Questions tagged [statistics]

For questions about the science that deals with classification, analysis and interpretation of numerical facts and data.

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What is the earliest use of the $\perp\!\!\!\!\perp$ symbol in statistics to denote statistical independence?

The symbol $\perp\!\!\!\!\perp$ in statistics is a way to denote statistical independence of a collection of random variables. I have seen two forms of it. The first is highly suitable in writing ...
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Can anyone recommend sources on the standardisation of research methods in modern (20th-21st c) science?

I’m interested in learning more about how statistical methodology and research design has changed over the course of the 20th and 21st century. I’m particularly interested in ways in which research ...
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Where does the abomination that is probability notation come from? [closed]

Those with experience may deny it, having suffered too long ago. But it stares you in the face with the somnolent, expressionless eyes of every student being exposed the first time. Probability ...
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Are statistics racist?

Evidence-Based Medicine (EBM) is a proposition and an area of study of medicine for which I am very fond. However, a few days ago, talking to some friends, I was confronted with a very critical ...
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Why some calculations noted as "sym^2" and "sym", while others noted as "symA" and "symB", where "symB" is the square root of "symA"?

Today I learnt that the standard deviation is calculated as square root of the mean of the squares of the deviations from the arithmetic mean of the distribution. The mean of the squares of the ...
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Why was the term random "variable" applied to a mapping?

I think I'm correct in saying a random variable is a mapping from the sample space to the real line (or more generally to $\mathbb{R}^n$. If I'm right then random variable seems a very odd way for a ...
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Who said that math or statistics is not free from class interest?

I'm not 100% sure this is the right site for this question, but here it goes. An already dead professor said in a lecture that Stalin (or perhaps another communist leader) wrote once something along ...
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Did Egon Pearson have a PhD?

Did the statistician Egon Pearson have a PhD? If not, to what extent did he write a dissertation?
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Who was the first person to propose the idea that consciousness arises from complexity?

The origin of consciousness has been a major scientific and philosophic debate since ever. Sometimes the origin is considered a philosophical issue, while others consider it a physics issue. Most ...
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Where can I find the historical information or the stats related to Winning WW2 with the minimum actions using The Bombe Machine of Alan Turing?

I am doing a marathon of data visualizations with real world datasets. I am interested in historical war datasets. Does anybody know about the historical data on The Bombe Machine cracking the codes ...
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In which work was Gibbs' Inequality introduced?

Gibbs' inequality $$-\sum\limits_{i=1}^n p_{i} \cdot \log{p_{i}} \le -\sum\limits_{i=1}^n p_{i} \cdot \log{q_{i}}$$ is such a popular thing that I cannot find where it was introduced. My findings I ...
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How long have people been debunking the P value (statistical significance) as commonly used in the human sciences: medicine, psychology and so on?

I have been puzzled for a long time at the way psychologists and medical researchers state that they have 'significant' results, and at the way this statement is relayed to the public who are misled ...
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Examples of when statistical distributions like Binomial or Normal distribution was critical in a law/policy decision, in a court case or otherwise

This was closed as off-topic on math.se, and it was suggested I post this here, so here goes. Firstly, I am aware that this thread exists, and I'll definitely be ordering a copy of the book, "...
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Stories about the consequences of statistical simplification?

I am currently preparing a presentation about the value of more complex (specically: non-Gaussian) statistical inference. I thought it might be interesting to start the presentation with a small real-...
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Where was statistics taught in the 17th and 18th centuries?

Here is a fragment from Anders Hald's A History of Probability and Statistics and Their Applications before 1750: The original meaning of statistics is thus a collection of facts of interest to a ...
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Why is William Playfair seldom heard about in mathematics?

William Playfair was a Scottish engineer and economist, who invented the pie and bar charts as well as the line graph, which have all played an indubitably ubiquitous role in modern statistics. I hadn'...
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How was mathematics used in World War II to "act on the right amount of intelligence"?

In the movie "The Imitation Game", Alan Turing along with his team crack the German encryption machine Enigma but advises his superiors to not act on all decrypted intelligence, as that might lead to ...
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Why is a time series not called a time sequence?

In pure mathematics, a sequence is a list of terms, for instance $1, \frac12, \frac14, \dots, \frac{1}{2^k},\dots$, and a series is the sum of an infinite sequence, for instance $\sum_{k=1}^\infty \...
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Significance level $\alpha$ values - who devised to use $\alpha = 5 \%$?

In a statistical hypotheses testing a significance level $\alpha$ has to be set. The most often, $\alpha$ is set to be 5 %, sometimes 1 % and 10 % values are used. Value of $\alpha$ tells us what is ...
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6 votes
1 answer
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Quotation about $\pi$ and the number of deaths

I read more than once a story which took place, if memory serves me well, in England, in the XIXth century. A statistician (or a mathematician) was making computations about life expectancy (or ...
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How did Weibull derive the three parameter Weibull distribution?

How did Weibull or any other mathematician arrive at the above expression? I saw the 1951 paper, but it is not clear to me. In 1939 he had published a book called "A Statistical Theory of the Strength ...
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Where does $M$ for expected value in Russian papers come from?

In modern papers in statistics, it is common to use the symbol $E[X]$ to refer to the expectation of a random variable $X$. While reading (a translated version of) "Convergence Rate of Nonparametric ...
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Why do many names of technical and scientific subjects end with "ics"?

The names of many technical and scientific subjects, like mathematics, physics, statistics, etc., etc., end with letters "ics". What is meant by this, if anything? Was there any logic behind it or is ...
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How is the word kernel associated with distributions?

I am trying to rationalize the meaning of the term kernel, especially when it is associated with distributions. The English and German etymology all show that the literal meaning is corn (English) and ...
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Introduction of shape parameters in the formulation of probability distribution

I'm familiar with the definition of location, scale, and shape parameters, and the type of distributions they parametrized. I'm interested in understanding how shape parameters became part of the ...
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Where did the story about Newcomb observing Benford’s Law come from?

The story goes that in the 1880s Newcomb noticed that logarithm tables were more worn down towards the beginning of the book (where the leading digit of the logs were 1). This led him to formulate an ...
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2 votes
1 answer
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How did Quetelet discover that the body mass is proportional to the squared height?

The Body Mass Index (BMI) compares body masses on the assumption they scale with height squared, not cubed, an example of allometry. BMI is due to Lambert Quetelet. Why did he settle on this power law?...
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Who came up with a number of the theoretical plates equation?

In chromatography, the signal is shaped like a Gaussian peak, and it is plotted against time vs. instrument's signal. https://en.wikipedia.org/wiki/Chromatography#/media/File:Rt_5_12.png (a) One of ...
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Real effects long thought to be coincidences

What examples are there of scientific effects or correlations that we now know to be real, and were known about for a long time but thought to be coincidences? To give an example of the kind of thing ...
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3 votes
2 answers
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What is the etymology of the term "mode" in statistics?

I saw that the word "mode" means "popular" in French, and I was wondering if this might be the etymology of the "mode" of a population in stat? I was wondering if anyone had sources for early use of ...
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Why statistical moments are called moments?

According to the Jeff Miller's Earliest Known Uses of the Words of Mathematics "Moment was taken into Statistics from Mechanics by Karl Pearson when he treated the frequency-curve (or observation ...
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Statistical Power as a Microscope Metaphor

An answer on this question on the cross validated stack exchange compared statistical power to a microscope, such that "in order to see small things you need a powerful microscope" is analogous to "in ...
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6 votes
1 answer
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Law of the Unconscious Statistician - history of the term?

The "Law of the Unconscious Statistician" states that, for a random variable $X$ with density $f_X(x)$ and a function of it $h(X)$ we have that $$E[h(X)] = \int_{-\infty}^{\infty} f_X(x)h(x) dx$$ ...
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6 votes
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What is Peirce doing in this pre-Chi-squared example?

In 1878, C. S. Peirce performed a calculation that (I think) would be better done using chi-squared testing — but Pearson hasn’t introduced that yet. What exactly is Peirce doing here in the last ...
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How was the idea of observation error introduced?

The first thing a contemporary student of physics learns is the measurement error. As far as I understand, the idea of imprecision was totally foreign to natural philosophers at least until the end of ...
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Historical development of role of astrology in medicine?

The OED defines "iatromathematics" as Practising medicine in conjunction with astrology. Pre-17th century, it seems most scientists (physicians included) believed in the influence of the stars on ...
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Galileo and normal distribution discovery

If differential equation theory was known and also studied by Galileo, so why he didn't manage to discover a normal distribution (its discovery had to wait for Laplace and Gauss)?
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What defines the 'name' of a score i.e. gamma, kappa etc

I was just wondering if there is a process or set of properties that exist to name a score, such as, Cohen’s Kappa, Fleiss’ Kappa, Krippendorff’s Alpha, or if it is just at the creators choice. ...
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When did error propagation become prominent in physics?

I think is well known that greek scientists and even founding fathers of modern science did not use error propagation in their calculations. Today, instead, is unacceptable to work out any prediction ...
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Raymond Cattell and History of Personality Traits Prior 1947

I find that papers reference Raymond Cattell suggesting 16 or 22, etc, traits, by factor analysis (basically regression), including all five of the modern reproducible traits (openness to experience, ...
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Origin of diagrammatics illustrating the relation between cumulants and moments?

The exponential-log transformation of exponential generating functions (see OEIS A036040 and A127671) relate the classical cumulants to their associated moments. Who were some of the first to ...
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Why do we often minimize in optimization?

Because of the following relation, \begin{equation*} \inf(S) = -\sup(-S), \end{equation*} minimization and maximization is essentially the same thing. However, take any optimization routine in R for ...
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Who developed Gaussian Mixture Model (GMM) and applied it to machine learning?

I searched about GMM (Gaussian mixture model), but only found that normal distribution was invented by Carl Friedrich Gauss. I'd like to know who contributed to the development of GMM itself, and to ...
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Name and history of probabilistic non-inevitability paradox?

A counterintuitive result in probability theory that may warrant the description of a veridical paradox is the fact that repeating an experiment with a nonzero chance of success infinitely often does ...
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23 votes
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Hypothesis testing: Fisher vs. Popper vs. Bayes

I try to make my question short. I am familiar with Popper’s philosophy as well as with statistical hypothesis testing after Fisher and Neyman-Pearson. I am not so familiar with the Bayesian approach ...
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Secular Status Difference Between Applied and Pure Mathematics

Coming from outside the field but with healthy curiosity I have been struck by what may be regarded as a discrepancy between the impact on science at large of the mathematics developed in the field of ...
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Why do we see the modern version of regression as "Fisher's regression"?

In Fisher's paper, he did not include the error term. http://psychclassics.yorku.ca/Fisher/Methods/chap5.htm But Durbin & Watson suggested the error term, and also made the matrix form of the ...
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3 votes
1 answer
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First usage of binomial distribution

As stated in the article binomial distribution by britannica.com the binomial distribution was used by Jakob Bernoulli when he said that "the probability of $k$ ... outcomes in $n$ repetitions is ...
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8 votes
1 answer
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Where does Markov operator come from?

I found this definition of "Markov operator" in the book Chaos, Fractals, and Noise by Lasota and Mackey. Denote by $L^1(\mu)$ the space of Lebesgue integrable functions according to the measure $\mu$...
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Who introduced random variables into probability?

I used to think that the answer is Kolmogorov. So the Shafer-Vovk's review of Kolmogorov's famous 1933 axiomatization of probability surprised me a bit:"Today, what Frechet and his contemporaries knew ...
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