Standard error of the difference: what it means and how to read it
In the report: Standard error of difference — How much the mean difference would vary from sample to sample.
How to read it
How precise the difference is: a small standard error means another sample would give a similar difference. It is used for t and the interval and is rarely reported on its own.
In plain words
A teacher found that third-year students scored 8 points higher than first-year students. She wondered how steady that gap is, since another group of students could give a different one. She counted the standard error of the difference and it came out 1.9. Now she can say that another group would probably give a gap not far from 8, within about 4 points either way. If it had come out about 8 points, the gap could jump almost anywhere, even to zero. She rarely writes this number in her report, but the add-on uses it to work out the other numbers for this pair.
How it is computed
Tukey, Bonferroni, Scheffé: se = √(msw · (1/n₁ + 1/n₂)), msw of all groups.Games–Howell: se = √(s²₁/n₁ + s²₂/n₂), the variances of the two groups only.Example
The cell with Standard error of difference is selected in each report; point at a label to see its note.
- — the sample data (50 rows) the examples use
- — regex selector: every column whose name starts with x
=STATS_ANOVA(Data!A1:T51, "/^x/") - — 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
- Standard deviation of the differences — The sample standard deviation of the row-by-row differences (n − 1).
- 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.
Get it in your sheet
One formula in a cell gives the whole report, Standard error of the difference included. ALS Stats is a free add-on for Google Sheets™.
Install ALS Stats from Google Workspace Marketplace (opens in a new tab)