1 Studies in the History of Statistics and Probability ... - Sheynin, Oscar

of various groups of machines, and this provides us a test forestimating the reliability of the insulation. Purely statistical methodscertainly do not concern the improvement of that reliability which is atechnological problem. But at least we may say whether the reliabilityof insulation had changed and in which direction or that it remained asit was previously. This is the practical significance of the work donewhich would not be so important had the comparatively high statisticalhomogeneity of the insulation not been established. [...]2.4. The naked eye study. We had assumed that smoothing bypolynomials is usually successful because the data for that treatment isselected beforehand by naked eye. It would have been improper to failto mention that physicists and engineers also often perform thesmoothing itself by naked eye without applying the method of leastsquares. And how do we decide that the smoothing in a given case wassuccessful? Perhaps because the curve derived by least squares passesexactly where it would have been if drawn without applying thatmethod?An experimental smoothing by naked eye of the broken line in § 2.2was carried out. Participants were mathematicians, workers at astatistical laboratory, and engineers. Each received a list of paper withonly that line shown [...]. The results achieved by an overwhelmingmajority were very good. Fifteen out of sixteen of those participatinghad almost completely drawn their curves between the two curves,p 1 (t) and p 3 (t) as shown on Fig. 2. [...]I. V. Girsanov, the chief of one of the sections of the statisticallaboratory, achieved the best result; he unfortunately perished in a latertourist mountain tour. [...] In general, the results of smoothing bynaked eye are quite comparable in precision with the method of leastsquares. Had we been only interested in curve p 2 (t), we could havewell drawn it without any calculations. However, a thorough statisticaltreatment demands an estimation of precision as well for which astatistical model and science in general are necessary.Thus, when estimating the probability of success in Bernoulli trials,we turn to frequencies, but for understanding how large can thedeviations of frequency from probability be, we should, first, considerthe trials independent (the statistical model) and second, apply the DeMoivre – Laplace theorem which (however done) is proven in acomplicated manner [in essence, by the former in 1733] and this isundoubtedly science.When smoothing a broken line by naked eye, we do not even haveto know the number of observations used for calculating its points [...]and anyway it is impossible to indicate the confidence region for thecurve sought. Here, we need all the science connected with the methodof least squares and still the almost complete coincidence of the areashown on Fig.2 with that between the curves p 1 (t) and p 3 (t) demands tobe somehow explained.Note, however, that for small values of t that first area is somewhatnarrower than the second one whereas that latter, as shown bycalculation, is 1.5 – 2 times narrower there than a thoroughlyconstructed confidence region with the usual confidence coefficient of0.70 – 0. 95. This means that the indefiniteness of the naked eye63