Effect Size Measure
Cramér's V calculator
How results are checked
Named statistical review pending. Selected automated reference cases are published on the validation page.Result on the example table
0.20V
A small association
χ²(1) = 4.00, p = .046
ObservedExpected if independent
| Cell | Observed | Expected |
|---|---|---|
| Group A · Yes | 20 | 25 |
| Group A · No | 30 | 25 |
| Group B · Yes | 30 | 25 |
| Group B · No | 20 | 25 |
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| Total | |||
|---|---|---|---|
| 50 | |||
| 50 | |||
| Total | 50 | 50 | 100 |
Cramér's V
0.200
small association · χ²(1) = 4.00, p = .046
χ²(1, N = 100) = 4.00, p = .046, V = .20
All statistics
| Pearson chi-square | χ² = 4.000, df = 1, p = .046 |
| G-test (likelihood ratio) | G = 4.027, df = 1, p = .045 |
| Chi-square with Yates' correction | χ² = 3.240, p = .072 |
| Fisher's exact test (two-sided) | p = .071 |
| Odds ratio | 0.444 (95% CI 0.200–0.989) |
| Cramér's V | 0.200 (small) |
| Phi coefficient (φ) | -0.200 |
| Contingency coefficient (C) | 0.196 |
| Lambda (symmetric / row|col / col|row) | 0.200 / 0.200 / 0.200 |
| Goodman–Kruskal gamma (γ) | -0.385 |
| Kendall's tau-b / tau-c | -0.200 / -0.200 |
| Somers' d | -0.200 / -0.200 / -0.200 |
| Theil's U | 0.029 / 0.029 / 0.029 |
Working from a data file? Run every SPSS CROSSTABS statistic (chi-square, Fisher, kappa, McNemar and more) with the SPSS crosstabs statistics guide.
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CSV, Excel, SPSS, Stata, SAS, R, Parquet, JSON, OpenDocument, Arrow/Feather or SQLite. Files are parsed locally before you enter the workspace.
Supported files and requirements
- CSV .csv .tsv .txt
- Excel .xlsx .xlsm .xls .xlsb
- SPSS .sav .zsav .por
- Stata .dta
- SAS .sas7bdat .xpt
- R .rds .rdata .rda
- Parquet .parquet
- JSON .json .jsonl .ndjson
- OpenDocument .ods .fods
- Arrow/Feather .arrow .feather .ipc
- SQLite .sqlite .sqlite3 .db
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The test
What is Cramér's V?
Cramér's V is an effect size statistic for the chi-square test of independence. It ranges from 0 to 1: 0 means no association at all; 1 means perfect association. Unlike the chi-square statistic itself, Cramér's V is not affected by sample size, so it gives a meaningful measure of how practically important a relationship is.
Named after Harald Cramér, it is calculated by normalising the chi-square statistic by both the sample size and the smaller table dimension. This makes it comparable across tables of different sizes — a V of 0.3 means the same thing whether your table is 2×2 or 4×5.
Cramér's V is the most widely reported effect size for categorical associations in academic publishing, market research reports, and policy analysis. Journals including APA publications now require reporting effect sizes alongside p-values.
When to use it
- You've run a chi-square test and want to quantify the practical significance of a statistically significant result.
- You need to compare the strength of associations across multiple crosstabs.
- You are writing up results for publication and need an APA-compliant effect size.
- Your table has more than two rows or columns (Phi coefficient only applies to 2×2 tables).
The method
Formula
V = √( χ² / (n × (k − 1)) )
where
- χ²
- chi-square statistic from your contingency table
- n
- total number of observations
- k
- min(rows, columns) — the smaller of the two table dimensions
- Range
- 0 (no association) to 1 (perfect association)
Using it well
Interpreting Cramér's V
Cohen (1988) proposed the following benchmarks for 2×2 tables. For larger tables, adjust thresholds downward — a V of 0.18 in a 4×4 table represents a medium effect.
0.00 – 0.10
Negligible
0.10 – 0.30
Small
0.30 – 0.50
Medium
0.50 – 1.00
Large
These are guidelines, not rules. Always interpret the effect size in the context of your domain. In clinical research a “small” effect can be highly consequential; in consumer surveys a “medium” effect may not be actionable.
Example
Worked example
Take a 2×2 table with cell counts [[20, 30], [30, 20]], for a total of n = 100 observations.
[[20, 30], [30, 20]] → n = 100, χ² = 4.00
Here k = min(rows, columns) = 2, so k − 1 = 1.
V = √( χ² / (n × (k − 1)) ) = √( 4 / (100 × 1) ) = √0.04 = 0.20.
A Cramér's V of 0.20 is a small effect — a real but modest association between the two variables.
Questions
Frequently asked questions
How do you interpret Cramér's V?
Cramér's V ranges from 0 (no association) to 1 (perfect association). As a rough guide, about 0.1 is small, 0.3 is medium, and 0.5 or more is large, though the thresholds should be adjusted for the table's degrees of freedom.
Is a Cramér's V of 0.2 strong?
A Cramér's V around 0.2 indicates a small-to-moderate association — real but modest. Interpret it together with the chi-square p-value and the context of your data.
What is the difference between Cramér's V and the phi coefficient?
For a 2×2 table they are identical. For larger tables phi can exceed 1 and loses meaning, so Cramér's V — which always stays between 0 and 1 — is the right choice.
Sources and next steps
References & further reading
- [1]Cramér, H. (1946). Mathematical Methods of Statistics.
- [2]Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences.
- [3]Cramér's V — Wikipediaen.wikipedia.org