The more detail the better. Thanks! We learned at the outset of the semester som

Question

The more detail the better. Thanks!

We learned at the outset of the semester some differences between Variance and Standard Deviation. One important difference is that variances (of independent variables) can be effectively added together to yield new information about the combination, while standard deviations cannot. We’re used to taking the square root of the Variance to get the Standard Deviation, although in ANOVA we don’t do that. Instead, we apply a Degree of Freedom to find a Mean Squared.

Discuss how and where the adding of Variance concept is being used in the ANOVA technique, and then discuss what is being described by the Mean Squares being calculated.

Explanation / Answer

Sum of square between groups: For the sum of the square between groups, we calculate the individual means of the group, then we take the deviation from the individual mean for each group. And finally, we will take the sum of all groups after the square of the individual group.
Sum of squares within group: In order to get the sum of squares within a group, we calculate the grand mean for all groups and then take the deviation from the individual group. The sum of all groups will be done after the square of the deviation.

Mean squared error. ... In statistics, the mean squared error (MSE) ormean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures the average of the squares of the errors or deviations—that is, the difference between the estimator and what is estimated.

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