# Computing the Chi Square Test of Independence (1 of 5)

The first step in computing the chi square test of independence is to compute the expected frequency for each cell under the assumption that the null hypothesis is true. To calculate the expected frequency of the first cell in the example (experimental condition, graduated), first calculate the proportion of subjects that graduated without considering the condition they were in. The table below shows that of the 167 subjects in the experiment, 116 graduated.

 Graduated Failed to Graduate Total Experimental 73 12 85 Control 43 39 82 Total 116 51 167

Therefore, 116/167 graduated. If the null hypothesis were true, the expected frequency for the first cell would equal the product of the number of people in the experimental condition (85) and the proportion of people graduating (116/167). This is equal to (85)(116)/167 = 59.042. Therefore, the expected frequency for this cell is 59.042. The general formula for expected cell frequencies is:

where Eij is the expected frequency for the cell in the ith row and the jth column, Ti is the total number of subjects in the ith row, Tj is the total number of subjects in the jth column, and N is the total number of subjects in the whole table.