So, the bit about standard deviation and standard error, yesterday. It made me feel like I should live up to my blog's name.
I think my confusion on such a simple question (aside from being embarrasing) is possibly indicative of something deeper. I had an argument with Jess a while back about whether psychology experiments were "real" science; whether they're as "real" as experiments in (her old field) molecular biology are, say. She said she doesn't really believe in the results of studies on a population with so much uncontrolled variability and such a great level of complexity. This is a reasonable point; I think I might have said something very similar a few years ago in explaining why I thought psychology in general was total bunk.
Here's my hypothesis as to the deeper issue:
Some scientists are accustomed to thinking of variables they're interested in as having one, exact real world value, which their observations only approximate because of measurement errors of various kinds. The freezing point of water "is" 32 degrees F, or 0 degrees C, right? If you add X ml of A to 1 liter of B, you get your reaction; if you really always had exactly 1 liter of B, the required X will always be exactly the same, right? In this frame of mind, there's not a whole lot of reason to conceptually differentiate the concepts of standard deviation and standard error, even if you learn the formulae and realize they're different. This was my default setting back when I was a physicist.
Cognitive psychologists don't, and can't think this way. We have to accept that we're working with populations - distributions - that have inherent variability; this variability isn't the result of unavoidable small fuck-ups by the experimenter, it's just there. But this is okay! This is why we have statistics! We can deal with this variability, and still do real science!
Of course, back in reality reality, there's very little that's near as exact as even scientists like to think of it as. What do you get once you dig deep enough into rigourous theoretical quantum mechanics that you can begin to set up the equations governing simple little atoms like hydrogen? You hit a wall, and have to revert to approximation methods as soon as you try to describe a helium atom. You don't have to know much at all about quantum to know that no "elementary particles" are close to exact in character, due to the uncertainty principle; an electron in an atom isn't in any one place, you have to describe its location in terms of - yeah, a distribution, with an inherent "spread" or variance just like a human population. Everything in theory that is elegant and exact yields itself up to variability and the necessity of approximation, when you get close enough to it in the real world. This isn't artifact. It's the way things really are.