So, I attend a weekly team trivia event at a local pub here. It’s a fun event, around 40 teams of 2-6 players answer 6 rounds of questions on sheets of paper which are graded and then the top 3 teams get prize money based on the number of teams who paid to play. The questions are mostly pop culture (music and movies being two of the rounds each week) but range over everything from neuroscience to history to Harry Potter.
This week, one of the questions was a poorly written statistics question in a science category. I’ll repeat it here, shuddering all the while: “At a confidence interval of 95%, a value of .06 would be considered: Significant, trending towards significant, or not significant.” Now, if you’ve taken a few stats classes before, this question should make you want to rip out your hair and/or write an essay on the different philosophies of statistics.* As the resident quant on the team, it was up to me to decide how to answer the question.
There are, of course, a few problems with the question: first of all, the logic of hypothesis testing (significance, etc.) and logic of confidence intervals are very different, even if the underlying computations are very similar. So it doesn’t make much sense to talk about “significance” in terms of a confidence interval. But, being charitable to the trivia master (who was both drunk and is not a particularly math-y guy), I rewrote the question as: “At a confidence level of 95%, a p-value of .06 would be considered: Significant, trending towards significant, or not significant.” Now I have a dilemma: if option 2 is a thing, clearly it is the answer the question is going for, as .06 is about as close to significant (.05) as you can get without actually getting there. Of course, the way I was taught statistics, “trending towards significant” is not a thing, it’s something you might say when you don’t actually get a result, but not something that appears in a stats text book. So what do I do?
If I answer the way I think the question is looking for (“trending towards”), but it was actually a trick question, I will have no leg to stand on – I will have known the “correct” answer and guessed wrong. But if I answer the way I believe is less likely to be the one taken as correct, but the one I believe in, I will be able to argue about getting it wrong (perhaps to some effect, but probably not). And, most importantly, I will be able to account for my action in a satisfactory way that fits with my conception of myself (as “quant-y”, in this set of people anyway).
So I went with “not significant”. As predicted, the desired answer was “trending towards”. I argued, along with one of the econ grad students and a plastic surgeon, getting back one of three points the question was worth. Out team ended up tied for first and lost the tiebreaker.
Ok, that was unnecessarily long and probably boring. Take home points: people (at least, this one) act in ways such that they can account for their actions, even if this might seem to be the wrong move from an efficiency/instrumental standpoint (hat tip Goffman). Also, poorly worded stats questions at bar trivia nights make social science grad students angry.
* And indeed, this was the response of the team of economics grad students sitting across from us.
A (Budding) Sociologist's Commonplace Book 
anomie
/ June 4, 2008I agree. It is either significant or not within the parameters that have been set. You totally should have gotten the points.
Natalie K.
/ June 4, 2008Ok first off, boo! and you know why.
Second off, think how I must have felt when they asked what the Hannukah lamp was called and wanted the answer “Menorah” rather than the correct answer, “Hannukiah.”
Actual binary, answer, wrong.
Perhaps the answer is, smarter trivia should be attended.
Natalie Cotton
/ June 5, 2008You’re mixing mechanisms in the description of what happened. The question is, account to whom?
In your analysis of the possibilities, you indicate that though you thought that you knew the answer, you were not sure. It could have been a trick question. So your description actually fits very well with an instrumental perspective: Choosing the answer which had an “accountable” possibility of error could result in partial points granted (which is what evidently happened), which you led you ex ante to chose that option after weighing the expectancies. Indeed you weigh the chances of getting partial points with the phrase “perhaps to some effect, but probably not” in the text above, which indicates a non-zero chance of partial points. Thus, accountability informs the mechanism of rational choice.
But you say also that choosing option 3 “fits with my conception of myself (as ‘quant-y'” — which indicates a different mechanism at work. Self-motives are powerful mechanisms motivating behavior; one of these self-motives is self-consistency. You chose the option that would lead to you being able to view yourself in a manner most consistent with your identity as “quant-y”. As a result, your notion of accountability is really a matter of accountability to yourself. You had your own self-concept to maintain.
Finally, you reference Goffman. I’m not an expert on Goffman, but from what I believe, his perspective points to a very different theory of identity. In his terms, it is the *presentation* of self which matters. Things are accountable to the degree that the other participants within that interaction would be able to understand and agree to your proposed presentation of self as “quant-y”. Your mental deliberation thus hinged on whether you thought the *other* people in the room would think of your account as a reasonable portrayal of a quant grad student.
So which was it really? Rational expectations, self-concept, or self-presentation? How many drinks did you have?
Methinks identity is at the base of this, but to know which theory of identity, you’d have to pose a counter factual. If the bar had been filled with bio-medical post-docs, making you the “softy” rather than “quanty”, and the question writer was a scientist, making it more likely to be a trick question, what would you have thought to do?
[sorry for the length of this comment; i take my prelims in 11 days and I’m procrastinating]
Dan Hirschman
/ June 5, 2008Let me add a bit more detail to my internal account:
I thought to myself, I’m 90%+ sure Geoff (the trivia guy) wants the 2nd answer. But I am unwilling to risk it. This account (like all accounts) can be squirreled into a rational choice framework, but it does not fit a “maximizing expected points” framework, as I thought (based on past arguments) my odds of arguing up to all 3 points were virtually nil and my odds of arguing up to only 1 point were only mediocre (we only got that one point because someone else argued much more forcefully and dickishly than I did, had I been on my own I would have gotten nothing). My internal calculations suggested that what I was doing would very much not maximize points (and thus chance of winning).
It is true that I was trying to maintain my own self-conception, but you are right to call me out on an imprecise bit of language. What I should have said was that ‘I will be able to account for my action in a satisfactory way that fits with the shared conception of myself held by myself and my teammates’, that is, the combination of my identity and my presented identity. No matter which answer I wrote down, I would internally know the ‘right’ answer, so my own identity as a quant – to myself – was not as much in play as my presented identity.
Bennett Holman
/ June 15, 2008It seems your utility function includes not only “win money and points”, but also “be right”, way to maximize!
frans bararuallo
/ February 13, 2012Step by step all of us can understand what is the difference beetween maximize and minimize in our life. But i still wait some comments about “how to win money” in our life. About the utility fuction, i still believe that this is one of the old concept (by Fisher theorem in 1932) of utility in the world, especially in economics.