In his address on Public Safety, on April 30, 2013, New York Mayor Bloomberg commended the NYPD for the record low homicides, 419 in 2012, the lowest annual homicides number in New York history. Then, he started comparing the homicide rate for NYC (419 murders in 2012 or 5.125 per 100,000 population) with the homicides rates for several cities and ended up, "... if we had a murder rate like Detroit's, we would have more than 4500 New Yorkers dead in 2012, not 419. That's a factor of 10."
Essentially, Bloomberg was using the ratio y/x where y is the number of homicides and x the population to compare various cities. NYC has a ratio of 5.125 which is about one-tenth the y/x for Detroit and so on.
This is also amazingly what Wall Street does. If company A had a profit margin of 20% it is better than company B with a profit margin of 5%.
This is also what I have been trying to call attention to here with my Instablog posts. A few seem to be taking notice and that is a good sign. This few must grow into hundreds and thousands to make the difference. And, a difference must be made.
And, so I urge everyone to read my analysis of what Mayor Bloomberg did and what he should have done. What is the valid basis for comparing the homicides rate for various cities? What is apples to apples and what is apples to oranges? How do we tell apples from oranges?
The solution lies in studying the nature of the underlying x-y relation, not just the y/x ratios. When we use y/x ratios, we are more likely to get into apples and oranges comparisons. The x-y diagrams, on the other hand, tells us what is apples and apples and oranges and oranges.
If you understand this, you will also understand how to compare different companies (based on profit margin, EPS, etc.), airlines (based on their On-Time arrivals ratios, missed baggages ratio, the denied boarding, etc.) and countries (based on debt/GDP ratio, for example, unemployment rates, etc) and literally hundreds and thousands of other problems of interest to us, where we use simple y/x ratios to make sense of our empirical observations. Here's the link to the full article.
My apologies again for doing this. Our forum here does not permit uploading of pdf files and I haven't quite figured out what to do with uploading of figures here using current posting tools.