| Contingency
tables are an application of the chi-square
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:
H0 there is no relationship
between taking leave and propensity for
sickness
H1 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 chi-square contributions for each cell
are calculate from:
The expected values and the chi-square
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 chi-square 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
p-value is 0.24; this would
not be accepted at the 0.05 level of significance.
|
