# Is there a standard for statistical symbols?

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.)

• 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 $<X>$ (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. $(a,b].$ Nov 6, 2020 at 11:05
• 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. Nov 6, 2020 at 11:19
• Does this answer your question? Is there any "standard" for statistical model notation? Nov 6, 2020 at 11:26
• 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. Nov 6, 2020 at 11:35
• 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 6, 2020 at 16:03

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
• How did you find these deviations? Nov 6, 2020 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 : iso.org/ics/01.040.03/x. Which allowed me to find the 4 iso I mentioned. Nov 6, 2020 at 15:28
• 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). Nov 6, 2020 at 15:34
• 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. Nov 6, 2020 at 15:40
• 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 6, 2020 at 15:55

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)

• 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. Nov 6, 2020 at 14:31
• this paper seems to disagree ... Nov 6, 2020 at 14:32
• Though your speech about Pearson is not very convincing about the non-existence of standards. Nov 6, 2020 at 14:33
• @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'. Nov 6, 2020 at 14:36
• Well, I guess you didn't understand the question then. Nov 6, 2020 at 14:39