# Increased for vs increased by

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?

"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.

• 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. " 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". 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. Sep 6, 2014 at 21:24