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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.
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