Contingency tables are an application of the chisquare test used to test the relationship between two variables. For example, an organization decides to investigate whether there is a relationship between employees who experience sickness and who take their full entitlement of annual leave. The hypothesis is:
H_{0} there is no relationship between taking leave and propensity for sickness
H_{1} there is a relationship between taking leave and sickness
The data are as follows:

Sick

Not Sick

Total

Take Leave 
65

55

120

Don't take leave 
50

30

80

Total 
115

85

200

The expected values for the individual cells are found from:
The chisquare contributions for each cell are calculate from:
The expected values and the chisquare contribution are

Sick

Not Sick

Total

Take Leave 
69 (0.23)

51 (0.31)

120

Don't take leave 
46 (0.35)

34 (0.47)

80

Total 
115

85

200

The total chisquare value is 1.36. The number of degrees of freedom can be calculated from:
(rows  1) x (column  1)
This gives one degree of freedom. The number of degrees of freedom may also be obtained by considering that given any cell and the totals, the values in the remaining cells can be calculated.
From Excel =CHIDIST(1.36,1) the pvalue is 0.24; this would not be accepted at the 0.05 level of significance.
