Chi-Square, Cramer's V, and Lambda
For a Rows by Columns Contingency Table

For a contingency table containing up to 5 rows and 5 columns, this page will:
~
perform a chi-square analysis [the logic and computational details of chi-square tests are described in Chapter 8 of Concepts and Applications];
~
calculate Cramer's V, which is a measure of the strength of association among the levels of the row and column variables [for a 2x2 table, Cramer's V is equal to the absolute value of the phi coefficient];
~
and calculate the two asymmetrical versions of lambda, the Goodman- Kruskal index of predictive association, along with some other measures relevant to categorical prediction. [Click here for a brief explanation of lambda.]

To begin, select the number of rows and the number of columns by clicking the appropriate buttons below; then enter your data into the appropriate cells of the data-entry matrix. After all data have been entered, click the «Calculate» button.


Select the number of rows: 
        
 
Select the number of columns: 
        
 


Data EntryQ
B1 B2 B3 B4 B5 Totals
A1 
A2 
A3 
A4 
A5 
Totals
   


Chi-Square df P
Cramer's V =
Percentage DeviationsQ
B1 B2 B3 B4 B5
 A1 
 A2 
 A3 
 A4 
 A5 
Standardized ResidualsQ
B1 B2 B3 B4 B5
 A1 
 A2 
 A3 
 A4 
 A5 

Lambda for predicting Standard
Error
.95 CI Limits
Lower Upper
A from B:
B from A:
[Click here for a brief explanation of lambda.]

Estimated Probability of Correct Prediction
when Predicting:
  A without knowledge of B   
A from B   
  B without knowledge of A   
B from A   

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©Richard Lowry 2001-
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