Since it's become clear that I'm not going to write one long post on statistics, I've decided to write an infinite series of short posts on statistics.
Don't say I didn't warn you.
In this post, I'll start with the purpose of statistics: the purpose of statistics is to tell us whether two sets of numbers, that differ based on some characteristic that we suspect might be important, are really different. Although it can get very sophisticated (for example, we sometimes don't know the second set of numbers), that's really all statistics does or can do.
In particular, statistics can't work backwards. We can't see that two sets of numbers are different, and then work our way back to figure out what the difference is. Theory must drive statistics, but statistics can't drive theory.
Next time, what alpha means, and what what alpha means means.