Statistics lesson: Interdependence

Ok then. I was asked by a student I had for one of my other courses about something she knows I teach. I’m humbled and honoured, so thankyou Nitya. Interdependence. Sounds like an overly complicated word doesn’t it? But the complexity has a method to its madness.

But first, remember what we’re trying to do with quantitative research. We’re trying to capture the essence of something with a number. Strange idea hey? But that’s a whole other discussion. Still once we put a number to something we call it a variable. Strangely the simplest variables are often the hardest ones to get people to tell you – age, income etc are a simple number, but try to get some people to tell it to you.

But in one sense that’s where dependence (association with an expectation of causality) might exist. So, if we take a hundred people and measure both their age and their income we could fine that (let’s say from 15 years old to 25) there is a positive correlation between age and income. And we might think that as someone goes from 15 to 25 they can do some more stuff and are worth more money. A hint of causality.

Interdependence

But where we can’t see an argument for causality, we are likely to be in the world of interdependence. I’ll take an example from a text I use. We get measurements for a “Cullen’s restaurant”. Six people give a rating for waiting time, cleanliness, friendly personnel, food taste, food temperature and food freshness. And the data looks like this:

Everyone clearly rates my restaurant low on waiting time, cleanliness and friendly personnel, but high on taste, temperature and freshness. (stragely that’s exactly how a restaurant would be if I ran one). Each of the items are first three items are related to each other (according to the data) but there is no (clear) indicator that one causes the other. Same with the last three items. They are associated - interdependent but not dependent.

OK now to just take this a little further. There is a procedure that helps us tangibilise interdependence – firstly we can look at the correlation coefficient between the variables. All three of the first items would be highly correlated to each other and weakly correlated to each of the last three. Then a cool piece of software called SPSS can mix that all around and come up with an argument that some of these variables belong together. That’s called “factor analysis” and helps draw pictures like this one:

It can get as complex as you like. But the story goes that once SPSS tell you that you have a clean “factor” of – say “food quality” then you can take the average of the variables A4, A5, and A5 and it give you a robust measure of an abstract construct. The idea of “food quality” just became a little less slippery. Some people call this “data reduction” but not in the world I grew up in. Other people call it a “fishing expedition” – measure a heap of things and see if SPSS can make some sense of it for you. That a bit harsh too, I think.

Still, those are my thought on what interdependence is.