Rejecting the Null
If you’re anything like I was at age eighteen, then you probably don’t have a great idea of what the image at the top of the page is referring to. I mean, you’re also probably living in Wilmette, Illinois and attending New Trier High School, but we can discount those two possibilities for the time being and move on to what the heck those two numbers mean.
For a start, they’re a snapshot of a page of my Economics honors thesis – page seventeen, to be specific – and they represent the culmination of months of collecting data. All so I can say the following: “According to my data, and with 73% confidence, approximately 22.5% of the variation in the vote share of pro-independence regional parties can be explained by the variation in seven macroeconomic indicators.” And that’s all there is to it. The R-squared value, up top, tells you the percentage of variation in Y that can be explained by variation in X. In my case Y is the vote share of independence parties in sub-national regions, like the Scottish National Party or Québec Solidaire, and X is the macroeconomic performance of Scotland or Québec, respectively.
The Prob. > F is a little bit more interesting. That number tells me the probability that, if there were nothing going on in the data (i.e. all of my macroeconomic variables were equal to zero), that I would still get the results that I did. It’s what statisticians call the probability of getting a Type I error. Typically in economics, you want numbers below 0.05 or 0.01 (meaning 95% or 99% confidence, respectively), but I’m pretty comfortable with my number, which implies approximately 73% confidence.
Why? Because up to this point, everybody has assumed that the vote share of regional independence parties is determined mostly by political factors like identity and nationalism, not by economic factors like the unemployment rate. If I can predict, as I can, that nearly a solid fifth of the variation in their vote total is completely economic – with 70% confidence – that’s not a bad result for a year’s work as an undergrad. And that’s what I like about Clark. My research is not the exception, and it’s not even particularly exceptional relative to the work other Clarkies (like Kevin) are putting out. It’s the norm to do research here, and I love that. It’s the creation of new knowledge. What’s not to like about that?