Cramer's+V

Cramer's V. A chi square- based measure of association. Appropriate for nominally measured variables that have been organized into a bivariate table of any number of rows and columns.

Step 1: Find the number of rows (r) and number of columns (c) in the table. Subtract 1 from the lesser of these two numbers to find (min r-1, c-1). Step 2: Multiply the value you found in step 1 by N. Step 3: Divide the value of chi square by the value you found in step 2. Step 4: Take the square root of the quantity you found in step 3. The resulting value is V. Cramer's V has an upper limit of 1.00 for a table of any size and will be the same value as Phi if the table has either two rows or two columns. Like phi, Cramer's v can be interpreted as an index that measures the strength of the association between two variables.
 * __Computing Cramer's V: __**

EXAMPLE: Table 13.4 (Healey)

**__ Membership __**
Chi square (obtained) =31.50 N =75, (min r-1, c-1) =2 V = 31.50/(75)(2), and get the square root of the found value... V = 0.46
 * **Academic Achievement** || **Fraternity or Sorority** || **Other Organization** || **No Membership** || Totals ||
 * Low || 4 || 4 || 17 || 25 ||
 * Moderate || 15 || 6 || 4 || 25 ||
 * High || 4 || 16 || 5 || 25 ||
 * Totals || 23 || 26 || 26 || 75 ||


 * NOTE:** Since Table 13.4 has the same number of rows and columns, we may use either (r-1) or (c-1) in the denominator. In either case, the value of the denominator is N multiplied by (3-1), or 2. The computed value of V of 0.46 means there is a strong association between club membership and academic achievement.