Cramer's V Calculator

Formula

The formula to calculate Cramer's V is:

\[ V = \sqrt{\frac{X^2 / n}{k - 1}} \]

Where:

\(V\) is Cramer's V
\(X^2\) is the Chi-Square value
\(n\) is the total sample size
\(k\) is the smaller number between the number of rows and the number of columns in the contingency table

What is Cramer's V?

Cramer's V is a statistical measure used to determine the strength of association between two nominal variables in a contingency table. Named after Harald Cramer, it provides a value between 0 and 1, where 0 indicates no association and 1 indicates a perfect association. It is a chi-square-based measure of correlation and is considered a more robust measure than the chi-square statistic alone, as it takes into account the sample size and the number of categories in the variables.

Example Calculation

Let's assume the following values:

Chi-Square Value (X²) = 10.5
Total Sample Size (n) = 100
Number of Rows = 3
Number of Columns = 4

Using the formula:

\[ V = \sqrt{\frac{10.5 / 100}{\min(3, 4) - 1}} = \sqrt{\frac{0.105}{2}} \approx 0.23 \]

Cramer's V is approximately 0.23.