Posthoc comparisons: what it means and how to read it
In the report: Posthoc tukey test at CI — Posthoc (pairwise) comparisons: every pair of groups compared after the ANOVA, with p corrected for the number of comparisons. Shown only when the ANOVA is significant (p < 0.05) and there are at least three groups — unlike SPSS ONEWAY, which prints a requested posthoc table whatever the ANOVA shows.
In plain words
A gardener tried three plant foods: A, B and C. The first test of all three together said the plants did not all grow to the same height, but not which plant food was different. So the add-on compared every pair: A with B, A with C and B with C. The answer: A and B looked alike, and plants with C were about 8 centimeters taller than with either of them, which was hard to put down to chance alone. With many pairs, luck can fool you more easily, so the add-on is stricter with each pair. These pairs appear only when the first test found a difference and there are at least three groups.
Example
The cell with Posthoc tukey test at CI 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
- Mean difference — The mean of the first group minus the mean of the second.
- Standard error of the difference — How much the mean difference would vary from sample to sample.
- 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).
Get it in your sheet
One formula in a cell gives the whole report, Posthoc comparisons included. ALS Stats is a free add-on for Google Sheets™.
Install ALS Stats from Google Workspace Marketplace (opens in a new tab)