics (standard deviation, in regression, in chi square, ANOVA, etc.)

The reason for n-1, is in standard deviation (or variance), we are estimating only 1 variable. In a linear regression equation degrees of freedom are n-2 because we are estimating two variables (y intercept and slope of the line).

[k.y.y]

The best part of your video is when you show the population curve and the sample curve. By comparing the two curves, the idea on why sample variance (or sample standard deviation) is smaller than population variance becomes very clear and easily understandable. Well done!

[pbog]

This is doesn't explain df. All you really did was show that n grows, subtracting just 1 has a smaller effect. You didn't need to go to all this trouble to make that point. This video is very misleading.

[nihleigleca]

If only all the instructors are this patient, clear, and informative 👍👍👍

[statisticsfun]

Yes I am. I have been teaching at the university level for about 10 years. AND thanks for the compliment.

Make sure you like MyBookSucks on FaceBook (see link in video description). This will help others find the educational videos.

[statisticsfun]

I plan to create videos for degrees of freedom for all the statistical tests including ANOVA. Since you asked, ANOVA will be the next degree of freedom video I create. I hope you saw the ANOVA videos on my channel -- I think I have 6 or so.

[statisticsfun]

The standard error of the mean is the standard deviation divided by the square root of the sample size. I don't have any videos on the quadratic mean, but I need to create some.

[statisticsfun]

Sorry Ryan, nothing on Monte Carlo Simulation.

Make sure you like MyBookSucks on FaceBook (see link in video description). This will help others find the educational videos.

[MrMjps]

I love your illustration method of explaining stats concepts, by far the most thorough method I've seen yet.

[drupeerd]

Ugh. This doesn't explain "Why are degrees of freedom (n-1) used in Variance and Standard Deviation". It explains "What happens when (n-1) is used in Variance and Standard Deviation".

[statisticsfun]

Technically I think you are correct. I am trying to show as n (sample size) gets large it equal N. I probably should have said the n --> N explicitly.

Thanks for the feedback and it is much appreciated.

[statisticsfun]

Thanks for the compliment. I use a variety of different software including photoshop, illustrator, HTML5, Final Cut, GarageBand and a few other products. Each video takes me a long time to create. My rule of thumb is each minute of video takes about 12 hours to create, so a 7 minute video takes me about 84 hours of development time.

[statisticsfun]

Do you mean Margin of Error? Because I do have some videos on Margin of Error or Confidence Intervals too. If you go to my channel statisticsfun and search on Margin of Error.

[mrwillia]

i have returned to school, after a couple decades, taking statistics. When I don't understand these subtleties I am left lost and unable to connect the dots. This video was tremendously helpful. Thank you.

[jannamoen]

I'm a graduate student in the third statistics class of my academic career, and I feel like I finally understand degrees of freedom after watching this. Thank you so much!!!

[statisticsfun]

Also, I have a video on "Margin of Error" if you go to the channel statisticsfun, you can search for the video. That should help you understand the relationship between sample size and error.

[kengking]

This is the kind of explanation that all my prof have tried to learn over the years and never mastered... I can sense alot of preparation and passion you have in this subject to teach than those academic prof who earns 5 digits and contribute to confused students so that they can retain in their academia world

[statisticsfun]

Interesting? If this is the case, then how does sample size impact margin of error? Look at the formula before you answer the question.

[dipayansarkar]

Simplification is not easy. And you have done the simplification. Kudos.