Cohen's d: what it means and how to read it
In the report: cohenD — The effect size: the difference in standard deviations, so it does not depend on the units of the data. Empty when there is no spread.
How to read it
How big the difference is, not only whether it exists: p says "not chance", d says "how much". Rough guide (Cohen): 0.2 small, 0.5 medium, 0.8 large; the sign follows the order of the columns.
APA asks for it next to the test: t(98) = 2.10, p = .038, d = 0.42.
In plain words
A coach tried a new warm-up. The runners who used it were 2 seconds faster on average than the others. Is 2 seconds a lot? Times in the group usually differ by about 4 seconds. She counted Cohen's d and got 0.5: the gap is half of those usual 4 seconds. Now she can picture it: take one runner from the new group and one from the old, and the new one is faster in about 64 pairs out of 100, where with no gap it would be 50. Reports call this a medium gap. The number stays the same in minutes instead of seconds. Whether the gap could be luck is a separate question.
Example
The cell with cohenD 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") - —
=STATS_INDEPENDENT(Data!A1:T51, "y,x1", "welch",0.95) - — 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_INDEPENDENT— Independent-samples t-test for two groups: the two selected columns are the groups.STATS_ANALYZE— Runs several analyses on one range and returns one report.
Related values
- Phi — The strength of the relation, from the chi-square: for a 2 × 2 table with the sign of the relation (the sign depends on the order of the categories), for a larger table it equals the square root of χ² / N.
- Cramér's V — The strength of the relation of two categorical variables, from 0 (none) to 1 (one determines the other).
- Eta squared (η²) — The share of the total variance explained by the groups: 0 — none, 1 — all.
- Omega squared (ω²) — The share of variance explained by the groups, corrected for sample size: a less biased η², slightly smaller. Can be below 0 when there is no effect.
- McFadden pseudo R² — How much the model improves the log-likelihood over the model with the intercept only.
Get it in your sheet
One formula in a cell gives the whole report, Cohen's d included. ALS Stats is a free add-on for Google Sheets™.
Install ALS Stats from Google Workspace Marketplace (opens in a new tab)