# Tag Info

## Hot answers tagged statistics

22

According to Mayo, Popper did not designate statistical tests implementing his logic of falsification, or as Hilborn and Mangel put it "Popper supplied the philosophy, and Fisher, Neyman and colleagues supplied the statistics", see references in Quinn and Keough's Experimental Design and Data Analysis for Biologists (Ch. 3). Popper viewed ...

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It is not random. These names are of Greek origin, and -ic or -ics are Anglicizations of the Greek suffix -ikos, which meant "pertaining to". In other languages it can be rendered as -ika or -ica, Wolfram's "Mathematica" uses such a version. From the Online Etymology Dictionary: "-ics in the names of sciences or disciplines (acoustics, aerobics, ...

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Almost. E P Wigner (1960), Communications on Pure and Applied Mathematics 13 1–14 The Unreasonable Effectiveness of Mathematics in the Natural Sciences THERE IS A story about two friends, who were classmates in high school, talking about their jobs. One of them became a statistician and was working on population trends. He showed a reprint to his former ...

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The notion of "rigged data" evolved with time. Some ancient scientists are accused (by modern scientists) in rigging of the data. One notable example is Ptolemy. I do not want to discuss here the accusation of Ptolemy by Robert Newton, but here is another well-known example. In his Optics, Ptolemy gives a table of refraction. It looks like he measured ...

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This question has no definitive answer, because people were operating with random variables long before any rigorous definition was given. Probability theory begins in 16-th century, if not earlier. Cardano wrote a book on it, for example. In 1773 de Moivre wrote an important book where he essentially introduced the principal method of modern probability (...

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Concerning the notation $\text{Pr}(|\xi|>\varepsilon)$ here's what I've found so far: Cajori's 1929 A History of Mathematical Notations says nothing on probability theory, which suggest that the subject had not yet developed any special or widely adopted notation around the beginning of the 20th century. This seems to be supported by Jeff Miller, who ...

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One would think that Russian usage stems from Kolmogorov's seminal works on probability. However, in Über die Summen durch den Zufall bestimmter unabhängiger Größen (1928) he uses $\mathfrak{M}$ to denote probability (presumably from messen, measure), not mathematical expectation. In the famous Grundbegriffe der Wahrscheinlichkeitsrechnung (1933), which gave ...

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Astronomers had to deal with experimental errors to parametrize their geometric models at least as early as Hipparchus, and possibly earlier. There are some techniques and ad hoc methods that can be seen in hindsight as dealing with them in Ptolemy's Almagest, he discusses interpolation, for example. Ptolemy's "massaging" of Hipparchus's data even became a ...

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This was discussed on Math Forum. According to Elliot, Halmos called it Fundamental Theorem of the Unconscious Statistician as early as 1946, and according to Bernier, Introduction to the Techniques of Operations Research by Hillier (1965) calls it the "Law of the Unconscious Statistician". But apparently the nickname only took off after Ross's "...

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This is a continuous analog of (transposed) stochastic matrix, the transition matrix in a Markov chain with discrete set of outcomes. These were introduced in 1906 by Markov apparently to disprove Nekrasov's claim that central limit theorems only applied to independent events, but later found many practical applications. Entries of a stochastic matrix are ...

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As @Dave L Renfro noticed, the distinction between series and sequence is not old, and it was possible for the same author to use the two terms with different meanings (also in the same article). Consider e.g. Gauss's Theoria Residuorum Biquadraticorum Commentatio Prima & Commentatio Secunda, we have some examples: article 5 cunctos numeros $1, 2, 3 \... 4 Into Popper's The Logic of Scientific Discovery (1934 - 1st Engl.ed.1959) you can find CH.VIII : Probability and several Appendces devoted to probability theory. Bayes [Bayes,Th. 144, 168n, 288–9] and Fisher [Fisher,R.A. 18&n, 326, 334, 384, 394n, 403] are presents into the Index of names, also if Keynes and von Mises are prominent. The basic "axiom" ... 4 I came across this question while trying to figure out when the "law of propagation of error" was first stated, which resulted in this question: When was the "Law of Propagation of Error" first stated? which now contains a reference to your question. Your question is about when error propagation become prominent (rather than about when it ... 4 The Oxford English Dictionary shows moment of a force appearing in 1830 in A Treatise on Mechanics by Henry Kater and Dionysius Lardner. So perhaps it is reasonable to guess that Stieltjes and/or Pearson took the term from mechanics. 4 This seems to depend on who you call a statistician, mathematician, or mechanician. Certainly Pearson sounds like he’s using, as a matter of course, a term also found in e.g. Stieltjes (1894, p. 48; 1885), Wittenbauer (1881), Reye (1870), Poinsot (1806), Euler (1752, p. 192), etc. I hadn’t heard of Commandino (1565): it would be interesting to see what ... 4 According to this article (in Italian) by Maurizio Codogno, the origin is in an article by Pearson dated 1895 (Contributions to the Mathematical Theory of Evolution. II. Skew Variation in Homogeneous Material). In fact, in the article by Pearson you can find the following note on page 2: I have found it convenient to use the term mode for the abscissa ... 4 BMI is now widely used for detecting obesity, but Quetelet's motivation was in defining the characteristics of an ‘average man’. Quetelet was one of the early enthusiasts of what we now call statistical studies and aspired to extend statistical analysis beyond demographic and anthropometric characteristics to other aptitudes, associated with behaviour, and ... 4 Rationalizations that "make sense" are often urban legends after the fact, people who introduce terms rarely make a point of it or report their reasons. The process of spreading is largely by accident and loose association, sometimes aided by invented backstories. Fredholm used the French version ("noyau") for integral equations, for whatever reasons, ... 3 It is not a story, Newcomb published his observation in a two page Note on the Frequency of Use of the Different Digits in Natural Numbers (American Journal of Mathematics Vol. 4, No. 1 (1881), pp. 39-40), which you can read under the link. Here is the opening paragraph: "That the ten digits do not occur with equal frequency must be evident to any one ... 3 Moments in mechanics and statistics are defined by the same formula: $$\int x \rho(x)dx,$$ for the first moment. In mechanics,$x$is distance, and$\rho$is the mass density. In statistics,$x$is anything (whatever your random variable represents) and$\rho$is the probability density. So it is not surprising that the name is the same. Moments in mechanics ... 3 The idea of using Gaussian mixtures was popularized by Duda and Hart in their seminal 1973 text, Pattern Classification and Scene Analysis. 3 Even aside from the fact that Galileo knew nothing of differential equations, or derivatives for that matter (he lived before Newton and Leibniz), and that the normal distribution was not discovered by Laplace and Gauss but by De Moivre, why the connection? De Moivre discovered the bell curve not by solving differential equations but looking for a good ... 3 Please allow a correction: I think your statement "he says that one should sincerely try to disproof hypotheses – and I am quite certain that he didn’t mean the null hypothesis that Fisher formulated but rather the hypothesis that is of critical importance to us" is not really correct. Actually, this is exactly how Fisher would have described "null ... 3 The paper "Strength of materials and the Weibull distribution" by Eric S. Lindquist in Probabilistic Engineering Mechanics 9 (1994) 191-194 probably has what you want. I found several online copies with a "weibull's original paper" google search, but they might be behind institutional paywalls. Weibull's 1939 paper "A statistical theory of the strength of ... 2 A Durfee square can be defined for every integer partition. It was introduced before 1883 (which makes it anterior to Pareto's work). It is the construct at the root of both Eddigton number and h-index. Example of a Durfee square : x x x * * * * x x x * * x x x * * * * * Here the Durfee square of the set {1,3,4,5,7} is the 3x3 square highlighted as there ... 2 The answer is certainly "no", they are not under-appreciated. A simple proof of this is the salary survey in mathematical sciences published yearly by the Notices of the American Mathematical society. From this survey you can see that the average salary (on all levels) is higher in statistics than in pure mathematics, and the highest one is in "bio ... 2 In The Oxford Guide to the History of Physics and Astronomy, under the heading Error and the personal equation, Kathryn Olesko writes: Since Greek times astronomers have recognized that observations were afflicted by errors, that results based on them might be only approximate, and that the quality of data varied. Astronomers in early modern Europe took ... 2 The Oxford English Dictionary divides its definitions of the noun mode into: "senses derived directly from the Latin" and "senses derived from French". The statistical meaning is listed in "senses derived from French". 2 Based on comments, the reasons for using$\alpha = 5\%$are these: The value was used by prominent statisticians (such as R. A. Fisher). In order to have statistical analysis comparable with others, statisticans started to follow their example. Probability 5 % and 95 % is connected with$2\sigma$interval under normal distribution The reason for using$\...

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