Mean squares are described as?

Mean squares are described as?

• A. A measure of average variability obtained by dividing a sum of squares by its degrees of freedom.
• B. The total variability in the observed scores.
• C. The square root of variance.
• D. The mean of all squared residuals.

Answer: (A)

Mean squares are averages of squared deviations. You obtain a mean square by taking a sum of squares and dividing it by its associated degrees of freedom, turning a total amount of variation into an average per degree of freedom. This provides an estimate of the variance component for that source (for example, variability due to a factor or due to error) and is what ANOVA uses to compare different sources of variation via F tests. This differs from the total variability, which is the sum of squares without dividing by degrees of freedom. It also isn’t the square root of variance, which is the standard deviation. And while the mean of all squared residuals sounds like a related idea, that specific quantity is the mean squared error in regression contexts; mean squares in ANOVA are SS divided by their respective df, giving an appropriate average variation for each source.

Mean squares are averages of squared deviations. You obtain a mean square by taking a sum of squares and dividing it by its associated degrees of freedom, turning a total amount of variation into an average per degree of freedom. This provides an estimate of the variance component for that source (for example, variability due to a factor or due to error) and is what ANOVA uses to compare different sources of variation via F tests.

This differs from the total variability, which is the sum of squares without dividing by degrees of freedom. It also isn’t the square root of variance, which is the standard deviation. And while the mean of all squared residuals sounds like a related idea, that specific quantity is the mean squared error in regression contexts; mean squares in ANOVA are SS divided by their respective df, giving an appropriate average variation for each source.