When I asked Steve Ansolabahere what to read as an intro to stats, he recommended this:

- Bulmer, M. G. 1967.
*Principles of Statistics*. 2nd Edition. Dover.

[Update: I first wrote 1966, which is between the first edition in ’65 and the second in ’67.]

As Mitzi says, clever boy, that Steve. This book is fantastic. It’s concise (250 page), incredibly clear and straightforward, and at just the right level of mathematical rigor not to get bogged down in extraneous details. And the price is right, US $10.17 brand new from Amazon. I’ve always been a fan of Dover Press.

In a few short chapters, with no dissertations on combinatorics or urns in sight, Bulmer lays out basic probability theory (e.g. conditional probability, chain rule, independence, etc.). He actually uses real data for examples. Random variables arise naturally after this rather than as some measure-theoretic notion that’s always way too abstract for a first pass at the material (Larsen and Marx’s *Mathematical Statistics* is very good if you really want the gory details for Euclidean space using the minimal amount of analysis).

There’s a wonderful discussion of expectations, variance and moments along with a very nice intro to moment generating functions with comprehensible examples. Throughout, the examples are only as complicated as they need to be to get the basic idea across.

Bulmer first goes into depth on the discrete distributions, binomial, Poisson, and exponential. There’s a very nice chapter on the normal distribution and its relation to the central limit theorem. What I liked best about the book, though, was its coverage of χ^{2} and t distributions and their relations to estimation. I just read it again and I marvel at how Bulmer explains this entire topic in 15 easy pages. Really. Read it.

After covering traditional point-estimate hypothesis testing (boo, hiss), Bulmer jumps into a philosophical discussion of statistical inference, providing a nice intro to Bayesian and non-Bayesian approaches. This is followed by a discussion of point estimates and estimation robustness. If you’re forced to go classical (why else would you?), this is a good way to think about things.

Finally, there’s a cursory section on regression which covers the linear case and then the bivariate case and its relation to correlation very cleanly without any matrix notation. Alas, no logistic regression. On the other hand, once you’ve read this, you should be ready for Gelman and Hill’s book on regression.

If you don’t believe me, read the reviews on Amazon. It’s a stack of love letters to the author for his or her insight.

May 22, 2009 at 7:08 pm |

While I haven’t seen Bulmer’s book, I can understand the appeal of old style texts. Modern texts seem driven by the publishers impression (maybe correct) that students wont feel they are getting value for money unless they have a large textbook with lots of colour. So rather than teaching principles there is a tendency to provide lots of examples with generally trivial differences between them, maybe what some of the negative reviewers of Bulmer’s book are looking for, a recipe for every occasion.

As a more general comment, it is rare to see a text that actually explains the reasons for differences between Wald and LRT statistics. It seems to be either assumed that it has been covered elsewhere or in most cases that it is too hard for the audience to understand, for example medical statistics texts coverage of logistic regression and survival analysis.

May 26, 2009 at 2:44 pm |

Here’s an interesting article on the subject of introductory statistics textbooks.

Click to access MAAFIXED.PDF