Mean square between groups: what it means and how to read it
In the report: msb — The between-group sum of squares per degree of freedom.
How to read it
ssb per degree of freedom — the average variation between the groups. In the classic ANOVA F = msb / msw; Welch's ANOVA reports its own weighted F, so there the ratio differs from F.
In plain words
The shop owner had ssb = 10000 for her three shops, but a big number like that is hard to compare with anything. She wanted the usual difference between the shops for each piece of information behind it. She counted msb, the 10000 shared out over the 2 degrees of freedom between groups, and it came out 5000. Now she can put it next to msw, the same kind of number for the days inside a shop. In the classic version of the test, the main result is just these two set against each other. In Welch's version that result is worked out another way, so there they do not match.
How it is computed
msb = ssb / (k − 1)Example
The cell with msb 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 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.
- Sum of squares between groups — The spread of the group means around the grand mean, weighted by group size.
Get it in your sheet
One formula in a cell gives the whole report, Mean square 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)