Finishing up my Ed.D. and I do have a master’s in math so get as technical as you want.
I have two lists of rankings that are probably related. As an example:
What do you prefer to play / What do you prefer to watch on TV
Baseball 1 / 2
Basketball 3 / 3
Football 2 / 1
My original thought was to measure the total deviation so in the above example the deviation would be 1+0+1=2. I’m not real happy with this but I’m not really sure what the standard deviation (0.8165) adds to the analysis. Of course, I may just be overthinking the issue.
So how about a matched pair t-test? That would work if I want to see IF the two lists are significantly different, but does the score itself tell me about the amount of difference between the two lists.
My ultimate goal is given a whole group of people, to see if the amount of difference for an individual correlates to another number like beers drunk in a week.
Since you only have ranks and not a continuous measure indicating the “absolute” enjoyment of doing/watching, I’d say the obvious answer is a Spearman’s rank correlation coefficient is one piece of data
But I suppose I shouldn’t be answering this question. Although I have a Ph.D., I don’t consider myself a “dopey Ph.D.”
Quite. I have a Ph.D. and I have no idea about this. It is not at all my field. On the other hand, I am sure plenty of people without doctorates understand enough statistics to be able to help you.