Contingency Table

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Contingency Table and Cross Tabulation


To provide a method of listing the observed and expected frequency of occurrence of classification variables in a matrix and place them in a contingency table.


Contingency Tables

Reference: Black Book


A. Variable A.

B. Variable B.

C. k – Number of columns (equal to number of levels of Variable A).

D. r – Number of rows (equal to number of levels of Variable B).

E. fij – observed frequency of joint occurrence of variables.

F. Fij – expected frequency of joint occurrence of variables.

G. Li – Total of all occurrences of Bi.

H. Cj – Total of all occurrences of Aj.

I. n – Total number of observations.

Major Considerations

The population must be sampled at random.

  • The sample size must be large enough for the expected frequency of each cell to be 5 or greater.
  • The variables are assumed to be independent.

Application Cookbook

1. Cross tabulate the variables and insert the observed frequencies into the contingency table.

2. From the observed values, calculate the expected frequencies and insert into the table. i.e. Fij = Cj Li

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