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If some measure of quality improves to 150 % of its original value in a study from condition A to condition B, would it be most appropriate, in terms of scientific writing (computer science specifically), to describe that as:
a 1.5-fold improvement
a 1.5× improvement
performing 1.5 times better
The following may seem a bit nitpicking, but such details are what separates the wheat from the chaff:
a 1.5-fold improvement
Bad. This implies that the improvement – not the quality measure – is 1.5 of something else, that is reasonably comparable, e.g., another improvement. This would make sense in a context like:
We compared different performance boosters and found that contrafibulaties yielded a 1.5-fold improvement compared to the improvement by pericombobulations.
(Note that I do not consider the above sentence an example of good writing as it is bound to be misunderstood by somebody, but it’s at least technically correct.)
a 1.5× improvement
Very bad. If I am benign, I read this as “1.5-fold improvement” (see above). If I am not, this does not make any sense at all. Replacing words with mathematical symbols just because they have some semantic relation is a very bad habit as it almost never yields a clear meaning, is bad style, and is indicative of deficiencies in basic mathematical concepts.
performing 1.5 times better
Meh. If we are being literal, it has problems similar to “a 1.5-fold improvement”: Does 1.5 times apply to better or something else? Now, linguistically, this is a fixed idiom with a clear meaning, so the situation is not that bad, but I would guess that some non-native speakers misunderstand it. Moreover, idioms do not stylistically mix very well with accurate, quantitative descriptions.
performing 50 % better
Almost Good. Similar to the above, but better, since 50 % is by far not as likely to be understood to apply to better than 1.5 times.
performing 1.5 times as well
performing 150 % as well
Good. These leave no room for misunderstanding as you make clear what 1.5 times or 50 % refer to, and it’s the correct thing, namely “goodness”, i.e., your measure of quality.
an improvement by 50 %
an improvement to 150 %
Good (with sufficient context). Again, it is clear, what the numbers actually refer to.
performing 50 % better than A
performing 1.5 times as well as A
performing 150 % as well as A
an improvement by 50 % in comparison to A
an improvement to 150 % of A’s performance
Very Good. By naming the actual reference, you avoid misunderstandings. However, with sufficient context, the expressions I labelled good may be preferable for brevity and avoiding unnecessary redundancy.
Note that all this assumes a measure of quality that increases with quality. If your measure decreases with quality (e.g., runtime), it’s probably best to directly talk about the measure, e.g.:
A’s runtime was 50 % of B’s.
A runs twice as fast as B.
150% of what? An apple? It only works if the value that improved was actually a percentage, as in "My grade improved to 90%". "an improvement by 50%" works because the context is made relative by "by".
In my opinion, the expression
1.5 times better
is to be avoided at all cost. It doesn't have any linguistic meaning. That is because "better" (like "bigger", "more") implies an addition to whatever thing is being measured:
this car goes 10 km/h faster than the other one
while "1.5 times" implies a multiplication.
(If we were to assign a meaning to it, because of the "additional" meaning, "1.5 times better" would mean "2.5 times as good").
Furthermore, if "1.5 times better" were to be allowed, what would "50% better" mean? When following the reasoning that would make "1.5 times better" mean "1.5 times as good", this would imply that it meant "50% as good". Which it of course never meant.
My suspicion is that the incorrect phrasing "1.5 times better" got into usage because people are unsure how to write "1.5 times as good as" and connecting it to the thing they are comparing.
I usually clarify that like this:
Condition A's performance was 1.5 times that of condition B.
That gets the condA = 1.5 × condB thing across, without the ambiguity of “improvement times x”.
Or draw them. There's no shame in being too clear.
In general, it's preferable to use the same arithmetic form when discussing relative change in processes of any kind. Consistency shows consideration for the reader. Where I live and translate, the typical writing style tends to like the "x times more than" and the "x-fold" forms mixed with percentages, which is not that easy to interpret as we can see from the discussion here. Percentages not only are more obvious but they also allow comparison with other percentages. So,
Rule #1, use the same form to compare across your entire discussion or report out of consideration for readers.
Rule #2, use percentages in preference to "times more/less than" or "-fold" forms, which are not as precise and require interpretation.
