Cramér's V

The chi-square test says whether an association is statistically established — not how strong it is. Because ${\chi }^2$ grows directly with sample size, the statistic itself is useless as a measure. Cramér's V normalises it to the range $[0,1]$:

Here $r$ and $c$ are the row and column counts of the contingency table and $n$ is the sample size. $V=0$ means complete independence, $V=1$ a deterministic association. For a $2\times 2$ table V coincides with the phi coefficient.

• $V\approx 0.1$ — weak association
• $V\approx 0.3$ — moderate association
• $V\ge 0.5$ — strong association