Statistical Inference for Everyone
This book interesting because it forgoes the traditional approach of most mathematical statistics books. The preface states that it is done like this in order to avoid the "cookbook" approach taken by many statistics students. This is why it is ironic that "Bayes' Recipe" appears 15 times in this text, and on page 131 there is a five step algorithm for parameter estimation, and my favourite, oft-repeated, never explained recipe - "n > 30, you'll be fine". There is no mention of the CLT, MLE, method of moments estimation, biasedness of estimators, convergence in probability, how sampling distributions arise, or any of the theory of distributions that underpin all of the inferential procedures detailed in the book. I think that excluding these topics actually increases the cookbooky-ness of the text.<p>It is important that students understand the provenance of the inferential techniques they use so that they don't land up doing bogus science (which hurts the world) by not knowing the failure modes of these techniques. Of course not all students of statistics know the requisite mathematics to understand it all, at the very least put the failure modes into a cookbook form.<p>For the sake of science please don't ever do any inferential statistics without knowing when the method you're using works and when it breaks, what it is robust to, and what assumptions it makes. Statistics is really easy to break when used naively. The mathematics of statistics is not easy, and often results are highly counter-intuitive.