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Mathematics have ISO 80000-2:2019 which specifies mathematical symbols, explains their meanings, and gives verbal equivalents and applications. Is there an equivalent for statistical symbols?

Edit: the question is broader than the question of statistical model notation since it also encompasses simpler topics (such as the symbol for average, median, etc.)

crocefisso
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    If there is one, I don't know about it. And it certainly isn't universally followed. Usage differs by country (US, England, fSU), discipline of application (psychology, economics, engineering, etc.) Examples: In US and western Europe the CDF $F_X(t) = P(Z\le t)$ in eastern Europe often $F_X(t) = P(X < t).$ in some disciplines $E(X)$ is written $$ (or with similar angle brackets). In some countries random variables are Greek letters $\xi, \zeta, \eta,$ etc, instead of $X, Y, Z.$ Different symbols for density fcns in frequentist and Bayesian statistics. Histogram bins $[a.b)$ vs. $(a,b].$ – BruceET Nov 06 '20 at 11:05
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    Also terminology: "repeated measures" can mean almost anything depending on discipline, "normalize" can refer to many kinds of tampering with data, "false positive" can mean $D^c \cap T$ or $D^c|T$ or $T|D^c,$ where $D$ signifies infected with disease and $T$ signifies positive test. "Independent variable" has several different meanings. "Outlier" has several useful definitions and many useless or meaningless ones. There is no standard "geometric" or "negative binomial" distribution. There is no standard parameterization of exponential, gamma, or Weibull distributions. – BruceET Nov 06 '20 at 11:19
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    Does this answer your question? Is there any "standard" for statistical model notation? – Xi'an Nov 06 '20 at 11:26
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    Well, the question was not to know if statisticians followed a standard, I already know they don't. I wanted to know if some standard supported by an institution or group of people working on this topic existed. – crocefisso Nov 06 '20 at 11:35
  • If statisticians don't follow any standard, then doesn't that a fortiori answer your question?? – whuber Nov 06 '20 at 12:39
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    Not at all. For example there are standards for project management methodology and you can be interested in knowing them, even if the majority of project managers don't follow them. – crocefisso Nov 06 '20 at 12:49
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    I have no interest in studying or following standards that don't apply to the literature I read or the audiences I want to reach. Life is too short. I suspect many others share this view. – whuber Nov 06 '20 at 16:03

2 Answers2

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So I found out that there is a standard. See

  • ISO 3534-1:2006 Statistics — Vocabulary and symbols — Part 1: General statistical terms and terms used in probability
  • ISO 3534-2:2006 Statistics — Vocabulary and symbols — Part 2: Applied statistics
  • ISO 3534-3:2013 Statistics — Vocabulary and symbols — Part 3: Design of experiments
  • ISO 3534-4:2014 Statistics — Vocabulary and symbols — Part 4: Survey sampling
crocefisso
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  • How did you find these deviations? – Sextus Empiricus Nov 06 '20 at 15:21
  • Well, first I had to find the official page of the iso provided in your comment, then I rooted it to the following page : https://www.iso.org/ics/01.040.03/x/. Which allowed me to find the 4 iso I mentioned. – crocefisso Nov 06 '20 at 15:28
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    All these sources are not open standards (did you acquire them yourself already? And have you been satisfied with them?). They require payments. Isn't being free a requirement for being a standard? I doubt that most statisticians have ever payed to get these documents (except whenever they were obliged by their corrupted governments). – Sextus Empiricus Nov 06 '20 at 15:34
  • Research papers are even more expensive. Anyways search engines can turn them free. – crocefisso Nov 06 '20 at 15:38
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    I would not regard research papers as equal to these standards. Most research papers are nowadays somewhat freely available or at least the crude originals (pre-standardized by publishers and reviewers) are available on some archive. But more importantly these standards should be free in order to be standards. Pearson never meant standard to be requiring a fee and I believe nobody does. – Sextus Empiricus Nov 06 '20 at 15:40
  • I challenge you to find a legal source, by means of search engine, for one of your four "standards" (I will give you a +500 bounty for it). – Sextus Empiricus Nov 06 '20 at 15:45
  • Well, in return I challenge you to find the equivalent open standard. I will edit my answer then. – crocefisso Nov 06 '20 at 15:47
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    The Website indicates these are not general standards: they are only used by one particular organization for one specific purpose (namely, describing other standards!). "ISO 3534-1:2006 defines general statistical terms and terms used in probability which may be used in the drafting of other International Standards." Although--because they are promulgated by the same organization referenced in the question--they are somewhat "equivalent" to the mathematical ones, their existence is of little general interest, as @Sextus argues, and have received no attention from statistical communities. – whuber Nov 06 '20 at 15:55
  • Well I think statistical communities should agree on a standard. Meanwhile, I'll use the mentioned standards for my notations. – crocefisso Nov 06 '20 at 15:59
  • How is ISO 3534-x:2006 in any way a standard when hardly anybody on this website (or any other statistician) has ever heard of it or isn't able to see it without paying some fee? I have given you the 'Oxford dictionary of statistical terms' as an answer (that one is at least free). But if it is a "standard" that you are looking for, whatever that may mean, (do you mean something official or something that needs to be payed for?) then maybe there is no standard answer possible. – Sextus Empiricus Nov 06 '20 at 16:26
  • Well as I said in a previous comment, a standard is something that should be evolutive since statistics in an ongoing "science". Your book is 70 years old. Though may be most ISO notations coincide with it. – crocefisso Nov 06 '20 at 16:31
  • Plus the book isn't free or FLOS and Yadolah Dodge is an Honorary Professor at the Institute of Statistics at the University of Neuchatel in Switzerland. – crocefisso Nov 06 '20 at 16:37
  • @SextusEmpiricus said... "Isn't being free a requirement for being a standard?" Not at all. ANSI, ISO, IEEE, IUPAC, all charge money for access to their standards documents, either by selling the documentation directly or through membership fees which grant access. This is, pardon the pun, standard procedure in the industry. – barbecue Nov 06 '20 at 21:40
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According to the Oxford dictionary of statistical terms (and probably many other standard works) the term 'standard' has already been claimed by Karl Pearson in 1894.

Quote from Contributions to the mathematical theory of evolution (emphasis is mine)

In the case of a frequency-curve whose components are two normal curves

...

each component normal curve has three variables : (i.) the position of its axis, (ii.) its “standard-deviation” (Gauss’s “Mean Error”, Airy’s “Error of Mean Square“). and (iii.) its area.

So, No, there aren't standards in statistics except for standard deviations and standard errors.

We can blame professor Pearson for not contacting the International Standards Organization to discuss about standards in statistics (or as Crocefisso notes, not Pearson personally, but his spirit).

Apparently, as Kjetil notes, there has been a small resistance and the ISO has also been working on statistics in ISO-3534 Statistics — Vocabulary and symbols (I am not sure I am linking correctly since I am not buying these standards)

Sextus Empiricus
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    Well, you can't blame Karl Pearson for not contacting ISO since he died in 1936 and ISO was created in 1947. Anyways standardization is an ongoing process and advances in statistics are not over. – crocefisso Nov 06 '20 at 14:31
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    this paper seems to disagree ... – kjetil b halvorsen Nov 06 '20 at 14:32
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    Though your speech about Pearson is not very convincing about the non-existence of standards. – crocefisso Nov 06 '20 at 14:33
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    @crocefisso according to the Oxford dictionary, which is a standard work, "standard" refers to Gauss' mean error in statistics. As in 'standard deviation' or 'standard error'. – Sextus Empiricus Nov 06 '20 at 14:36
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    Well, I guess you didn't understand the question then. – crocefisso Nov 06 '20 at 14:39
  • @crocefisso "The organization began in the 1920s as the International Federation of the National Standardizing Associations (ISA)." So Karl Pearson could have an influence on it. But... the term 'standardizing' was also already taken at that time in statistics. (So maybe we should indeed blame the organisations for starting too late) – Sextus Empiricus Nov 06 '20 at 14:40
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    @crocefisso "I guess you didn't understand the question then" We are speaking about statistics not? The symbols are chosen randomly. – Sextus Empiricus Nov 06 '20 at 14:48
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    @kjetil you refer to International Organization for Standardization. 3534-1:2006 Statistics – Vocabulary and symbols – Part 1:General statistical terms and terms used in probability:2006 ISO, Geneva. among others. But from personal experience I would not trust sources from Switzerland. – Sextus Empiricus Nov 06 '20 at 14:54
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    I've lived 1 year in Geneva and I find Swiss people very trustable. – crocefisso Nov 06 '20 at 15:31
  • Let us continue this discussion in chat. – crocefisso Nov 06 '20 at 16:45