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Questions tagged [statistics]

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

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31 votes
2 answers
824 views

Was fake/rigged data common prior to the 20th century?

In one of the lab courses I took as an undergraduate, I remember that the professor noted while discussing some statistical test (almost certainly chi-squared) that one could use it to show that a lot ...
Logan M's user avatar
  • 2,832
29 votes
3 answers
4k views

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 ...
Conifold's user avatar
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23 votes
3 answers
6k views

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 ...
Stefan's user avatar
  • 333
20 votes
1 answer
242 views

Markov chains origins and how is Christianity involved

In a book called Advanced Data Analysis from an Elementary Point of View by Cosma Rohilla Shalizi, page 405, the first instance of "Markov process" is accompanied by a footnote which reads ...
user avatar
19 votes
2 answers
2k views

Did Ronald Fisher ever say anything on varying the threshold of significance level?

There has been a growing chorus against the conventional NHST (Null Hypothesis Significance Testing). One thing is the blind usage of a monolithic significance level $5\%.$ In a recent thread at CV, ...
User1865345's user avatar
13 votes
2 answers
5k views

Who coined the term "signal-to-noise ratio" and when did statisticians start using the term "noise" to describe randomness?

I'm writing about the history of the concept of noise and am having trouble tracking down references from when the term "noise" started being associated with statistical noise such as ...
vy32's user avatar
  • 655
12 votes
0 answers
84 views

Why are the classic statistical approaches to NLP mostly generative models while the most recent ones are mostly discriminative?

Looking at the classic statistical approaches to natural language processing (e.g. tagging, parsing, etc.), I see that they are mostly generative models: n-gram models, Naive Bayes classifiers, hidden ...
Franck Dernoncourt's user avatar
9 votes
1 answer
199 views

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 ...
AChem's user avatar
  • 4,079
9 votes
0 answers
95 views

On the history of population dynamics of territorial species

I am interested in the historical priority in population biology, essays or monographs, discussing the concept of territoriality prior to 1950. What is it? In the early 18th century discussions of ...
Gottfried William's user avatar
9 votes
0 answers
205 views

Mathematical counterintelligence at Bletchley during World War 2

Popular works of fiction claim that after breaking the Enigma in Bletchley, some sophisticated mathematics or statistical techniques were used to hide this fact of breaking (not necessarily by the ...
puslet88's user avatar
  • 191
8 votes
1 answer
2k views

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 ...
FAHDI GORSY's user avatar
8 votes
1 answer
2k views

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 $\mu$...
Adam's user avatar
  • 377
7 votes
1 answer
1k views

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 ...
M. Al.'s user avatar
  • 71
6 votes
4 answers
1k views

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 ...
AChem's user avatar
  • 4,079
6 votes
1 answer
415 views

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 ...
José Carlos Santos's user avatar
6 votes
1 answer
457 views

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 $$E[h(X)] = \int_{-\infty}^{\infty} f_X(x)h(x) dx$$ ...
Alecos Papadopoulos's user avatar
6 votes
1 answer
96 views

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 ...
JPM's user avatar
  • 171
5 votes
1 answer
256 views

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 ...
lfba's user avatar
  • 171
5 votes
3 answers
235 views

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 ...
user58697's user avatar
  • 330
5 votes
4 answers
586 views

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 ...
Rho Phi's user avatar
  • 161
5 votes
1 answer
114 views

What is the S notation in Student's The Probable Error of a Mean?

In William S. Gosset's The Probable Error of a Mean (JSTOR), he begins to derive the $t$ sampling distribution as follows. Samples of $n$ individuals are drawn out of a population distributed ...
Sam Gallagher's user avatar
5 votes
1 answer
265 views

construct for h-index and Eddington number

There is a construct very useful to measure the efficiency taking into account both quantity and quality, which states something like N is the highest number that fulfils the statement "in this set, ...
Eynar Oxartum's user avatar
4 votes
1 answer
212 views

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 ...
Matthew Christopher Bartsh's user avatar
4 votes
1 answer
129 views

What factors influence whether an invention is not patented?

Various inventions that have become well-known were never patented, including matches, emoticons, and the magnetic strip. Other noteworthy examples include the polio vaccine (Jonas Salk), monoclonal ...
Max Muller's user avatar
4 votes
1 answer
217 views

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 ...
Antoni Parellada's user avatar
4 votes
0 answers
150 views

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 ...
Charlie's user avatar
  • 149
3 votes
2 answers
1k views

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 ...
yberman's user avatar
  • 173
3 votes
1 answer
141 views

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 ...
TonyK's user avatar
  • 345
3 votes
1 answer
153 views

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 ...
Alice.Sumarno's user avatar
3 votes
1 answer
114 views

Historical examples of frauds discovered because someone tried to mimic a uniform random sequence

So, I'm preparing a talk about the well known fact that humans are bad at the task of generating uniformly random sequences of numbers when asked to do so. I would like to spice the talk a bit by ...
Swike's user avatar
  • 131
3 votes
1 answer
102 views

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 ...
Uri Granta's user avatar
  • 1,204
3 votes
1 answer
2k views

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 ...
Stephan Kulla's user avatar
3 votes
0 answers
73 views

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, ...
Gottfried William's user avatar
3 votes
0 answers
106 views

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 ...
user2986288's user avatar
2 votes
1 answer
163 views

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 ...
cdwe's user avatar
  • 123
2 votes
1 answer
267 views

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 \...
Federico Poloni's user avatar
2 votes
1 answer
421 views

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?...
J.G.'s user avatar
  • 1,720
2 votes
1 answer
111 views

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 ...
Martin Vesely's user avatar
2 votes
0 answers
123 views

Kolmogorov on frequentists versus Bayesians

What was Kolmogorov's attitude regarding the frequentist versus Bayesian statistics controversies? Did he ever write or speak about his own views on Fisher or de Finetti, Jeffreys, etc.? Or were those ...
hyportnex's user avatar
  • 347
2 votes
0 answers
143 views

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 ...
Mitch's user avatar
  • 191
2 votes
0 answers
102 views

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'...
TheQuantumObsession's user avatar
1 vote
1 answer
166 views

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 ...
boeing777's user avatar
1 vote
1 answer
305 views

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)?
Lil'Lobster's user avatar
1 vote
1 answer
200 views

When did E. Hopf say "ergodic theory is statistics and statistics is measure theory"?

In the archived version of Kolmogorov's Foundations of the Theory of Probability, at the very end of the book, p. $84,$ few books have been listed, one being E. Hopf's Ergodentheorie, where it is ...
User1865345's user avatar
1 vote
1 answer
76 views

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 ...
Galen's user avatar
  • 309
1 vote
1 answer
138 views

Why Was Sequential Analysis Classified?

In the Introduction of his "Sequential Analysis" Wald writes that Because of the usefulness of the sequential probability ratio test in development work on military and naval equipment, it ...
hyportnex's user avatar
  • 347
1 vote
1 answer
102 views

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, "...
Adam Rubinson's user avatar
1 vote
1 answer
131 views

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-...
J.Galt's user avatar
  • 111
1 vote
0 answers
95 views

Were many (famous) theoretical laws in science based on "Statistical Regression"?

In a essay about the meaning of life, the famous scientist Schrodinger once said "Physical laws rest on atomic statistics and are therefore only approximate" (http://www.whatislife.ie/...
stats_noob's user avatar
1 vote
0 answers
55 views

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 ...
Know-Nothing-Bozo's user avatar