Cramér's V: what it means and how to read it
In the report: V — The strength of the relation of two categorical variables, from 0 (none) to 1 (one determines the other).
How to read it
A common guide (Cohen) for a 2 × k table: 0.1 small, 0.3 medium, 0.5 large; with more categories on both sides the thresholds are lower.
In a paper: V = .08, χ²(2, N = 50) = 0.31, p = .859.
In plain words
A teacher asked 25 boys and 25 girls which club they joined: chess, art or sport. Does the choice go with being a boy or girl? Boys picked them 10, 8 and 7 times, girls 8, 9 and 8. Cramér's V came out 0.08. It runs from 0, no link, to 1, where the club tells you boy or girl every time. Guess for each club the group with more children in it: boys for chess, girls for art and sport. That is 10 + 9 + 8 = 27 right out of 50, or 54 out of 100, hardly better than 50 for a coin. So boys and girls pick clubs in almost the same way.
How it is computed
V = √(χ² / (N · min(Rows − 1, Columns − 1)))Example
The cell with V is selected in each report; point at a label to see its note.
- — the sample data (50 rows) the examples use
- — with the Chi-Square Tests and Symmetric Measures tables at the end
=STATS_CHI2(Data!A1:T51, "gender", "group", TRUE) - —
=STATS_CRAMER(Data!A1:T51, "gender", "group")
Where you see it
STATS_CHI2— Pearson chi-square test for association between two categorical columns.STATS_CRAMER— Cramer's V effect size for association between two categorical columns.
Related values
- 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.
- Cox & Snell pseudo R² — A pseudo R² from the likelihood ratio; even a perfect model stays below 1.
- Nagelkerke pseudo R² — Cox & Snell R² rescaled so that a perfect model reaches 1.
Get it in your sheet
One formula in a cell gives the whole report, Cramér's V included. ALS Stats is a free add-on for Google Sheets™.
Install ALS Stats from Google Workspace Marketplace (opens in a new tab)