How to Compute Cramér’s V for Categorical Data: Steps and Example

Cramér’s V Coefficient

Cramér’s V is an index that indicates the strength of association between two categorical variables.

Key points about the formula:

The denominator uses the smaller of the number of rows or columns.

To eliminate the influence of sample size (prevent V increasing with more observations), the numerator is divided by the total number of observations, reflecting the average difference between observed and expected frequencies.

Since the numerator is squared, the final step takes the square root to “undo” the squaring.

General steps:

Organize the contingency table and count the frequencies for each category.

Compute the chi‑square statistic.

Plug the values into the Cramér’s V formula to obtain the coefficient.

Example

Company A, which runs a family restaurant, is experiencing poor business and conducts a random survey of residents in Japan with households of 20 or more. The questionnaire asks “What type of dishes are most frequently ordered at the family restaurant?” and “If a free after‑meal drink is offered, which do you prefer, coffee or tea?” Compute the Cramér’s V for these two questions.

Images illustrating the example and solution are shown below.

References

Takahashi, Shin. Comic Statistics . Science Press, 2009 (translated by Chen Gang).