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

IIV. N. TutubalinTreatment of Observational SeriesStatisticheskaia Obrabotka Riadov Nabliudenii. Moscow, 1973IntroductionFacts are known to be the breath of the scholar’s life. In our centuryof exact scientific methods, observation usually means measure, andfacts which we have to deal with, are as a rule expressed in numbers.In any scientific establishment you will be shown long series ofnumbers also represented by graphs drawn by coloured pencils onsquared paper. All of them are observational series. What benefit can4we elicit of such coloured splendour whose collection demandedmany long years of efforts by many authors?Observational series often lead to some evident conclusion. Thus,after the introduction of antibiotics into medical practice, mortalityfrom most infectious diseases sharply declined, but no mathematicaltreatment for such conclusions is necessary: the result speaks for itself.In other cases, however, conclusions can be not so unquestionable, andwe have to apply statistical treatment and attempt to make them morereliable by mathematical methods.It is important to imagine that in many cases the statistical treatmentis beneficial but that perhaps even more often it is useless andsometimes even harmful since it prompts us to make wrongconclusions. Thus, antibiotics are useless in cases of viral infection.This booklet deals with instances in which statistical treatment isscientifically justified.1. Two Main Mathematical Models of Observational Series1.1. Why is statistical treatment needed? As stated in theIntroduction, it can be not necessary at all. One more such exampleconcerns the reliability of machinery. Suppose we discovered somepreventive measure that obviously lowers the number of failures. Ourobservational series (for example, the number of failures over someyears) certainly confirms the efficacy of our finding and we may besatisfied. Human nature, however, is incessantly wishing somewhatbetter; since there are less failures, we will wish to have none of themat all, so we propose another development and desire to confirm itsefficacy by showing that the number of yearly failures will lower stillmore.You can guarantee that this will not be so easy. When the number ofyearly failures is small, it will be noticeably influenced by randomcauses. This does not yet mean that it can be studied by purelystatistical methods, because their applicability demands the probablylacking statistical homogeneity [i]. However, such models allow toreach some important conclusions which we need to bear in mind. Inaddition, once a good technological result is already achieved, and westrive for a still better outcome, statistical homogeneity occurs ratheroften.47