SS Between Calculator

Formula

To calculate the Sum of Squares Between (SSB):

\[ SSB = \sum n \cdot (M - GM)^2 \]

Where:

\(SSB\) is the sum of squares between groups
\(n\) is the number of scores in each group
\(M\) is the mean score for each group
\(GM\) is the grand mean (the mean score of all scores)

SS Between Definition

SS Between, also known as Sum of Squares Between, is a statistical measure used in analysis of variance (ANOVA). It quantifies the variability between group means in a dataset. In other words, it measures how much each group's mean differs from the overall mean of the data. A larger SS Between indicates a greater difference between group means, suggesting that the grouping variable has a significant effect on the data.

Example Calculation 1

Let's assume the following values:

Group Sizes: 5, 5, 5
Group Means: 10, 20, 30
Grand Mean: 20

Using the formula:

\[ SSB = 5 \cdot (10 - 20)^2 + 5 \cdot (20 - 20)^2 + 5 \cdot (30 - 20)^2 = 500 + 0 + 500 = 1000 \]

The Sum of Squares Between (SSB) is 1000.

Example Calculation 2

Let's assume the following values:

Group Sizes: 3, 4, 3
Group Means: 15, 25, 35
Grand Mean: 25

Using the formula:

\[ SSB = 3 \cdot (15 - 25)^2 + 4 \cdot (25 - 25)^2 + 3 \cdot (35 - 25)^2 = 300 + 0 + 300 = 600 \]

The Sum of Squares Between (SSB) is 600.