Accuracy, Exactitude, and Precision

Dictionaries and thesauri often treat accuracy and precision as synonymous, or as nearly so. But the words accuracy and precision and their coördinates[1] are each most strongly associated with a distinct and important notion. The word exactitude (often treated as synonymous with the previous two) and coördinates are most strongly associated with something rather like the combined sense of those other two, but with a notable difference.

When we say that a specification is precise, we do not necessarily mean that it were correct when judged against the underlying objectives. We may merely mean that it were given with considerable explicit or implicit detail. If I tell you that a musical show will begin at 8:15:03 PM, then I am being precise (indeed, surprisingly so). But the show may begin at some other time; in fact, it may never have been planned to begin at that stated time; I can be both precise and wrong.

If your friend tells you that the show will begin shortly after 9 PM, then she may be accurate, though she was far less precise than I.[2] The word accuracy and coördinates are associated with closeness to the truth; and, in everyday discourse, she might be said to be more accurate were she to be more precise while remaining within the range implied by shortly after 9 PM. But the word is also associated with encompassing the truth; if the precision seemed to narrow the range of possibilities in a way that excluded what proved to be the truth, then she might be regarded a having become less accurate. (If one is told that the show is to begin at 9:15 PM, but it begins at 9:05 PM, then one might feel more misled than had one been less precisely told shortly after 9 PM.)

(Note that it would be seen as self-contradiction to say that someone were accurately wrong, though we sometimes encounter the phrase precisely wrong. The latter carries with it the sense — usually hyperbolic — that the someone had managed to be so wrong that even the slightest deviation from what he or she had said or done would be an improvement.)

Although some people might jocularly, eristically, or sophistically pretend that one truth were somehow truer than another, any meaningful proposition is either simply true or simply false (though which may be unknown and there are degrees of plausibility). If Tom and Dick each go to the store, then it is true that one of them has gone to the store. It is not closer to the truth that two of them have gone to the store. It might be said that it were more accurate that two of them have gone to the store, but this seems to imply that it is truer that two went than that one went, and this implication is false. Fortunately, we have a word and coördinates that can carry with them a particular sense of accuracy and precision, with exclusion. These words are exact, exactly, and exactitude.[3] It is true that one person has gone to the store, but it is not true that exactly one person has gone to the store.[4]

(The expression exactly wrong is usually in hyperbolic contrast with exactly right, but is sometimes applied elliptically, when there is believed to be exactly one way in which to have been wrong.)

Even if one is not greatly concerned with rigor, these distinctions can be important. Asking members of an audience to be more accurate when one wants them to be more precise may inadvertently suggest to the audience that one thinks them to have been untruthful! Typically, risking that inference brings no benefit. It would then be better to ask them to be more precise or more exact.[5] The latter may work best with the passive-aggressive or with the autistic, who might otherwise be more precise while less accurate.

[1] The coördinates of a word are simply the other parts of speech built of the same root and carrying the same general sense adapted to a different grammatical rôle. For example, the adjective accurate and the adverb accurately are coördinate with the abstract noun accuracy.

[2] In discussions of computer science, the everyday distinction between accuracy and precision is made more emphatic, because the mathematics of computing is discrete, and limitations in detail have important implications. For example, ordinary floating-point encoding imperfectly represents numbers such as 1/10. That's why calculators and computers so often seem to add or to subtract tiny fractions to or from the ends of numbers. Number-crunching scientist who do not themselves recognize this issue have generated spurious results by proceeding as if computers have unlimited precision, and thus by mistaking artefacts of limited precision for something meaningful within the data. I strongly suspect that a major reason that so many reported econometric results were not subsequently found by other researchers poring over the very same data was that the original researchers (or, sometimes, the later researchers!) were not taking into account the implications of limited precision.

[3] The words just and only can carry the same meaning, but often bring normative implications.

[4] In mathematics, x translates to for some x, while ∃!x translates to for exactly one x.

[5] Asking a person to be more just or more only would almost surely provoke bafflement.

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