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- Largest value depends on number of rows and columns Cramer’s V
When k is the smaller number of rows or columns It can attain a value of 1 Examples
level of ownership * foreign firm Crosstabulation
P2 =32920
Note that although values of M and C aren’t equal, they are of the same magnitude but ‘they are not particularly large’ is not a very satisfactory way to have an interpretation. Alternatives to P2 are based on the idea of proportional reduction in error or PRE.They have a clean interpretation based on how well you can predict the value of dependent variables if you know the value of the independent. 8 = lambda 8 = misclassified in situation 1 - misclassified in situation 2 misclassified in situation 1 Use most common category to predict if you don’t know anything else. For situation 1 use one of the variables, say the row, this should be the dependent variable count the number of cases misclassified. For situation 2 use the other variable. The rule is straight forward : For each category of the independent variable, predicts the category of the dependent that occurs most frequently. Example
Situation 1 : - assume row is dependent - we would choose widely held and would misclassify 248882 ties Situation 2 : - we would pick for domestic => widely held and misclassify 172398 ties for foreign we pick legally held and misclassify 60422 ties 8 = 248882 - 232820 248882 8 = 0.065The 8 tells you the proportion by which you reduce your error in predicting the dependent variable if you know the independent that’s why its called a Proportional Reduction In Error measure.The largest the value can be is 1. When variables are independent, 8 = 0.8 is not symmetric its value depends on which is the independent variable.
8 = 121063 - 121063 121063 8 = 0. Symmetric 8 If you have no reason to pick one as dependent or independent, use symmetric 8 . Symmetric 8 =E of 2 differences/E of denominator Example 8 =16062 369945 8 = 0.043
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