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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?

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  • $\begingroup$ Are you asking for the name of the statistical test for this, or just a name for the descriptive data manipulation process you've described? $\endgroup$ – gung - Reinstate Monica Mar 7 '14 at 22:14
  • $\begingroup$ Any information would be fine! Name of the process, or function, or whatever! $\endgroup$ – Nienu Froo Mar 7 '14 at 22:27
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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).

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  • $\begingroup$ The expected count would be proportional to row_sum * column_sum, whereas the proposed calculation is inversely proportional to that. It could be understood as being proportional to the ratio of the squared cell value to the expectation (under independence) and that in turn bears an obvious but somewhat indirect relationship to the chi-squared residual. $\endgroup$ – whuber Mar 7 '14 at 23:23
  • $\begingroup$ @whuber, I may have mis-read it. TBH, I'm not completely sure. The text description connotes the expected count under independence to me, but then the formula seems like the conditional probabilities (w/i the row & w/i the column). Since I can't say for sure, maybe I should delete this. $\endgroup$ – gung - Reinstate Monica Mar 8 '14 at 3:34
  • $\begingroup$ Thank you gung and whuber! This is exactly the information I was looking for. It would be probably enough for me just to give a description of these calculated values. However, is there a way to compute if those differences (between observed and expected values) are significant, one-by-one? E.g., for the "doctors doing sports" combination? My calculated values range between 0.00 - 0.07 - what other test should I perform to show their individual significance? $\endgroup$ – Nienu Froo Mar 8 '14 at 13:14
  • $\begingroup$ Nienu, gung's answer addresses the question of independence that you ask in your comment. The key idea is that--perhaps a little surprisingly--the right way to measure discrepancies is by means of appropriately standardized differences rather than using the ratios implicit in your method. That is what a chi-squared test does. $\endgroup$ – whuber Mar 8 '14 at 21:59

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