I have hit a . . . data analysis sticking point with some empirical work that I am doing, and I thought I’d toss the problem out there to see if any of you see something that I do not see. I am a bit embarrassed, however, to admit that I am having a problem analyzing my data, so please refrain from starting any of your comments with “Did you skip 12th grade calc., Nowicki?” or “when, if ever, have you taken a stats class?”
I have calculated the annual percentage change in pay for the CEOs of ten large, publicly traded corporations. I am then comparing those annual percentage changes to the annual percentage changes in profits for those ten corporations, to see if there is a relationship between percentage changes in pay and percentage changes in corporate profits (such as a 10% increase in annual profit being accompanied with a 10% increase in CEO pay).
My ratios of percentage change in pay as compared to percentage change in profit are not producing what I expected to get, however. I have taken my annual percentage changes in pay and divided them by my annual percentage change in profit (for each CEO, for each year).
I expected to be able to then say “A result of 1 or a number greater than 1 is a bad thing” (because it means that the percentage change in pay is GREATER than any percentage change in profit). But things get confusing when I have percentage decreases – I frequently end up with negative numbers that are sometimes indicative of a “good” relationship (a negative percentage change in CEO pay accompanied by a percentage increase in profit, for example) and sometimes indicative of a BAD relationship (a positive percentage pay change accompanied by a NEGATIVE percentage profit change).
Given that I have negative numbers that are sometimes indicating a “good” pay/profit relationship and sometimes indicating a “bad” pay/profit relationship, I am stymied. What am I not seeing? Why am I not able to say “a number greater than 1 is a BAD thing for shareholders in terms of the CEO pay/profit relationship and a number less than one is a good thing”?