Enter the chi-square value and total sample size, as well as the smaller number between the number of rows and columns in the contingency table into the calculator to determine Cramer’s V.
Cramers V Formula
The following formula is used to calculate Cramer’s V.
V = sqrt((X^2/n) / (k - 1))
Variables:
- 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
To calculate Cramer’s V, first calculate the chi-square value and square it. Divide this value by the total sample size. Then, find the smaller number between the number of rows and the number of columns in the contingency table and subtract 1 from it. Finally, take the square root of the result obtained from dividing the first result by the second result.
What is a Cramers V?
Cramers 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.
How to Calculate Cramers V?
The following steps outline how to calculate Cramer’s V using the given formula:
- First, determine the chi-square value (X^2).
- Next, determine the total sample size (n).
- Next, determine the smaller number between the number of rows and the number of columns in the contingency table (k).
- Next, calculate (X^2/n).
- Next, calculate ((X^2/n) / (k – 1)).
- Finally, calculate Cramer’s V by taking the square root of ((X^2/n) / (k – 1)).
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem:
Use the following variables as an example problem to test your knowledge:
chi-square value (X^2) = 25
total sample size (n) = 100
smaller number between the number of rows and the number of columns (k) = 3
