Mean square

Definition

Mean square is the average of the squared deviations from the mean. It is used in ANOVA to measure variance within and between groups.

5 Must Know Facts For Your Next Test

1. Mean square is calculated by dividing the sum of squares by its associated degrees of freedom.
2. Within-group mean square (MSW) estimates variance within each group.
3. Between-group mean square (MSB) estimates variance among group means.
4. The F-ratio in ANOVA is the ratio of MSB to MSW, used to determine statistical significance.
5. Higher MSB relative to MSW suggests significant differences between group means.

Review Questions

• How do you calculate mean square?
• What does a higher between-group mean square indicate?
• Why is the F-ratio important in ANOVA?

Related terms

Sum of Squares:

A measure of variability that sums the squared differences from the mean.

Degrees of Freedom:

The number of independent values or quantities which can be assigned to a statistical distribution.

F-Ratio: $\frac{MSB}{MSW}$, used in ANOVA tests to compare variances and test hypotheses.