: Replacing actually with a more formal alternative I have a sentence that reads as follows, "This study shows that performance of method X and method Y are almost identical in ranking task and

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This study shows that performance of method X and method Y are almost identical in ranking task while method X significantly outperforms method Y in user recommendation task by about 30%.

"Significantly" adds a bit of weight to the result and should work as long as you're not directly involved with statistics where it's more precise meaning could cause the reader to ask, "significant at what probability level?" "While" instead of "and" serves to subtly differentiate the two results instead of lumping them together with "and".

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I would go full-bore on the emphasis and make the distinction clear. For example,
"This study shows that performance of method X and method Y are almost identical in ranking task. However, they differ greatly in that method X outperforms method Y in user recommendation task by about 30%."

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Since this appears to be a sentence from a scientific paper, I would think the reviewer's problem is not actually with the choice of word, but with lapsing from cold academic style.

In scientific papers the author is expected to stay detached from the results. This is an utter fiction, of course, as the whole point of publishing a paper is to boast in your success; but this is expected to be masked with an appearance of sober objectivity. The world "actually" here betrays emotions.

I second Kris's suggestion: it allows you to emphasize the result you are interested in, in a subtle way that would be acceptable in a scientific context.

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The intention of the reviewer seems to be to avoid words that may reflect personal opinion.
I would suggest that you break it into two sentences.

"This study shows that performance of method X and method Y are almost identical in ranking task."<
"Furthermore, method X outperforms method Y in user recommendation task by about 30%."<

Here, you are not including your interpretation/ opinion in an implied way, as is the case with saying actually. Note that the implication actually is not part of the findings of the study as such.

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I don't think 'actually' is particularly casual, and I agree with Dale Emery that the other words have different meanings. I'd stick with 'actually', myself.

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In this situation, I would read each term differently:

actually indicates disconfirmation of a prediction
(either the author's or the imagined reader's),
or perhaps the author's surprise at the general nature of the result
(as if the author hadn't even considered the possibility).
indeed indicates confirmation of a prediction
(or at least a possibility)
already explicitly expressed by the author.
in fact could indicate either surprise or confirmation.
lack of any of these terms makes a bare statement, without reference to predictions or expectations.

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