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This module tests the hypothesis about independence of two categorical variables A, B based on experimentally observed occurence of combinations of particular levels of A, B. Number of levels of A is denoted r, number of levels of B is denoted c. The data are organized in the table of frequencies. Only the thick bordered box needs to be specified, the totals are calculated automatically.

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Contingency Tables

Example:
The the following table we have volumes of products of three types 1, 2 3 sold to 4 different markets, Europe, Asia, USA, and Africa. We want to test if there is a difference in structure between products or between markets. Practically, we test if the proportion between products is the same for any market and simultaneously if the proportion between markets is the same for any product.

Data:
Contingency Tables

Contingency Tables

Output:

Analysis of contingency table        
         
Task name : Market Analysis      
         
Table of counts        
  Product1 Product2 Product3 Total
Europe 114 25 301 440
Theoretical: -117 -31 -292  
Asia 68 20 225 313
Theoretical: -83 -22 -208  
USA 131 30 240 401
Theoretical: -107 -28 -266  
Africa 57 23 159 239
Theoretical: -63 -17 -159  
Total 370 98 925 1393
         
Table of ratios and probabilities      
  Product1 Product2 Product3 Total
Europe 0.081838 0.017947 0.21608 0.315865
Theoretical: -0.083898 -0.022222 -0.209745  
Asia 0.048816 0.014358 0.161522 0.224695
Theoretical: -0.059682 -0.015808 -0.149205  
USA 0.094042 0.021536 0.17229 0.287868
Theoretical: -0.076462 -0.020252 -0.191154  
Africa 0.040919 0.016511 0.114142 0.171572
Theoretical: -0.045572 -0.01207 -0.11393  
Total 0.265614 0.070352 0.664034 1
         
Conclusion Independence of variables is rejected
Significance level 0.05      
Degrees of freedom 6      
Chi2 statistic 17.11555756      
Critical value 12.59158724      
p-value 0.008867805      
 
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