I have recently read a book about the history of statistics, and the author made me aware of several books by R. A Fisher, or, to give his full name, Sir Ronald A. Fisher, Sc.D., FRS, one of the giants of the field.
Fisher produced three books in particular that are the main source of his fame. These are “Statistical Methods for Research Workers”, “The Design of Experiments”, and “Statistical Methods and Scientific Inference”, and all three are available in an omnibus edition for a reasonable price.
“Statistical Methods for Research Workers” is exactly this, a no-nonsense textbook introducing the reader to the most important statistical inference techniques with worked examples and a minimum of notation. The exposition is of a clarity that I have so far only seen in David Colquhoun‘s excellent textbook. For example, Chapter 2 is on diagrams and contains such excellent advice as to usually make the aspect ratio of a diagram close to one because otherwise real trends will be hard to see. (This is done by default in R.) On hypothesis testing he explicitly gives the often-neglected advice that hypotheses are never accepted, but only rejected. He introduces the standard error of the mean, the Chi-square test, significance testing, and other concepts in such a natural and effortless way that it makes you wonder why you ever had difficulties understanding them. All is accompanied by real tables with real data, showing you how to solve real research problems.
The only point where I disagree is his dismissal of Bayes’s theorem (which he calls “axiom”) as a way to assign probabilities to hypotheses from observations. I don’t see what the big deal is, even though he makes the excellent point that Bayes is no good as an axiom because it is not self-evidently true. On the other hand, the fifth Peano axiom (depending on how you count; I was taught that it was the fifth, others seem to number it differently) or the parallel axiom aren’t exactly models of self-evidentiality either. Anyway, I tend to use frequentist of Bayesian models of statistics whenever they suit me. I may said to be statistically dogma-agnostic.
“The Design of Experiments” is another very practical no-nonsense book about how to design experiments so that their results can meaningfully answer the questions that they were meant to answer. in Chapter 2, he gives the famous example of the lady tasting tea, the eponymous book about which made me aware of R. A. Fisher and his excellent books. This example concerns a lady who claims that, given a cup of tea with milk, she can distinguish whether the tea or the milk is poured first. No matter that no mechanism is known that would make such a claim plausible, Fisher sets out a number of tests which, should the woman pass them, he would be satisfied that something is happening that is too unlikely to have come about by chance alone. In explaining how these tests must be done, he lays bare the foundation upon which the validity of our conclusions are based. It is randomisation, he says, which ultimately makes reasoning about experiments possible.
As an aside, in the course of Section 4, he shows himself to be a devoted secularist and humanist, being wedded to the Enlightenment ideals of free inquiry as a means to improve upon humanity.
So, go forth and read these classic texts. If you’re just a bit like me, many a scale will fall from your eyes, and many things will become much clearer. And you will become an improved member of humanity. I’m sure Fisher would like that.