Sum of squares within groups: what it means and how to read it
In the report: ssw — The spread of values around their own group mean, summed over all groups.
How to read it
The other ingredient of F: how much individuals differ within their own group — the part that the groups do not explain.
In plain words
The same shop owner knew her three shops differed, but the days inside each shop differed too: some days sold far more than others. She wanted one number for how far the days are from their own shop's average. She counted ssw and it came out 54000. If every day in a shop had sold exactly the same, ssw would be 0, and the more the days jump around, the bigger it gets. Next to ssb, which was 10000, she can see that most of the ups and downs in sales go with the day, not with the shop. It is the other building block of the main result.
How it is computed
ssw = Σᵢ Σⱼ (xᵢⱼ − x̄ᵢ)²Example
The cell with ssw 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
- 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.
- Mean square — The sum of squares divided by its degrees of freedom.
Get it in your sheet
One formula in a cell gives the whole report, Sum of squares within groups included. ALS Stats is a free add-on for Google Sheets™.
Install ALS Stats from Google Workspace Marketplace (opens in a new tab)