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When I first started learning statistics, procedures like the t-test, ANOVA, chi-squared and linear regression each appeared to be very different creatures. But now I realise these procedures each do more or less the same thing. And likewise, values such as the variance, residuals, standard error and mean also measure more or less the same thing.

So I reckon all of these procedures and values, and indeed all of statistics, can be described in just one simple sentence:

What is the expected value and what is the variation around this value?

The word expected could be replaced by any of these words: hypothesised, predicted, or central.

How would other people describe statistics in one sentence?

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    $\begingroup$ @Trynna This description is far too narrow: it characterizes only point estimation. It is like describing mathematics as adding and multiplying numbers--which very well might be the perspective of someone who has studied arithmetic for a few years in school--but falls far short of what the field comprises. $\endgroup$ – whuber Mar 5 '15 at 22:39

17 Answers 17

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Statistics provides the reasoning and methods for producing and understanding data.

American Statistical Association

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  • $\begingroup$ +1 I was trying to come up with an expression of something very close to this notion. I'd have added something about coming to conclusions on the basis of data, but it's not quite so succinct. $\endgroup$ – Glen_b Mar 5 '15 at 22:40
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    $\begingroup$ @Glen You can tell that a lot of thought was put into this characterization. I like having it here somewhere on our site. That, and a similarly pithy description of machine learning, ought to belong in our help pages. $\endgroup$ – whuber Mar 5 '15 at 22:41
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    $\begingroup$ I am not sure I agree with the quote (though it is a lovely aspiration). As an epidemiologist, I know that I know things about study design and the production of data and causal inference around same which is outside the ken of many of the fine statisticians around me. Indeed the fancy causal inference for recursive causal graphs originated in three fields not named statistics (epidemiology, computer science, and sociology, as I understand it). Not raising this in a bellicose spirit, but because the quoted sentence describes much of science, and doesn't nail down stats per se. $\endgroup$ – Alexis Mar 6 '15 at 0:07
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    $\begingroup$ The ASA description is much more about statistics as a domain of human knowledge and activity, not marking out who a "statistician" might be. Until WW2 professional statisticians were a rarity, but that doesn't mean stats wasn't being applied in commercial and academic settings. I don't think a good definition of statistics could be limited to what professional statisticians do. $\endgroup$ – Silverfish Mar 6 '15 at 8:37
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    $\begingroup$ @Alexis Perhaps there's some difficulty with the level of understanding implied by the word "understanding", which the ASA definition leaves rather ambiguous in its brevity. A wider interpretation might be over-encompassing. Certainly if we include substantive physical or social interpretion and underlying mechanisms as part of "understanding", then it goes beyond "mere" statistics. On the other hand, it's not clear to me why inference from data, causal or otherwise, can't lie within the domains of both scientific and statistical endeavour. $\endgroup$ – Silverfish Mar 6 '15 at 17:59
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Statistics is fundamentally concerned with the understanding of structure in data.

Bill Venables and Brian Ripley, first sentence in Chapter 1 of Modern Applied Statistics with S

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    $\begingroup$ This is an interesting take on statistics, albeit a limited one. The possible ambiguities are revealing: a computer scientist would understand "structure in data" in a non-statistical way. (Venables and Ripley work at the intersection of statistics and computing.) $\endgroup$ – whuber Mar 6 '15 at 23:15
  • $\begingroup$ @whuber I agree with you. There's nothing to suggest that V&R intended it to be a one-sentence description of all of statistics, but ever since I first read it, I've thought it was a nice description. I interpret "structure in data" as "characteristics of the population from which the sample was taken". $\endgroup$ – markseeto Mar 7 '15 at 1:32
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Statistics provides the reasoning and methods for converting data to meaningful information.

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In the words of the late Leo Breiman:

The goals in statistics are to use data to predict and to get information about the underlying data mechanism.

http://projecteuclid.org/euclid.ss/1009213726

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Personally, I like the following quote from Stephen Senn in Dicing with death. Chance, Risk and Health (Cambridge University Press, 2003). I highlighted one sentence (or two) that, I believe, summarize his main point, although the whole paragraph is worth reading.

Statistics are and statistics is.
Statistics, singular, contrary to the popular perception, is not really about facts; it is about how we know, or suspect, or believe, that something is a fact. Because knowing about things involves counting and measuring them, then, it is true, that statistics plural are part of the concern of statistics singular, which is the science of quantitative reasoning. This science has much more in common with philosophy (in particular epistemology) than it does with accounting. Statisticians are applied philosophers. Philosophers argue how many angels can dance on the head of a needle; statisticians count them. Or rather, count how many can probably dance. Probability is the heart of the matter, the heart of all matter if the quantum physicists can be believed. As far as the statistician is concerned this is true, whether the world is strictly deterministic as Einstein believed or whether there is a residual ineluctable indeterminacy. We can predict nothing with certainty but we can predict how uncertain our predictions will be, on average that is. Statistics is the science that tells us how.

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Statistics is the science of learning from data and measuring, controlling, and communicating uncertainty.

Marie Davidian & Thomas Louis

They continue:

; and it thereby provides the navigation essential for controlling the course of scientific and societal advances

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  • $\begingroup$ I like this definition because it singles out the "uncertainty" aspect. The second part is nice because it says that statistics does not exist only by itself, but has to be seen in a broader context. To be completely satisfied however, I would perhaps merge that with the ASA one to: $\endgroup$ – Momo Mar 6 '15 at 17:45
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    $\begingroup$ Statistics as the science of learning from data and measuring, controlling, and communicating uncertainty provides the reasoning and methods for producing and understanding data. $\endgroup$ – Momo Mar 6 '15 at 17:46
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Statistics is a kitbag of methods and modes of thought that help people to make clear conclusions from noisy information.

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Because we are not a godlike all-knowing creature we have to deal with uncertainty and Statistics provides methods to incorporate and reflect that uncertainty.

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statistics is a sub-field of philosophy that deals with the following question 'how we learn from observations' using rigorous mathematical concepts.

just a side note you can make 'one sentence' very long, there is a book written by B. Hrabal that consist of one long sentence, see: Dancing Lessons for the Advanced in Age

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Statistics is both the science of uncertainty and the technology of extracting information from data

David J. Hand

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Statistics is a set of logical principles and mathematical methods for summarizing quantified information in accurate, relevant ways.

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In my own words

Statistics is the science of what might be

This is sort of tongue-in-cheek.

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    $\begingroup$ If you were to mask the first word and ask people to fill in the blank, I suspect "statistics" would not be the first thing they come up with--and perhaps not the second or third, either. "Futurology," "speculation," "science fiction," and maybe--getting a little closer to your intent--"prediction" and "forecasting"--would likely be popular choices. Even "oneirology" and "apotropaism" would be possibilities. :-) $\endgroup$ – whuber Mar 6 '15 at 23:29
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Fisher (1922) gave his view on the essence of statistics in the following quote (bold font added by me for the one sentence requirement):

In order to arrive at a distinct formulation of statistical problems, it is necessary to define the task which the statistician sets himself: briefly, and in its most concrete form, the object of statistical methods is the reduction of data. A quantity of data, which usually by its mere bulk is incapable of entering the mind, is to be replaced by relatively few quantities which shall adequately represent the whole, or which, in other words, shall contain as much as possible, ideally the whole, of the relevant information contained in the original data.

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A results-oriented (and so not really descriptive) one-liner would be, for me,

Statistics is what makes the human world go round, irrespective of what is that does the same for Nature.

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    $\begingroup$ Are you confusing statistics with politics? Or maybe with love? $\endgroup$ – whuber Mar 7 '15 at 18:35
  • $\begingroup$ @whuber (+1) No. Both make most of their decisions based on Statistics, whether they realize it or not. $\endgroup$ – Alecos Papadopoulos Mar 7 '15 at 18:39
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    $\begingroup$ I can see it now, in an upcoming movie, when the male lead gets on his knees to propose: "Baby, you're my UMVUE, will you marry me?" :-) (Let's use a shrinkage estimator and bring our coefficients together...) $\endgroup$ – whuber Mar 7 '15 at 18:41
  • $\begingroup$ @whuber (+2) ...this is the "don't realize it" part: this is exactly what the male lead means, even though he does not use the language! (I concede that I may be guilty of philosophical imperialism here). $\endgroup$ – Alecos Papadopoulos Mar 7 '15 at 18:44
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    $\begingroup$ Your deeply respectable cultural background (insofar as your name and location allow one to infer it), which one can trace back at least to the early Sophists, allows you quite a bit of latitude in that regard. :-) $\endgroup$ – whuber Mar 7 '15 at 18:46
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Statistics is a tool for modeling the generation of data by uncertain and/or probabilistic processes.

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Statistics is about torturing data long enough until it confess anything you want to show.

I am paraphrasing Ronald Coase, see link

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  • $\begingroup$ -1, was this intended as tongue in cheek? $\endgroup$ – gung Mar 5 '15 at 21:58
  • $\begingroup$ @gung yes and no, I was quoting Ronald Coase. $\endgroup$ – Vladislavs Dovgalecs Mar 5 '15 at 21:59
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    $\begingroup$ Based on the version here, it is at best a bad paraphrase. That isn't a good 1-sentence summary of what statistics is. $\endgroup$ – gung Mar 5 '15 at 22:19
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    $\begingroup$ @gung well, the OP asked how different people would describe it. It will always be his or her point of view or opinion. It will be different for different people. OP tried to gather different opinions IMHO. $\endgroup$ – Vladislavs Dovgalecs Mar 5 '15 at 22:46
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    $\begingroup$ xeon it would be a great kindness to Coase to edit your answer to properly cite and source the attribution. $\endgroup$ – Alexis Mar 6 '15 at 0:09
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Statistics is the mathematical science that allows you to figure out if the difference between sets of observations are just random or not.

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    $\begingroup$ Describes a narrow subset of what the field is. $\endgroup$ – rolando2 Mar 5 '15 at 23:43
  • $\begingroup$ I see it differently. Ultimately, whether you are conducting hypothesis testing, regression modeling, or any other estimation you most always measure whether the difference between your estimate vs a naïve model, or difference in observations are statistically significant or not. My sentence captures the essence of statistical significance vs. randomness. If others agree, can you give me some up votes, so my comment that is easily justifiable is not treated as a plain wrong answer just because of one individual's subjective interpretation of narrowness. $\endgroup$ – Sympa Mar 6 '15 at 0:03
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    $\begingroup$ please consider these types of questions that one often seeks to answer using statistics: What is the shape of this distribution? What is the nature of the relationship between these 2 variables? How can these many variables be grouped so that we can see the common issues/themes/topics/dimensions? How can these many cases be grouped so that we can see the common types/profiles? What is the best way to describe this web of relationships with an eye toward causality? What captures the trend of this variable over time? What is the best way to forecast future values? $\endgroup$ – rolando2 Mar 6 '15 at 0:11
  • $\begingroup$ In each of those cases, the answer to those questions has a strong element of statistical significance and whether what you are looking at in any shape or form is different vs. what could occur by sheer randomness. To most of us a negative vote means an explicitly wrong answer. I don't see how my answer could be categorized as such. $\endgroup$ – Sympa Mar 6 '15 at 21:42
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    $\begingroup$ The hover text over the downvote arrow states "this answer is not useful." I find it interesting--and therefore not unuseful--because it is thought-provoking, but I have not upvoted it for several reasons. The first is the assertion that stats is a "mathematical science": that comes uncomfortably close to the misconception (especially among certain mathematicians) that stats is just a branch of mathematics. The second is that it seems only to characterize two-sample hypothesis testing, which is a very narrow (albeit pervasive) part of statistics. $\endgroup$ – whuber Mar 6 '15 at 23:19

protected by whuber Mar 8 '15 at 18:43

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