Dear James

Yes, I saw this kind of confusing technical terms a lot of times. I remember for example the use of the term "White noise" as synonimus of a standard gaussian function in an statistical congress which may be or not correct within its particular context.  https://en.wikipedia.org/wiki/White_noise

Dear James

Yes, I saw this kind of confusing technical terms a lot of times. I remember for example the use of the term "White noise" as synonimus of a standard gaussian function in an statistical congress which may be or not correct within its particular context.  https://en.wikipedia.org/wiki/White_noise

Dear James

Thank you to invite me  to this question:

While 21st century skills are relevant to all areas of schooling and academic study, and the skills may be taught in a wide variety of in-school and outside-of-school settings, there are a few primary ways in which 21st century skills intersect with efforts to improve schools:

Teachers may be more intentional about teaching cross-disciplinary skills in subject-area courses. For example, in a science course students might be required to learn research methods that can also be applied in other disciplines; articulate technical scientific concepts in verbal, written, and graphic forms; present lab results to a panel of working scientists; or use sophisticated technologies, software programs, and multimedia applications as an extension of an assigned project.

States, accrediting organizations, and schools may require 21st century skills to be taught and assessed in courses. For example, states can adopt learning standards that explicitly describe cross-disciplinary skills, and assessments may be designed or modified to evaluate whether students have acquired and mastered certain skills.

Schools and teachers may use educational approaches that inherently encourage or facilitate the acquisition of cross-disciplinary skills. For example, educational strategies such as authentic learning, demonstrations of learning, or project-based learning tend to be cross-disciplinary in nature, and students—in the process of completing a research project, for example—may have to use a variety of applied skills, multiple technologies, and new ways of analyzing and processing information, while also taking initiative, thinking creatively, planning out the process, and working collaboratively in teams with other students.

Schools may allow students to pursue alternative learning pathways in which students earn academic credit and satisfy graduation requirements by completing an internship, apprenticeship, or volunteer experience, for example. In this case, students might acquire a variety of practical, job-related skills and work habits, while also completing academic coursework and meeting the same learning standards required of students in more traditional academic courses.

Hope this will be helpful for you 

Regards 

Remi -  I noted with interest that  "economic science" made your list of confusing or misleading terms.  I think that the difference between natural and social "sciences" is one that many could argue.  I would put economic science in a somewhat in-between area, I think.  Interesting.  -  I guess this is greatly influenced by each person's definition/notion of "the scientific method." 

Thank you all. 

How about this one: "statistical science."  As a statistician, I would argue that the scientific method is applicable through the disciplines using statistics, and perhaps in the development of theory to cover those applications.  Other than that, one might argue that math is a science, but again it depends upon your definition. 

By the way, John Tukey was rather well known, and known for saying this: "The best thing about being a statistician is that you get to play in everyone's backyard.'' 

 http://mobile.nytimes.com/2000/07/28/us/john-tukey-85-statistician-coined-the-word-software.html

....

What other words have different meanings in different contexts?  I am particularly interested in technical terms which may have different meanings in different disciplines, and/or have technical meanings that are very different and perhaps misleading compared to everyday/common use ... such as "significance," or "prediction." 

statistical science should really only be reserved for sciences that are stochastic in nature like statistical mechanics. Statistics should be just called statistics. As for whether it should be classified as part of science or mathematics (or both); I would say neither. I would argue that probability should be part of deductive modal logic (graded modal logic) and statistics part of inductive graded modal logic.

As for misleading terms; I am sure but I know of mis-interpreted terms, such as

1.AThat signficance tests can be context dependent, ie if one expands the number of possible hypothesis from A and ~A to the every element of the disjunction in ~A; taken as individual hypothesis, they all may fail the test

1. That the conjunction fallacy; is a misuse of the multiplicative axiom; not its not, there is no such multiplicative axiom , and if anything its a misuse of monotonicity, perhaps the only thing we know about probability.

2. The Gamblers fallacy; Not necessarily a fallacy, in a long run, unless one holds to the kolmogorov interpretation of IID trials. Likewise with the base rate fallacy i guess.

3. Inverting the strong law of large numbers' you cant necessarily do that; not even in the infinite limit, if the priors are too small.Unless you are a frequentists (but it still has to be in the infinite limit).

3. Conflations between logical, or graded entailment (rational degree of belief_/meta-linguistic probability 1, and probability 2 chance. For example, that the probability is uniquely given by such and such via gleasons theorem. THe chance or the probability?

4. Conflations between representability by probability axioms; and derivability

5. With high probability, with probability=x; ie the first step. What does this even mean.

6. 'That Kolmogorov did not derive his axioms nor did he have an interpretation' unlike Cox, or Savage-de-finetti-Ramsey (dutch-books, representation theorem, Cox' one true representation theorem which is more then a representation theorem).

That is false. he had both. it was only that. it is as much of a derivation as a non-derivation may be, and as much of an interpretation as a non interpretation may be. Likewise that quantum probability stands in need of interpretation; which ones, the chances equal in values to the born rule probabilities, or the rational degrees of belief equal also in values. Also, it also has interpretation, call the amplitudes squared interpretation, which than is meta-interpreted by measure theory by some (a meta- meta interpretation) and then one asks for an interpretation of these hagain (frequencies, propensities, subjective or logical degrees of belief) (three levels), and then the distinction between chance ((contingent subjectivee or objective degrees of belief, propensities and frequencies) and probabilities (the one true degrees of necesstation, rational objective degrees of belief, or degrees of support) entailed by the former. Four kinds interpretations that appear to be compossible, and not conflicting apparently.

His which appears to just an infinite version of the classical or single case propensity approach. T

7. Or that Kolmogorov was a frequentist 'just look at the limit theorems'!.

I have seen that cited many a time, which whilst if correct with regard to his personal opinions and liking of von mises approach. It is not true with relata to his calculus, and has nothing to with these 'theorems' which are not in themselves theorems of his calculus by itself (perhaps that was the only way that they were inspired by von mises, or frequentism). Nor do they hold with 'certainty'. nor, are they 'not derivable' within a non frequentist, 'classical finite approach, proportion of equi-possible/indifference,  apriori laplacean/liebniz,carnap outcome approach'

In fact they are derivable, 'if not more derivable' in a combinatorial fashion ; not that they means much. In fact these theorems are not derivable in a frequentist approach, for various reason,  and why would the frequentist  want to do so anyway?.

In any case, the frequentist cannot even make a great deal of sense for kolmogorovs generalization of the 'strong law of large number' of non-identically but independently distributed trials. Such a theorem is not even applicable to the frequentist. By definition, if they are part of the same collective, they are identically distributed for the frequentist, modulo, certain randomness, or homogeneity tests.

8.. Bayes theorem or axiom; the multiplicative axiom, the law of total probability axiom, the axiom of addivity for non disjoint events. These are not axioms nor theorems under the conventional kolmogorov formalization. These are definitions. The independence axiom.

9. That kolmogorov probability is basically just measure theory plus independence and conditional probability, bayes rules. No its measure theory plus these defintitions, which means in the conventional approach that is only measure theory scaled to [0,1]. You can get a substance from a definition, which is just word to the effect that the ratio of two probabilities equals the ratio of two probabilities. Which is why the limit theorems and conditional probabilities, need not be even definable to have a space that is, or is representable by the kolmogorov probability calculus; and as a consequence, the limit theorems are not theorems of said calculus in and of themselves. but only as a result of conjoining spaces, so that in effect, they are individual IID distrinct trials on distinct space to begin with, leaving the 'theorems' then they already are.

and conflations with relation to the central limit theorm; ie where people confuse the two limits;  I sometimes see people interpreting it as, 'the number of samples of fixed finite size increases, ie tends toward infinity, the empirical distribution of these 'sample means', will have a 'mean and variance', that  will be,  or will be 'almost surely', normally distributed. As opposed to 'as  the size of the sample itself increases, the probability distribution of the sample mean, will progressively approximate a normal distrubution. Of course perhaps the former  may be preferred, as it would then actually have, a useful and empirical meaning but that is not what the CLT says.

10.(A)'probability one 'statements as are present in the strong law of large numbers,,and other apparently weaker or stronger limit theorems,which is often conflated with certainty;

The frequentist can say this, but they do not need to derive the strong law of large numbers; why would they want to derive their model theory, or analysis, or definition of probability, or semantics, (and the wrong semantics, at that, as they insist, on absolute convergence), from their proof theory, which is derived from their model theory, semantics etc. Seems strange

(B)or otherwise Prob 1 is conflated with 'almost all' infinite sequences (in the combinatorial sense; as opposed to 'almost all' the probability measure. Which generally is not the case except for ternary trials with prob 1/3, binary with prob 1/2).

Terms such as 'almost all' or 'almost everywhere' do not help unless Kolmogorov, really did mean that there were uncountably many possible outcomes, on his unit sphere, where each number of point, depicts a possible world, so that the proportions and the measures match up.

I know that in these banach spaces, with stronger or faster limit theorems, they use other terms. Like uniform, almost uniform, unconditional, absolute, 'convergence in law' (as opposed to distribution) , as in Dudley 'uniform central limit theorems' )which apparently is stronger then just 'almost sure' convergence and has something to with their version of the central limit theorem (Donsker  type theorems) . I know these limit theorems are stronger and apparently have a more combinatorial, proportion based /geometrical flavour, where often it means all but countably infinite many sequences will converge ;

Although I do not know if that 'countable refers to a proportion, that there literally are, amongst the uncountably many infinitely countably long sequences,, merely countably many non-convergent sequences, or that the relative sizes of the measures between the convergent and non-convergent, differs by a grade in cardinality; as if you could map the measure of the entire set of sequences to the continuum,aleph 1 (instead of [0,1] and the measure of the non-convergent sequences; comes out, as countable. As if in some way, some number, or infinity (non convergent sequences) divided by aleph1=aleph0, I apologize if this abusing terminilogy)

(C) Or 'almost all or almost all the measure, even if (B) did hold is' is conflated with an empirical measure or combinatorial proportion; 'ie'almost all distinct infinite sequences, comprised, of the same IID trials, will converge, if trialled together (hypothetically) together., to such and such relative frequency That is trials, that are already distinct prior to the outcome (and thus not merely in virtue of their having different outcomes)

This conflates a quantification of proportions of possible outcomes, or measures over possible outcomes, of  a single trial,with the the proportion or trials that will realize a singular outcome. That a 'trial has six possible outcomes', does not entail  'out of six trialings,  one and only one trialing will realize that outcomes' nor does it entail it, 'either exactly or in the mean or in measure, almost all the measure, almost all combinatorially, or empirical', 'that six t.

That is not to say that this kind of result would not be more welcome, as it has a stronger connection to frequency.

Nonetheless, 'almost all countably infinite binary outcome sequences have such a limiting relative frequency'

does NOT entail that

'almost all countably infinite binary trial sequences of IID trials, , if trialled, together (actually or hypothetically), in an ensemble of uncountable (or countably infinitely many such infinite sequencess), will  converge, to such and such a outcome limiting relative frequency. Where each sequence is (identically distributed, qualitiative identical,but numerically distinct trial sequence already prior to the outcome. Much less does it entail

'all of them, in uncountable ensemble or a countable ensemble, or almost all in a countable ensemble, taken as limiting frequency over a limiting frequency,

or 'almost all', in un-countably many, such countably infinite sequences where some combinatorial method is used to quantify this 'almost all, as the number of such infinite sequences, grows towards uncountable, using some kind of geometrical sequence countably many sequences, then countable^2 or some such,  measure theoretically(ie 'almost surely; that is when 'almost all the original measure',when this measure is taken over the trials or trial sequences, not the outcomes, or outcome sequences, as if were some some splicing or splitting process, not a branching process, will be placed on the convergent sequences, if such could be done or made sense of') .

This holds even  if there were as many or more of these distinct but qualitative identical 'trial' sequences, than the number of 'the uncountably many possible infinite 'outcome' sequences that could be produced by a single infinite sequence of IID trials, as used, to get the original a priori proportion, or almost certain/sure measure' in the strong law of large numbers .

11. Something something about convergence of opinion results, under a bayesian or prequentist approach or dominated or uniform convergence, martingale and super-martingale convergence theorems; that somehow these are certain results, not almost sure; which does not appear to be the case. They are still only almost sure results as I can see

Dear James R Knaub, 

Below are the 15 most common mistakes:

1. Lack of information about the product;

2. Hiding contact information;

3. Long or misleading the ordering process;

4. The requirement for the account of the order;

5. Inadequate search;

6. Poor service function service;

7. Tiny product images;

8. Only one picture of the product;

9. The poor design of the basket;

10. The lack of payment options;

11. Do not include related products;

12. Navigation, misleading;

13. Do not include transport costs;

14. Do not talk about the store policy;

15. Do not focus on the product.

Regards, Shafagat

In structural equation modeling, a significant chi-square does not indicate a satisfactory model fit. Joreskog and Sorbom (1989) and Bentler (1990) warned against the sole use of the chi-square value in assessing the model fit because of the sensitivity of the chi-square to the sample size. 

Dear James,

Some of the commonly confused terms are e.g., “asocial” with “antisocial,” “external validity” with “ecological validity,” “negative reinforcement” with “punishment,” “mass murderer” with ‘serial killer’. Others are chemical imbalance of neurotransmitters, antidepressant medication,  genetically determined, reliable and valid, statistically reliable, scientific proof, psychiatric control group etc.

Happy new year and regards 

Dr Ranjita

Dear James,

Thank you for sharing this valuable issue. There are confused between using Limnology, Inland water ecology and freshwater ecology.

Thanks for sharing this important question in technical and scientific communication. I concur that definitions are fundamental must be fully and widely understood and that some basic terms in each scientific area can be hardly substituted in specific contexts. However in my opinion, the format (the significant) is not essential, and the important is always what we want to express that must be explained always with clearness. Also, scientific language is not dead, and can be always improved. However, we need always to define with accuracy all symbols, words, and expressions that we use when we communicate. In my opinion, in scientific communication, just language enclosed in itself MAY possibly in some circumstances show some emptiness and some sort of vanity or superficiality that must be avoidable.

... may be you can have a look at two of my questions (dissipation of heat , static pressure) ...

regards

H.H.

Steam, vapor and gas are an example for frequent confusion to my students. 

Regards

SM Najim

Regarding the "normal" distribution, that is not really a good word for it, even strictly considering a statistical context.  The central limit theorem (CLT) may be responsible for this misnomer I suppose, but many people assume a 'normal' distribution must be used when it is either not really necessary, not expected, or even completely inappropriate.  I have seen a number of cases of that on ResearchGate.  Often it is assumed that the variables in a regression should be 'normally' distributed, when that can be completely wrong.  The estimated random factors of the estimated residuals might be best distributed that way, and the CLT may be helpful for prediction intervals, but continuous y and regressor variable data can have any distribution. 

I also saw an article in Significance Magazine a few months ago - ironically, as "significance" is a terrible choice for a term, so horribly misinterpreted - I do not recall the author, but he was noting that there had been a huge problem in businesses where it had been assumed that the distribution of employee performance would be normal, when in fact it is highly skewed.  Apparently this had caused huge problems with some major companies, regarding employee performance evaluations. 

It would probably be much better if we just used "Gaussian distribution," and stopped saying "normal."  Fewer would be misled.  As far as "significance," as a statistical term, it represents a concept that is not complete in itself, and raises practical issues.  If I mean something is "significant" in a statistical setting, but do not mean that misnomer, I often say "substantial" - because "significance" as a statistical term does not mean substantial, and very often it does not designate a meaningful result at all.  (Yet there is a statistics magazine called "Significance."  Ugh!) 

While i am mentioning this, I'll note that I had a letter published in Significance Magazine where I drew attention to the fact that "prediction" and "forecasting" can be very different in statistics.  Prediction with regard to finite population sampling has nothing to do with forecasting. 

Another example I can think of is OLS (ordinary least squares) regression,  when in many cases, homoscedasticity is not "ordinary" at all, and weighted least squares (WLS) regression is needed. (OLS is a special case of WLS.) 

.....

But this question is one for which I'd like to continue to see examples from other disciplines as well.  I noted "sample" from biology in the write-up above for this question.  That is an example of a word sometimes used differently from one discipline to another. 

Regardless, I suspect that many can state more terms which need to be remembered may have special meanings in a given context, which are not very intuitive.  Some may be used in just one discipline, I suppose, and some may differ from one discipline to another.

Thank you everyone, for your participation.  

Basically, there aren't enough words to go round. The International Union of Pure and Applied Chemistry published a 16-page recommendation entitled 'Nomenclature for sampling in analytical chemistry'. (Pure & Appl Chem. 1990, 62(6), 1193-2108; free to download).

It makes a lot of sense, but as others have said here, one adapts the degree of rigour to the context, even in scientific writing. Someone who hasn't read the IUPAC document may still use the word 'sample' for 'test portion'. It could be said that your document needs to be clear only to a reader versed in the particular art. However, that can lead to misinterpretation of analytical methods because they concern so many people who are not primarily analysts.

Compendia of legal standing such as the pharmacopeias cover a narrow range of disciplines and have their own rules of nomenclature that must be followed.

I think we come across a lot during reading articles, yet our minds translate the words instantly and we go along with what the author chose to refer to a certain statistical term according to their background. I don't have a specific example right now, but often while I'm reading, the author might refer to "this" meaning "that" and my brain just says oh you meant "that" instead of "this" it is rather annoying sometimes. :)