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The source https://en.wikipedia.org/wiki/Accuracy_and_precision says that in statistics "precision" is understood to be a measure of statistical variability within samples. The lower the variability within the sample, the higher the "precision." That's okay. It is a technical term. But I wonder if there a standard term in statistics for this other thing:

Suppose one study of the heights to students in various high schools measures the heights to the nearest inch, and another measures them to the nearest millimeter. (I intentionally use an implausibly small unit here. A person's head rises and falls more than one millimeter just by breathing.) In a colloquial sense the second study reports "more precise" numbers than the first -- even if those numbers are no more reliable and the "precision" is illusory.

Is there a standard term in statistics to describe how closely a given quantity is being described -- the way heights to the nearest millimeter are given "more closely" than heights to the nearest inch?

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    $\begingroup$ Interesting. Kind of like bin size but not quite. $\endgroup$
    – Bjørn Kjos-Hanssen
    Nov 2, 2019 at 22:48
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    $\begingroup$ Some non-technical terms include “more fine-grained” (which has a positive connotation) or “more digits” / “more digits after the decimal point” (which has a negative connotation, at least for anyone influenced by Tufte) $\endgroup$
    – user44143
    Nov 3, 2019 at 11:47
  • $\begingroup$ I would call it the "graduation" or the "minimum increment" of the measurement $\endgroup$
    – Yoav Kallus
    Dec 17, 2019 at 14:06
  • $\begingroup$ Another term that might make sense but is less self-explanatory is "nominal precision" $\endgroup$
    – Yoav Kallus
    Dec 17, 2019 at 14:09

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I have heard statisticians and data scientists use the word 'granularity' to express the idea you are looking for. Here is a quote from the dedicated Wikipedia article: 'The granularity of data refers to the size in which data fields are sub-divided'. The article also gives an enlightening example of proper usage: 'A kilometer broken into centimeters has finer granularity than a kilometer broken into meters'. Here is the link to the article: https://en.wikipedia.org/wiki/Granularity#Data_granularity.

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I don't think there is perfect standard terminology, but I think we can reason our way to a viable option.

Let us imagine that we are using a person's height as a feature for a classification problem, like predicting health outcomes or athletic performance. How do we expect the model to change if we are able to measure height accurately to within a millimeter rather than just an inch? It is natural to expect the model accuracy to improve, but this could depend on the details of how the model is fit to data - using millimeters could cause it to overfit, for instance.

I would argue that the direct, first-order effect of using millimeters instead of inches is that the model will likely become more discriminative: the probabilities that it assigns to different classes will be more concentrated in a small number of classes with the more refined units. So it makes sense to me to apply this label to the units of measurement and say that millimeters are more "discriminative" than inches. If we need a noun like "precision" then I guess it would be "discriminativity", though I'm not sure that's actually a word.

This choice of terminology has a number of nice properties. It has a generally positive connotation (discriminative models are usually desirable), though the statistically literate reader will be cautious about overfitting and wonder how much of an effect making certain measurements more discriminative will have on the statistical power of the overall study. This is probably how the reader should approach a study which measures a person's height in millimeters rather than inches, so it fits your example well, at least.

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  • $\begingroup$ I think terms like scale, refinement, and sensitivity might come closer, especially when understood as measurement scale, measurement refinement, and measurement sensitivity. Gerhard "Within An Order Of Magnitude" Paseman, 2019.12.02. $\endgroup$
    – Gerhard Paseman
    Dec 3, 2019 at 5:45
  • $\begingroup$ I considered both "refinement" and "sensitivity", but I was worried about collisions with other terms in statistics. Refinement is often used to refer to restricting from a type to a subtype, like from $H \in \mathbb{N}$ to $\{H \in \mathbb{N}, H < 100 \}$. I didn't like sensitivity for two reasons: 1. sensitivity is used in statistics as a synonym for recall, which isn't the right meaning here, and 2. the other connotation is something like "risk of greater error", whereas the difference here is that millimeters can measure error more accurately than inches, not that the error is greater. $\endgroup$
    – Paul Siegel
    Dec 3, 2019 at 7:23
  • $\begingroup$ "Scale" is a good term here, though it is awkward to use for comparisons - does "more scale" mean larger or smaller units? It also doesn't hint at the strengths and weaknesses of different choices the way "discriminative" does. $\endgroup$
    – Paul Siegel
    Dec 3, 2019 at 7:27
  • $\begingroup$ The connotation will be negative for many people, who associate discrimination with negative decisions based on gender or race. $\endgroup$
    – user44143
    Dec 3, 2019 at 10:17
  • $\begingroup$ That could indeed be a worthwhile consideration, but in this case "discriminative" is already a statistical term of art, and I am only proposing that we extend its meaning in a modest way. $\endgroup$
    – Paul Siegel
    Dec 3, 2019 at 14:18
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What about "resolution"?

See e.g. Accuracy, Precision, Resolution & Sensitivity

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As far as I know, there is no completely standard term, but this Wikipedia article suggests that terms like "false precision" or "overprecision" are commonly used to describe this situation. For example, one often sees false precision in the reporting on polls in the news media.

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  • $\begingroup$ I am not asking how to refer to false precision. I am asking for a term that describes giving more significant figures in your statistics, including the case where they are quite accurate (in the colloquial sense of accurate). Statisticians cannot just call that "precision", since "precision" means something else. $\endgroup$
    – Colin McLarty
    Nov 4, 2019 at 17:34
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    $\begingroup$ I understand what you want, but I don't believe there is a standard term for it within statistics. Of course, "precision" has a broader meaning outside statistics. You would probably be understood if you distinguished between "numerical precision" and "statistical precision." $\endgroup$
    – Evan Patterson
    Nov 4, 2019 at 17:49

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