Stephen Stigler’s “The History of Statistics: The Measurement of Uncertainty before 1900”

finished reading Stephen  M. Stigler‘s History of Statistics: The Measurement of Uncertainty before 1900.  Statistics.  Harvard U. Press. 1990 I I confess I  not understand a lot of it, but it left me the math but this book left me thirsting for what I hope will be a the sequel.  I was impressed with the quality of  his writing and story telling, attempting and purporting to get inside the intentions of the historical figures of whom he writes.  Most of my lack of understanding I think is due to my own lack of understanding of maths and statistics, not to Stigler, although there are occasional  lapses I think on his part; but these weren’t fatal, just minor annoyances.
This book gave me what I think is a much better insight into the stakes, and into the problems of my own research is the sociology of scientist development, the success of which will depend heavily on the success of the statistical l techniques of social science, which is largely Stigler’s thread.
The problem he wanted to address was “why did it take so long for statistics to be adopted by the social sciences” (my framing).  One of the conclusions is that in astronomy and geodesy there was a relatively simple mathematical theory of gravitation and motion in which there were assumed constants (g, etc).  It was necessary to develop a theory of observational error and a theory of statistical analysis to allow the combination of multiple and diverse observations in order to determine the value of these constants, but little disagreement as to whether there were such constants.  (A notable exception, which Stigler does not mention, was the question of whether c, the speed of light, was to be a constant.  This wasn’t settled theoretically until Einstein and experimentally not really until perhaps Michelson‘s measurements.)   Nonetheless, the assumption of gravitational constants and power laws such as Kepler’s Laws of motion, meant that the utility of statistical analysis was readily appreciated.  Moreover, in the physical sciences it was possible to used controlled experiments independently to verify the constants.
In contrast, it wasn’t clear in the social sciences that the was anything like a “constant”.  The mean values of Quetelet‘s “Homme Moyen” were statistical constructs, not universal constants.  Part of the struggle that took 200 years to complete was to re-vision the problem as well as advance the math.  In particular, it took quite a long time for the notion to become established that variability itself was an object of interest.  The “analysis of variance” (“ANOVA”) is a technique useful in physical sciences as well, but in social science it is also a field of interest.  A good bit of this came from advances in genetics- Francis Galton and Karl Pearson and in the 20th Century Ronald Fisher were driven by problems of biology, genetics, evolution, in which Variability rather than Constants is of prime interest. 

This tension is potent today when some of struggle with whether to represent our data in terms of mean +/- standard deviation (SD)  or mean +/- standard error of the mean (SEM).  The latter presentation always “looks better” in a graph but emphasizes the value of the mean itself- how well do we know the average value, as if the average value itself was important.   The former presentation emphasizes the variability of the data.  SEM can be made arbitrarily small, simply by making more measurements. If we are measuring a constant such as g, this makes great sense.  SEM is high when our technical methods of measuring the constant are weak, so the SEM is inversely related to our technical prowess.   SD reflects the “natural” spread in the population, which makes sense in biological and social situations when we think there is natural variability. We might even be more interested in the SD than the mean value, so that we wish to know the error in the SD!   Nevertheless, technical prowess still plays a role, since crummy measurements will still poison our measurements.  This is a persistent conundrum.

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