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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

HSchmale
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    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 http://statweb.stanford.edu/~cgates/PERSI/papers/freedman79.pdf – Nick Cox Mar 15 '17 at 18:01
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    @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%. – Cleared Mar 16 '17 at 14:49
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    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) – njzk2 Mar 16 '17 at 18:45
  • @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. – Nick Cox Mar 16 '17 at 19:32

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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.

Penguin_Knight
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    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. – user428517 Mar 15 '17 at 18:17
  • 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. – PLL Mar 16 '17 at 15:51