Sum of squares between groups: what it means and how to read it
In the report: ssb — The spread of the group means around the grand mean, weighted by group size.
How to read it
An ingredient of F: how much the group averages differ from the overall average. You rarely report it; it is shown for checking and for SPSS-style tables.
In plain words
A shop owner had three shops that sold 90, 100 and 110 dollars a day on average over 50 days each, while all three together averaged 100. She wanted one number for how far apart the shop averages are. She counted ssb and it came out 10000. On its own that number is hard to read, but she knows how it behaves: if all three shops had averaged exactly 100, it would be 0, and the farther apart the shops, the bigger it gets. She does not put it in a report. It is one of the building blocks of the main result of the test.
How it is computed
ssb = Σ nᵢ(x̄ᵢ − x̄)², x̄ — the mean of all values.Example
The cell with ssb is selected in each report; point at a label to see its note.
- — the sample data (50 rows) the examples use
- — classic one-way ANOVA
=STATS_ANOVA(Data!A1:T51, "x1,x2") - — new syntax, 3 reports
=STATS_ANALYZE(Data!A1:T51, "PAIRED('before,after', 0.99, 'greater') ANOVA('x1,x2,x') DESCRIPTIVE('mean,std,n', 'x1,x2')")
Where you see it
STATS_ANOVA— One-way ANOVA: each selected column is a group. Classic (Student) or Welch ANOVA, chosen by welch (auto by default), with homogeneity of variances and post-hoc comparisons.STATS_ANALYZE— Runs several analyses on one range and returns one report.
Related values
- Sum of squares within groups — The spread of values around their own group mean, summed over all groups.
- Mean square between groups — The between-group sum of squares per degree of freedom.
- Mean square within groups — The within-group sum of squares per degree of freedom: the pooled variance of the groups.
- ANOVA of the model — Whether the model as a whole explains Y: the variance of Y split into the part the model explains (Regression) and the rest (Residual), with the F test — as the SPSS ANOVA table of a regression.
- Sum of squares — The sum of squares of each part of the variance.
Get it in your sheet
One formula in a cell gives the whole report, Sum of squares between groups included. ALS Stats is a free add-on for Google Sheets™.
Install ALS Stats from Google Workspace Marketplace (opens in a new tab)