I can't be more clear because I have never actually seen this test and I could not find it on the internet.

This is the comp question that raised my question:

"In the marginal table [I assume they mean a contingency table with education added although no details are given]... the chi squared value of 35.8 for the independence test is extremely high. On the other hand, for each level of education, the conditional chi squared test for independence of Aptitude and occupation is substantially lower, and three out of four of these tests fail to reach significance."

Aptitude and Occupation are the two variables being tested with education apparently being a control. I do not have the actual data that those taking the test looked at, just the questions.

Looks like they are calculating a seperate chi square for each level of education, but I have never seen chi squared done this way.