I am a second-year undergraduate student, studying Math, and I've been talking to one of my professors a good amount about the difference between mathematical ability and statistical ability. One of the key differences he brought up was "data sense" which he explained as a combination of technical ability while operating within a set of what I'll informally call "common sense restraints" i.e. not losing sight of the reality of the problem amidst a lot of theory. This is an example of what I was talking about, which appeared on Gowers's blog:
In several parts of the UK the police gathered statistics on where road accidents took place, identified accident blackspots, put speed cameras there, and gathered more statistics. There was a definite tendency for the number of accidents at these blackspots to go down after the speed cameras had been installed. Does this show conclusively that speed cameras improve road safety?
The same person who argued for the randomized strategy in the negotiation game basically knew the answer to this question already. He said no, since if you pick out the extreme cases then you would expect them to be less extreme if you run the experiment again. I decided to move on quickly from this question since there wasn’t a lot more to say. But I told people about a plan I had had, which was to do a bogus telepathy experiment. I would get them to guess the outcomes of 20 coin tosses, which I would attempt to beam to them telepathically. I would then pick the three best performers and the three worst, and would toss the coins again, this time asking the best ones to help me beam the answers to the worst ones. People could see easily that the performances would be expected to improve and that it would have nothing to do with telepathy.
What I'm asking is how to learn more about this "data sense", through any publications on the subject, if they exist, or through what other users have found to be helpful in developing this skill. I'm sorry if this question needs clarifying; if so, please post your questions! Thanks.