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.
