Mean square

Definition

Mean square is the average of squared deviations from the mean. It is used in ANOVA to compare variances and calculate the F-ratio.

5 Must Know Facts For Your Next Test

1. Mean square is calculated by dividing the sum of squares by their respective degrees of freedom.
2. In one-way ANOVA, there are two mean squares: Mean Square Between (MSB) and Mean Square Within (MSW).
3. MSB measures the variance between group means while MSW measures variance within groups.
4. The F-ratio is calculated as MSB divided by MSW.
5. A larger F-ratio indicates a greater likelihood that the group means are significantly different.

Review Questions

• How do you calculate mean square in ANOVA?
• $What does MSB represent in an ANOVA test?$
• $What is indicated by a larger F-ratio in terms of group means?$

Related terms

Sum of Squares (SS): A measure of total variability; it is partitioned into components such as SS Between and SS Within.

Degrees of Freedom (df): The number of independent values that can vary in an analysis without breaking any constraints.

$F$-ratio: $The ratio of Mean Square Between to Mean Square Within, used to determine if there are significant differences between group means.$