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.
ANOVA in R with Free datasets for R and R scripts examples: (https://goo.gl/kY4kyE)
ANOVA: F Statistic and P Value Video: (   • ANOVA Part III: F Statistic and P Val...  )

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▶︎▶︎ 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



▶︎▶︎ Watch More

▶︎ R ANOVA Tutorial: https://goo.gl/kY4kyE
▶︎ Analysis of Variance (ANOVA) Statistics and ANOVA with R: https://bit.ly/2zBwjgL
▶︎ Two Sample t test for independent groups    • Two Sample t-test for Independent Gro...  
▶︎ Paired t test    • Paired t Test | Statistics Tutorial #...  
► Intro to Statistics Complete Course: https://bit.ly/2SQOxDH
►Data Science with R Complete Course https://bit.ly/1A1Pixc
►Getting Started with R (Series 1): https://bit.ly/2PkTneg
►Graphs and Descriptive Statistics in R (Series 2): https://bit.ly/2PkTneg
►Probability distributions in R (Series 3): https://bit.ly/2AT3wpI
►Bivariate analysis in R (Series 4): https://bit.ly/2SXvcRi
►Linear Regression in R (Series 5): https://bit.ly/1iytAtm



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