I recently read "The Seven Pillars of Statistical Wisdom," recommended by my friend and colleague Scott Nestler. It is an interesting and well written guide to statistics. It is unique because it includes advanced mathematics like
interwoven with readable text.
It includes interesting stories about how statistics shaped society and Man's understanding of the world, as well as how statistics came into its own as a scientific discipline. The first chapter, Aggregation, tells the story of how statistical reasoning helped early scientists determine the ratio and shape of the Earth.
One passage that struck me in particular was the discussion of Frank Weldon's experimental exploration of a question posed by Karl Pearson. I repeat it in its entirety:
...In a heroic effort to gain a better understanding of chance, Frank Weldon had thrown 12 dice at a time and for each group of 12 counted how many of the dice showed a 5 or a 6. He repeated that experiment a total of 26,306 times. The total number of single die tosses was then 315,672.... Imagine one man doing all of that by hand. In one report, Weldon did indicate that his wife had assisted him; one can still wonder about the stress on the marriage. (p. 181)
Since this article is written in Markdown (see previous blog post), we can repeat that experiment right now, using our computer:
tot.time = system.time({nreps = 26306 result = vector() for(i in 1:nreps){ result[i] = sum(sample(x = 1:6, size = 12, replace = TRUE)>4) }}) hist(result, main = paste("Histogram of 5s and 6s in ", nreps, " replicatons"))
This procedure took 1.03 seconds on my laptop. It is astonishing - and humbling - to think of what early statisticians had to do to convince themselves that their theories were, in fact, sound.
(Markdown is a simple formatting syntax for authoring HTML, PDF, and MS Word documents. For more details on using R Markdown see http://rmarkdown.rstudio.com).