I was reading this paper about aquaponics and some of the stats did not make any sense with regard to the percents listed. What method would allow these percents to exist?

The most commonly raised aquatic animals by percent were tilapia (69%), ornamental fish (43%), catfish (25%), other aquatic animals (18%), perch (16%), bluegill (15%), trout (10%), and bass (7%). ~ http://www.sciencedirect.com/science/article/pii/S0044848614004724

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    $\begingroup$ Even when components are disjoint, and there is no silly calculation or reporting error, rounding error can still bite. A simple example is (1 + 1 + 1)/3 yielding as percentages 33, 33, 33 or 33.3, 33.3, 33.3 or .... Here more decimal places just means smaller rounding error, but it never becomes 0. An immensely deeper analysis is provided by Diaconis and Freedman in JASA 1979, accessible, perhaps illicitly, at statweb.stanford.edu/~cgates/PERSI/papers/freedman79.pdf $\endgroup$
    – Nick Cox
    Commented Mar 15, 2017 at 18:01
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    $\begingroup$ @NickCox If you take alook at the numbers again you can easily see that that is not the reason in this case. Rounding errors can never give you a sum of 203%. $\endgroup$
    – Cleared
    Commented Mar 16, 2017 at 14:49
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    $\begingroup$ consider this: "have you ever raised: a] a cat, b] a dog". Result could be something like a] 62% b] 74%. Because they are not mutually exclusive (and not even covering the whole spectrum) $\endgroup$
    – njzk2
    Commented Mar 16, 2017 at 18:45
  • $\begingroup$ @Cleared Sure, and I took that to be both obvious and the answer in this specific case. My comment starts "Even when components are disjoint...". Sorry that was not clear to you, but I could and can do the mental arithmetic of 69 $+$ 43 and immediately see that rounding is not the issue. If you take a look again at the title of the thread, then you should see that there is more than one reason why people might visit it. $\endgroup$
    – Nick Cox
    Commented Mar 16, 2017 at 19:32

1 Answer 1


This kind of results can be due to questionnaire items that allow multiple choices (aka, "Check all that apply.")

Each option then essentially becomes a binary variable, where 1 can represents yes and 0 represents no. Their means will become those statistics you saw in the abstract.

Essentially, out of 257 responses, 69% of 257 of them kept tilapia; 43% of 257 kept ornamental fish, so on so forth. It's possible to see more than one type of animals within a single facility.

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    $\begingroup$ Or think of it this way. They do add up to 100%. You're just adding the wrong numbers. We get 100% by adding the 69% of people who kept tilapia with the 31% of people who didn't. And same for the other values. $\endgroup$
    – user428517
    Commented Mar 15, 2017 at 18:17
  • $\begingroup$ Essentially this comes down to ambiguous writing in the abstract: they say “most commonly raised … by percent”, which doesn’t really make clear what each percentage represents. In fact, as you say, it’s intended as “percentage of respondents who raise this category of aquaculture animals”, but it can equally naturally be understood as “percentage of all aquacultured animals that are in this category”, and under that, percentages summing to substantially over 100% (more than rounding errors can account for) would indeed be impossible. $\endgroup$
    – PLL
    Commented Mar 16, 2017 at 15:51

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