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Contingency Tables
 

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:

chi square equation

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.

 

Analytical and descriptive statistics are covered in the MiC Quality online course Primer in Statistics.

Try out our courses by taking the first module of the Primer in Statistics free of charge.

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