This might be a basic question, but I have no clue what this descriptive method could be named. Simplified, I have a cross-table with Occupations (e.g., doctor, lawyer, engineer) as rows, and Hobbies (e.g., sports, reading, gardening) as columns. Cell values are integer occurrences of the corresponding OH combinations. I am interested in the typicality of these combinations. So I made 2 cross-tables: Table O tells the percentages of hobbies within an Occupation, i.e, rows summing up at 100%. Table H tells the percentages of occupations within a Hobby, i.e, columns summing up at 100%. Note that these two may be different, e.g., doctors may do most typically sports, but sports-doers may be most typically lawyers, etc. As I am looking for typicalities of OH combinations, I multiplied the percentage-values in those two tables (of course I could have done it in one step: value/row_sum * value/column_sum). After scaling up by 100 and rounding, I get result values ranging between 0-7, nicely illustrating typicalities of the OH combinations. Is there a name for this simple method?
If I follow you correctly, what you have done is a step in computing the chi-squared test for independence. Specifically, you seem to have calculated the expected count for each cell in the contingency table under independence. It is quite reasonable that the rows and columns of your table will not be independent, which means the observed counts will differ from the expected counts that you have calculated. To determine if they have differed by an amount more than you deem reasonable to occur by chance alone, you can actually conduct the test (although I'm not sure it that is important for you).