Plural of 'performance'

More context is needed. If you are referring to two different performances (the new one and the existing one), it should be plural, and the verb of which 'performances' is the subject should also be plural. This, in that case, is the correct sentence:

The performances of the new and existing methods are compared.

On the other hand, there might be one performance that features both methods. In that case, use this:

The performance of the new and existing methods is compared.

In either case, this is incorrect:

The performance of the new and existing methods are compared.

because the verb and subject do not agree.

With all due respect to Peter Shor - I'm under the impression that two different interpretations of the same work were being compared.

You could liken the situation to the first time any story about the character "Sherlock Holmes" was produced for stage or screen to the most recent interpretation, being the series "Sherlock" starring Benedict Cumberbatch in the titular role. There's a world of difference between the settings and the portrayal of many of the central characters, yet the 2010-2016 productions are still clearly recognizable as Sherlock Holmes to someone who has read any of the the original works by Sir Arthur Conan Doyle...

Anyway, back to the original question! I agree with CHEESE that the sentence was no doubt flagged by MS Word as the verb and subject do not agree. Given the lack of context I think that CHEESE delivered a clear and concise answer to the dilemma at hand.

All I can really add as advice is that relying entirely on MS Word°° for grammatical help is an abysmal idea in general (although for a personal journal its at least excusable!). For students it is not, and for "Journalists" even less so.

°°Or any relevant analogs including the automatic spell/grammar check software for mobile phones

"is compared" sounds wrong and illogical. Use "are compared", and adjust the sentence to that. Use "performances" and "are".

I see performance is being used like the word efficiency. I've heard of efficiencies (semi-awkward), but performances is confusing unless you're referring to staged shows etc. It's not in the question, but you could switch "is" to "gets" (easier on the ear and uses singular), or switch "performances" to "efficacies" (less confusing).

ADDED: "is compared" makes me wonder, is compared to what? Those two methods could be compared as a whole to two other methods. That's why plural helps.

MSWord grammar checker is correct as far as it goes. You can either use the plural "performances" with "are", or the singular (or uncountable) "performance" with "is".

The real question here is whether "performance" is countable or not.

According to Oxford Learners Dictionaries, this usage of "performance" (meaning 3) can be either countable or uncountable. So that doesn't really clear the matter up!

In your particular situation you could pluralise it, and use "are", but it doesn't quite feel right to me. Presumably it doesn't to you either, or you wouldn't be asking the question! If you say:

The performances of the new and existing methods are compared

then it sounds to my ear as if both the new method and the existing method have multiple performances, which are being compared (presumably Performance n new method being compared with Performance n existing method).

The problem, though, is that you can't compare one "uncountable" item to another, because you'd have to have two of them to compare one against the other, and you can't have two of something that is uncountable. So uncountable "performance" with "is" isn't an option.

Your only other option is to reword the sentence to avoid the situation.

I would suggest:

The performance of the new method is compared to that of the existing method

or possibly

The relative performance of the new and existing method is evaluated.

"Performances" in plural may be acceptable for different shows. Here we are not speaking of an act of performing, but how well a method does (i.e. performs), for which one may speak of "levels of performance". Therefore, in my opinion, "performance" should not be pluralized in such contexts.