ANOVA (Analysis of Variance) and Sum of Squares | Statistics Tutorial #26 | MarinStatsLectures

ANOVA (Analysis of Variance) and Sum of Squares: Learn how to calculate and interpret sum of squares in the context of ANOVA and more with examples.

▶︎▶︎ In this ANOVA video tutorial, we learn about sum of squares calculations and interpretations, the explained sum of squares, the unexplained sum of squares, between group and within group variability, signal and noise and the larger concept of Analysis of Variance (ANOVA) through examples.

Analysis of Variance ANOVA is a concept in the statistical sciences (One-Way analysis of variance is the hypothesis test many are familiar with)
▶︎ What is the Total Sum of Squares (SST)? It is a measure of the total variability in Y. In fact, it is the numerator in the formula for calculating the variance of Y.
▶︎ What is Between group Sum of Squares (SSB) and Within group Sum of Squares (SSW)? The first thing to mention is that SST=SSB+SSW. The total sum of squares can be divided up into 2 parts...the amount of the sum of squares that can be explained by X (SSB) or the variability between groups, and the amount of the total sum of squares that is unexplained by X (SSW) or the variability that goes on within a group.
▶︎ What are the other names used for Between Groups Sum of Squares (SSB)? Explained Sum of Squares, Treatment Sum of Squares (SSt), Model Sum of Squares (SSm), Regression Sum of Squares (SSr). There are more. Also, these can all be reversed in order, such as Sum of Squares Treatment, and so on...
▶︎ What are the other names used for Within Group Sum of Squares (SSW)? Unexplained Sum of Squares, Sum of Squared Error (SSe), Sum of Squared Residuals (SSr). There are more. Also, these can all be reversed in order, such as Residual Sum of Squares, and so on...

▶︎ In the following tutorials we will introduce the calculation of the test statistic for one-way anova, conducting post-hoc multiple comparisons and show how to implement one-way ANOVA

■Table of Content:

0:01:02 What is the overall mean or grand mean in statistics?
0:01:15 What is Total Sum of Squares and How to Calculate it?
0:01:44 Total Sum of Squares Formula
0:02:13 Total sum of squares visual explanation
0:02:37 Explained Sum of Squares and Unexplained Sum of Squares with example
0:07:01 Between group variability and Within group variability
0:07:21 Visual (graphical) Explanation of explained and unexplained sum of squares
0:09:04 The sum of squares between groups or explained sum of squares or the between groups variance or the mean squared between groups formula: step by step
0:11:01 The sum of squares within groups or Unexplained sum of squares or the within groups variance or the mean squared within groups formula: step by step
0:13:30 Sum of Squares Formula visual explanation
0:15:05 what is sum of squares treatment or sum of square regression
0:15:17 what is the mean square treatment or mean squared regression
0:15:30 what is sum of squared error or squared residual error
0:16:51 what is signal and noise
0:17:20 introducing the test statistic for ANOVA (analysis of Variance) test

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[michaelhealey]

You deserve a Medal of Freedom. Thank you.

[Tntpker]

How does this not have more views? 10 times better than Crashcourse statistics series, because you go more indepth regarding the math

[buihung]

The fact that all books and blog posts lack of consistency in naming concepts is one of the main reasons why I loved your lectures. You use 1 and you stick with it till the end.

[MarvelousNysa]

This was so so helpful, I don't think this has ever been so clear to me before, thanks!

[donovanlucibello]

Another great video Mike, you have a gift for demystifying stats.

[ayman]

I cannot thank you enough! the whole playlist is amazing!

[baotranquoc]

This is the most in-depth tutorial about ANOVA I have ever seen. Thank you for sharing your knowledge. 1 subscribe for you. Help me alot in the upcoming final exam.

[Pedro-uoss]

Best ANOVA explanation i have ever seen !

[DM-qbjm]

Thank you for putting together such a clear and thoughtful video giving us the intuition behind ANOVA!! This is exactly what I was looking for.

[ahmednafir]

One of my absolute favorite youtube channels. The effort put into making these videos is amazing, and it is much appreciated indeed. Thank you Martin, you are a legend. Keep up the great work 🙌

[VenkatAkkinepally]

This was ridiculously well explained. Thank you so much, definitely deserves more views.

[rakeshk.]

All of your videos are very nicely explained and refreshing to watch... Thank you!

[Minely]

This is the best explanation I have ever found for the sum of squares. After 10 years I can clearly understand what this means. Thanks a lot! I am your new suscritor.

[zuhaibalisiddiqui]

Great and simple way of teaching you clear my much of the doubts related to anova...

[effylu]

hi Martin, thanks for your extraordinary video, now I have a much better understanding of ANOVA now.

[irazibbu]

This is one of the best videos on the topic!

[bincynarath]

It was one of the best explanations, I ever heard. Great video !!! Thank you :)

[asimbuyumwangala]

Thank you so much. My lectures use the terms SStreatment and SSerror so now it all makes so much sense ❤️

[sriderthiru]

wow .. that was so clearly explained.. amazing video..

[RudradeepMukherjee]

Thank you Prof. Marin for your great videos. They give a gist of the thought-processes that the statisticians used to create these tests.
For proper study and getting hands-on experience with exercises, do you recommend books?
Thank you for the time you spent on these lectures and the generosity in sharing them to the public.