Calculating the Expected Frequencies (E) in a Chi-Square Test of Independence

I have had several students ask me to review how to calculate a cell’s “E,” the value of the expected frequency under the null hypothesis, across all cells in a Chi-Square Test of Independence. The process is simple: To calculate each cell’s E, you take the cell’s corresponding column marginal total and multiply that number by that cell’s corresponding row marginal total and then divide by n (sample size). This procedure is summarized in the following 2x2 table below.

                    

Note that this procedure differs from the one variable Chi-Square "Goodness of Fit" test.  To obtain the expected frequencies for each cell in the "Goodness of FIt" test, divide the sample size by the number of columns.

I hope this helps!

Professor Ziner