To emphasize the essentials of applied stats, and not get mislead by the literature (what is in the literature is often not optimal) there are 4 books I recommend, because I’ve learned a lot from them.
- Biostatistics for Biomedical Research (link) by Frank Harrell – A good complement to any intro level textbook.
- Resampling Methods by Philip I. Good. A great applied text on modern frequentist statistics that substitutes computation for mathematical theory. There is a trend in intro statistics education to emphasize simulation methods, and link them to the classical parametric models to improve intuition.
- Permutation, Parametric, and Bootstrap Tests of Hypotheses by Philip I. Good. This is a more theory intensive text that complements Resampling Methods.
- Regression Modelling Strategies by by Frank Harrell – hard to go wrong here, as he emphasizes semi-parametric models, which are very flexible as a general rule. The big advantage is that he has filtered out the large number of techniques (which have value in particular contexts) in favor of an approach that is reasonable in almost any context. No one who understands statistics could fault you for properly using his approach. This might be tough to tackle as a first text, but having studied 1 or 2 will make the student well prepared.
Bayesian texts require a bit more math. I’ll post a few recommendations later.