Assumptions of the Chi Square Test of Independence (1 of 2)

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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 non-preferred hand. The data are shown below:

	Hit	Missed
Preferred hand	9	3
Non-preferred 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 non-preferred hand. The total of the cell frequencies in the table is 24 but the total number of subjects is only 12.