Standard deviation of the differences: what it means and how to read it
In the report: sdDelta — The sample standard deviation of the row-by-row differences (n − 1).
How to read it
How much the change differs from person to person. A small sdDelta next to a clear meanDelta means nearly everyone changed the same way.
In plain words
A teacher asked 30 students to take a quiz before and after a course. On average they gained 5 points. But did everybody gain about 5? She asked for sdDelta. It came out 1.5, so nearly everyone changed in the same way, with gains between about 3 and 7 points. If it had come out 10, some students would have gained 25 points and others would have lost 15. Now she knows how much the change differs from student to student, and that the 5 point gain is true for almost the whole class.
How it is computed
√(Σ (d − d̄)² / (n − 1)), d = x₁ − x₂Example
The cell with sdDelta is selected in each report; point at a label to see its note.
- — the sample data (50 rows) the examples use
- —
=STATS_PAIRED(Data!A1:T51, "before,after",0.95,"two-sided") - — 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_PAIRED— Paired-samples t-test for two related measurements (e.g., pre vs post).STATS_ANALYZE— Runs several analyses on one range and returns one report.
Related values
- Mean of the group — The mean of the values of the group.
- Standard deviation of the group — The sample standard deviation of the group (n − 1).
- N — The number of valid values in the group of the row.
- Mean rank — The average rank of the values of the group; rank 1 is the smallest value of all groups together.
- Sum of ranks — The sum of the ranks of the values of the group.
Get it in your sheet
One formula in a cell gives the whole report, Standard deviation of the differences included. ALS Stats is a free add-on for Google Sheets™.
Install ALS Stats from Google Workspace Marketplace (opens in a new tab)