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Some Theory of Sampling

William Edwards Deming
Dover Publications
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The Basic Library List Committee recommends this book for acquisition by undergraduate mathematics libraries.

[Reviewed by
Tom Schulte
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During a decade of statistical process control (SPC) quality analytics software development, I often found myself with Quality Control staff in a cramped, lab-like shop floor office. When the name of William Edwards Deming arose, comment would be made on his work in Japan. There would be a moment of silent reverie about this priest of product quality and his religion of the application of statistical methods. It would be affirmed and agreed that this prophet cast out from his own land found a following in Japan and gave it the knowledge to engineer high-quality products eventually giving it economic power. Funny, though, I do not recall ever seeing Deming’s work on the shelves in those offices already groaning with reference texts, although I have espied texts of Donald J. Wheeler, Deming’s disciple. Now that Dover has made this paperback available, I would like to revisit each of those offices and drop off a copy.

Not only as an SPC evangelist, but as a math teacher I find this unabridged republication of the 1950 edition valuable. For instance, I have not seen a textbook published since that lays out to the student a logical transition over a few pages from an ideal bowl of chips in two colors to the binomial coefficient to the Bernoulli and hypergeometric series. The same can be said for the plain and careful exploration of deciding sample size for required confidence. Over two hundred pages this key concept is explored as the crucial underpinnings to “the sample as a basis for action.” It is finding this action to improve quality, improve the world, which the field statistician lives for. And, in helping the budding statistician get there, Deming never lacks in patience. Even over three hundred pages into the book, he is still willing to go back to the simplest four-chip universe and reveal what can be learned from two-chip samples.

Further, Deming’s careful distinction between enumerative and analytics aims in data gathering and tabulation speaks plainly to the heart of the intuition a beginning statistics student needs to develop. That student need not yet have taken calculus (nor to remember what calculus he or she has taken) to benefit from reading this work. As Deming remarks, “The student whose calculus is shaky need not be frightened by the principles involved in this integration… The principles are more important than the actual manipulation of integral signs, which, after all, are merely shortcuts.” So, go ahead and drink in the list of possible applications for ratio estimates and skip through the technical definition of the gamma and beta functions. Deming would approve.

Indeed, part of the joy of reading this work is the author’s anti-academic pragmatism, which I have also seen in the Quality Control technicians that revere him. Deming acknowledges a conflict between rote and reality: “For any account so small… in my own practice I either put a floor at 25 or omit such an account altogether… If public education were not involved, there would be no problem… However much time and effort may be lost trying to explain to the court why a sample of (e.g.) only 8 items is sufficient… and it may be cheaper to increase the sample.” Deming here is teaching not only the theory, but the practice of doing statistical analysis in the field, apparently a field dangerously full of the products of law school.

There can be much unlearning required to forge ahead in this thicket. He observes, “Graduates in mathematical statistics, when taking up practice, discover yawning gaps between theory and practice: the better their theoretical training, the wider the gap.” Deming explicitly wrote a half-dozen of the chapters in this book to “bridge this gap.” If you have an interest in statistics, read those chapters, even if the mathematical rigor in the others makes you yawn. It is not just Deming himself that is witty and world-wise. He manages to find a quote of the same tone for nearly every chapter which helps keep the work inviting and accessible to any interested reader.

In this upcoming election year, polls begin to come at us with growing frequency, creating a Doppler Effect of ever shrill pronouncements. A core thread of real-world examples and experience detailed in Some Theory is a grounds-up methodology for polls and surveys from interview techniques to data analysis. It is a good time to consider polls, their planning, and their preparation. Deming lays out how it is done and how it works. The cover image is from a post-WWII survey of Greek households, which is a particularly enlightening example of meeting real-world goals by applying sampling theory in a difficult field situation. Another government project, referred to throughout, is getting an accurate survey of utility pole conditions at minimum cost but required accuracy.

The book is structured somewhat like a textbook, in that each chapter concludes with exercises. Many of these exercises have hints or guided solutions present on the same page. Future social scientists, quality managers, and others can independently read this work to obtain a sound basis for their craft. College algebra is enough to gain entry into Deming’s insight into sampling. It is no wonder that the American Statistical Association Journal called it "The 'bible' of sampling statisticians."

Tom Schulte spent a decade as a software engineer specializing in statistical process control (SPC) analytics at Plex Systems in Auburn Hills, MI.

The table of contents is not available.