Mean square within groups: what it means and how to read it
In the report: msw — The within-group sum of squares per degree of freedom: the pooled variance of the groups.
How to read it
ssw per degree of freedom — the average variation inside the groups. In the classic ANOVA F = msb / msw; after Welch the F is computed differently.
In plain words
The shop owner had ssw = 54000 for the days inside her three shops, 150 days in all. She wanted the usual difference between days inside one shop, in a form she could set next to msb. She counted msw and it came out about 367. Now she can compare: msb was 5000, far bigger than 367, so the shops are much farther apart than ordinary ups and downs from day to day would lead her to expect. In the classic version of the test, the main result is just these two set against each other. After Welch's version that no longer holds.
How it is computed
msw = ssw / (N − k)Example
The cell with msw 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
- 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.
- Sum of squares between groups — The spread of the group means around the grand mean, weighted by group size.
- Sum of squares within groups — The spread of values around their own group mean, summed over all groups.
Get it in your sheet
One formula in a cell gives the whole report, Mean square 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)