Mean square: what it means and how to read it
In the report: MS — The sum of squares divided by its degrees of freedom.
How to read it
F is MS Regression divided by MS Residual.
In plain words
A teacher's table showed 450 for the part of the differences in marks that her guess from study hours matches, and 150 for the part left over. But the two rest on very different amounts of information: the matched part on 1 column, the left-over part on 38 degrees of freedom from her 40 pupils. So the two totals could not be compared fairly. She looked at MS, which gives each part per degree of freedom: 450 for the matched part and about 4 for the left-over part. Now she can see the matched part is far bigger than the leftover noise. Set against each other, these two give the main result of the table.
How it is computed
MS = SS / dfExample
The cell with MS is selected in each report; point at a label to see its note.
- — the sample data (50 rows) the examples use
- —
=STATS_LINEAR(Data!A1:T51, "y", "x1,x2", 0) - — old syntax: regression steps, one-sample test against 15
=STATS_ANALYZE(Data!A1:T51, "linear(y|x1|x2) oneSample(x1|15)")
Where you see it
STATS_LINEAR— Multiple linear regression (OLS) with hierarchical steps separated by | and interactions a*b.STATS_ANALYZE— Runs several analyses on one range and returns one report.
Related values
- 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.
- 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.
Get it in your sheet
One formula in a cell gives the whole report, Mean square included. ALS Stats is a free add-on for Google Sheets™.
Install ALS Stats from Google Workspace Marketplace (opens in a new tab)