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For a thesis, thus scientific writing, I want to say something similar to:

"There is a factor 2-3x improvement."

What is the correct formal writing style for this? I should not use numbers, I know, but I'm unsure due to the format.

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    If you ignore the "range" element in your context, you'd end up with a factor 2x improvement (by which I assume you mean a factor two times improvement). But native speakers wouldn't use "factor two times" as a multi-word adjective before a noun (improvement, here). You could say [whatever you're talking about] improved by a factor of two or three, but I think it's somewhat clumsy. In a "scientific" context you should probably strive for clarity and accuracy. Usually when people say something is twice as good (a two times improvement?) the "doubling" is an arbitrary amount. – FumbleFingers May 11 '15 at 15:51
  • Hi Sven, and welcome to the site! I expect that your question, unfortunately, will be closed as "primarily opinion-based" rather than having a (more or less) objectively "best" answer, but I'd probably go with something like "There was an improvement of 200 to 300 percent". It also depends heavily on what has actually improved; you might say "performance doubled" or "execution time was halved". – Hellion May 11 '15 at 15:52
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    In scientific writing, the point is not to save time, like it is in speech; in scientific writing, the point is to give all the important information. Use more than three words if you actually have facts to report. Something like "As can be seen in Figure 3, the improvement factor was approximately 2.71" is what it should be. Save the readers' time, not your own; answer the distracting questions before they have a chance to come up. – John Lawler May 11 '15 at 15:56
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There are several ways of paraphrasing that phrase, with subtle differences in each case:

There is an improvement by a factor of two or three.

This is improved twice or thrice. (if you want to be archaic...)

This has improved twice or thrice.

This has been improved twice or thrice.

There is an improvement in the range of two or three times.

The improvement is of about two or three times.

The improvement is around two or three times.

There is improvement of 3 to 5 dB. (if you're an engineer and want to be... cool or a dick? It all depends on the context...)

Again, as the commenters have said above, this is a matter of taste and in scientific works one should strive for precision, answering the question wholly and not settling for the smaller range of the entire set of real numbers between 2 and 3. But then again, uncertainty is part of science too, if you can't give a precise answer, maybe give the uncertainty value of it or explain why you couldn't have been more precise. The rest is up to you, Sven!

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