An eminent statistician and historian of the field examines the seven key concepts that form the basis of the modern theory of statistical inference and analysis. [519.5]
Stephen Stigler of the University of Chicago has written extensively on the historical development of the discipline of statistics. This book examines the history of the seven key concepts of statistical theory. These are the concepts that underlie our understanding of what it is that we are doing when we accept statistics as the reflection of reality and when we use statistics to guide our judgements.
For many of these concepts, Stigler finds their origins in the 17th century or earlier. This should not be surprising: the intellectual questions that are addressed have, most likely, been at the core of our thinking about the world. But, the full mathematical development and elaboration of the methods is surprisingly modern. Most of these can be traced to sources such as Galton (1880s) or Laplace (1770s) for the first clear realization of what would be required. The final development had to await the work of such moderns as Sir Ronald Fisher at the agricultural laboratory at Rothamsted (1920s) or Jerzy Neyman in the 1940s. Suddenly, statistics, which likes to trace its lineage to the 18th century, is seen as an exceptionally new science.
The keys to statistics lie in these discoveries:
- Aggregation. What is necessary to summarize a collection of observations? What may now be called sufficient statistics, think of the mean and variance, pose a puzzle; this reduced set of information may reveal as much about the parent population as the full record of observations.
- Information. How much do additional observations add to our knowledge? A critical rule in statistics, under standard assumptions, is that doubling the sample size does not double the information content. Information is found to increase with the square root of the number of observations; to double the information in a sample, one must quadruple the size. This situation means that sampling must balance economy with information.
- Likelihood. What do the observations tell us about the underlying probability distribution, among all possible distributions, that was most likely to be the source of the data? Likelihood methods become our tool for making inferences about how the world works.
- Intercomparison. How can observations be meaningful without reference to an external standard? The variability within the samples can provide a basis for judging whether subsamples are from the same parent or not.
- Regression. How does one explain the tendency of populations to remain clustered around central values rather than spreading out continuously? The issues were critical for the survival of Darwin's theory of evolution; they are the basis of our model building today.
- Design. How can experiments be planned to yield the sharpest distinction among factors influencing the outcome? How can randomization strengthen our conclusions? The pioneer work of Sir Ronald Fisher in agricultural experiments blossomed into the field of experimental design that guides marketing and medical research.
- Residual. How are complicated phenomena sorted to reveal relationships when some factors are stripped away?
This may be a particularly difficult book to read. Although Stigler tries to make the argument accessible to non-specialists, he is still limited in how much he can reduce the mathematics or the logic of the arguments to everyday speech. The author also assumes that the reader may be familiar with the pioneers of statistical logic. Still, for the reader with a basic background in statistics and probability, this may be an intriguing book.
With that qualification, the book is highly recommended.
