Sum of squares

Definition

The sum of squares (SS) is a measure of the total variability within a data set. It quantifies the deviation of individual data points from the mean.

5 Must Know Facts For Your Next Test

1. Sum of squares is used to calculate variance and standard deviation.
2. In ANOVA, it helps partition the total variation into components attributed to different sources.
3. There are different types of sums of squares in ANOVA: Total Sum of Squares (SST), Between-Groups Sum of Squares (SSB), and Within-Groups Sum of Squares (SSW).
4. The formula for Total Sum of Squares (SST) is $$ SST = \sum (X_i - \bar{X})^2 $$ where $X_i$ are individual data points and $\bar{X}$ is the mean.
5. Sum of squares is essential for calculating the F-ratio in ANOVA, which determines if there are significant differences between group means.

Review Questions

• What role does the sum of squares play in calculating variance?
• How is Total Sum of Squares (SST) calculated in ANOVA?
• What are the different types of sums of squares used in ANOVA?

Related terms

Variance: A measure of how much values in a dataset deviate from the mean. Calculated as the average squared deviation from the mean.

ANOVA: Analysis Of Variance, a statistical method used to compare means across multiple groups to see if at least one differs significantly.

F-Ratio: A ratio used in ANOVA that compares between-group variability to within-group variability. Calculated as $$ F = \dfrac{MSB}{MSW} $$ where MSB is Mean Square Between groups and MSW is Mean Square Within groups.