Adjusted p of the pair: what it means and how to read it
In the report: Adjusted p — The p of the pair corrected for the number of comparisons by the posthoc method.
How to read it
The p of the pair after the correction for making many comparisons at once — this is the one to use. Below 0.05 — these two groups differ significantly. It can be exactly 1: the correction left no difference at all — write p > .99.
Below 0.05 — these two groups differ.
In a paper: "Group 2 scored higher than group 3 (Tukey, p = .021)."
In plain words
A teacher compared four groups, which gave six pairs. Looked at on its own, one pair seemed to stand out. But with six pairs, some will look special by luck alone. She looked at the adjusted p for that pair, which is stricter and counts all six pairs, and it came out 0.21: luck alone would give such a gap about 21 times in 100. Now she knows that pair could easily be luck. For another pair it was about 2 times in 100, and that gap is hard to put down to chance alone. So she uses the adjusted p, not the plain one. It can even come out exactly 1: then nothing of the gap is left.
How it is computed
Tukey, Games–Howell: the studentized range distribution, P(Q(k, df) > |t| · √2).Bonferroni: min(1, m · p), m — the number of pairs.Scheffé: P(F(k − 1, df) > t² / (k − 1)).Example
The cell with Adjusted p 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
- Lower bound of the interval — The lower bound of the confidence interval, at the level in the label.
- Upper bound of the interval — The upper bound of the confidence interval, at the level in the label.
- p of the F change — The p of F Change: P(F(df1, df2) > F Change). Empty when F Change is.
- Confidence interval — The confidence interval of the estimate: its level and its two bounds.
- Confidence level — The confidence level of the interval: ciLevel, 0.95 by default.
Get it in your sheet
One formula in a cell gives the whole report, Adjusted p of the pair included. ALS Stats is a free add-on for Google Sheets™.
Install ALS Stats from Google Workspace Marketplace (opens in a new tab)