# Statistical intuition/data sense

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.

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How to lie with statistics is a great place to start. –  MånsT Aug 2 '12 at 6:46
Looks interesting! Thanks! –  Zvpunry Aug 2 '12 at 7:12
The Drunkard's Walk also places statistics in an accessible, commonsense framework. –  Marcus Morrisey Aug 2 '12 at 13:15

I would first say that we shouldn't slight mathematics. It is an important tool in the development of statistical theory and statistical methods are justified by theory. Theory aslo tells you what is wrong and what techniuqes might be better (e.g. more efficient). So I think mathematical knowledge and thinking is important (almost necessary) to be a good statistician. But it is definitely not sufficient. I think the books referenced in comments are good. Let me give some others.

Making Sense of Data: A Practical Guide to Exploratory Data Analysis and Data Mining

Making Sense of Data II: A Practical Guide to Data Visualization, Advanced Data Mining Methods, and Applications

The Role of Statistics in Business and Industry

A Career in Statistics: Beyond the Numbers

The books by Hahn and Snee are particularly valuable and interesting because these are famous industrial statisticians with the mathematical skills and the practical experience.

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Thanks for the links and commentary. I think that generally answers can be improved by using the [manuscript title](uri) link markdown. After a long day, I find coming across answers with long hyperlinks can be subconsciously jarring, and unfortunately might bias a reader against an otherwise good answer. –  jthetzel Aug 2 '12 at 15:49
@jthetzel I can see why it is better to have a name replacing the url in a link. When I have time I will learn to do it. I know it is easy. But I gave three or four links. it takes almost no time to click on the link and see what it is. so I don't really understand why so many community members make a big deal over it. –  Michael Chernick Aug 2 '12 at 16:04

A nice, free resource is the Chance News Wiki. It has many examples pulled from real examples along with discussion of good and bad points in how people interpret data and statistics. Often there are discussion questions as well (part of the motivation of the sight is to give teachers of statistics real world examples to discuss with students).

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In the example you mention, the core issue is causal inference. A good place to start for causal inference is this triple-book-review by Andrew Gelman, and the books reviewed therein. In addition to learning about causal inference, you should learn about the value of exploratory data analysis, description, and prediction.

I've learned an incredible amount by hearing social scientists criticize each other's research in published work, blogs, seminars, and in personal conversations - there are lots of ways to learn. Follow this site, and Andrew Gelman's blog.

Of course, if you want data-sense, you need practice working with real data. There are general data-sense skills, but there is also data-sense which is specific to a problem area, or even more specifically, data-sense specific to a particular dataset.

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Let me add one more strategy that I've found enormously helpful: I think it's worth your time to learn a little (statistical) programming. You don't have to be terribly good at it (I'm known for writing "comically inefficient" code). However, once you can write some basic procedural code (say in R), you can simulate. It would be hard for me to overemphasize how much being able to conduct even very simple simulations can help. One thing you can use this for is, when in the course of your studies, you read about some property you can explore it. For instance, if you know (abstractly) that it is difficult to empirically determine whether a logit or a probit model is better for a dataset, you can code up simple simulations of this and play with them to understand the idea more fully. This will also provide you with experience, but of a slightly different type, and will also help you develop your data sense.