The foundations of statistical science: A history of textbook presentations

We discuss how the foundations of statistical science have been presented historically in textbooks, with focus on the first half of the twentieth century after the field had become better defined by advances due to Francis Galton, Karl Pearson, and R. A. Fisher. Our main emphasis is on books that presented the theory underlying the subject, often identified as mathematical statistics, with primary focus on books authored by G. Udny Yule, Maurice Kendall, Samuel Wilks, and Harald Cramér. We also discuss influential books on statistical methods by R. A. Fisher and George Snedecor that showed scientists how to implement the theory. We then survey textbooks published in the quarter century after World War 2, as Statistics gathered more visibility as an academic subject and Departments of Statistics were formed at many universities. We also summarize how Bayesian presentations of Statistics emerged. In each section, we describe how the books were evaluated in reviews shortly after their publications. We conclude by briefly discussing the recent past, the present, and the future of textbooks on the foundations of statistical science and include comments about this by several notable statisticians.