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For both experiments, method A has increased the number of correct solutions found for 72.33% and 75%, compared to method B.

vs

For both experiments, method A has increased the number of correct solutions found by 72.33% and 75%, compared to method B.

may I know which one is grammatical?

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1 Answer 1

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"By" is correct.

I would also not use "for both" in your introductory clause, rather

In these two experiments, method A increased the number of correct solutions found by 72.33% and 75%, compared to method B.

Using "both" implies the two experiments had identical results, which the rest of the sentence contradicts by giving two different values.

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  • I think there are two experiments- one that yielded a 72.3% increase and one a 75% increase, and method A increased the number of correct solutions in both of them. I'd add a "respectively" after the 75%. Or better, "In each experiment, method A increased the number of correct solutions found ..."
    – Jim
    Sep 5, 2014 at 23:52
  • @Jim To use "respectively" there need to be two lists, like "in experiment A and experiment B we measured 5% and 10% improvement, respectively. "
    – The Photon
    Sep 6, 2014 at 15:31
  • The way I read the statement I think there are two experiments. Each experiment uses both Method A and Method B to find a number of correct solutions. In the first experiment Method A found 72.3% more correct solutions than Method B and the second experiment Method A found 75% more correct solutions. So you can say that in the two experiments Method A found, respectively, 72.3% (Exp 1) and 75% (Exp 2) more solutions than Method B. Anyway that's how I understood OP's sentence.
    – Jim
    Sep 6, 2014 at 20:04
  • @Jim, I agree there were two experiments. But "respectively" means you're listing the results in the same order you've listed the experiments. Since s/he didn't list the experiments in any particular order, there's no reason to use "respectively".
    – The Photon
    Sep 6, 2014 at 21:13
  • If I say "the three cars are red, green, and blue [respectively]" I just know I have a red car, a green car, and a blue car. Adding "respectively" tells me nothing extra. If I say, "John, Bill, and Mary's cars are red, green, and blue, respectively" then I know John's car is red, Bill's is green, and Mary's is blue, because "respectively" tells me the colors are listed in the same order as the corresponding owners.
    – The Photon
    Sep 6, 2014 at 21:24

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