Everything I've tried has been absolutely horrible except for "An Introduction to Error Analysis" by John Taylor (yeah the classical mechanics guy). Unfortunately it's a bit basic...
Everything I've tried has been absolutely horrible except for "An Introduction to Error Analysis" by John Taylor (yeah the classical mechanics guy). Unfortunately it's a bit basic...
Intermediate: Rice, "Mathematical Statistics and Data Analysis"
Wasserman's "All of Statistics" is also a very good book except that it is too terse to be a primary text.
Goes over the commonly used methods in science but only explains the intuition behind the method and what you can and cannot expect from the results, drawbacks etc. Written in a very conversational and opinionated style, I enjoyed it.
It rarely explains how any of it works (you'd be hard pressed to find the formula for a probability distribution function, for instance), so it's just a one-stop collection for a lot of useful tests and the circumstances under which they should be used.
It's less of a textbook, and more of a reference for someone who needs to occasionally work with statistics and can't remember offhand when the T-test is appropriate or the procedures to undergo for a chi-squared test or whatever.
Bayesian Data Analysis by Gelman et al.