Assumptions of the Chi Square Test of Independence (1 of 2)
A key assumption of the chi square test of independence is that each subject
contributes data to only one cell. Therefore the sum of all cell frequencies
in the table must be the same as the number of subjects in the experiment.
Consider
an experiment in which each of 12 subjects threw a dart at a target once using
his or her preferred hand and once using his or her nonpreferred hand. The data
are shown below:

Hit 
Missed 
Preferred hand 
9 
3 
Nonpreferred hand 
4 
8 
It would not be valid to use the chi square test of independence on these
data since each subject contributed data to two cells: one cell based on
their performance with their preferred hand and one cell based on their
performance with their nonpreferred hand. The total of the cell frequencies
in the table is 24 but the total number of subjects is only 12.