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I have encountered some occurrences of phrases of the type:

the correlation between variables is strong, and significantly so...

and was asked to explain what the part after the comma meant. Although I know the meaning, I couldn't give a precise answer despite searching for a formal description.

Could someone please explain what the construction used here is and provide some more examples (which do not use the word significantly but have the same construction).

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    It is a common construction that is used to refer back to something that has already been mentioned: ‘Is he coming?’ ‘I hope so.’ (I hope he is coming) - ‘Did they mind?’ ‘I don't think so.’ - If she notices, she never says so. - The correlation is strong in a significant way. – user66974 Mar 27 '17 at 12:46
  • In the example provided, the context seems to be statistical analysis. I'm not sure if this is an accident, because the word "signficant" carries a particular meaning here (see en.wikipedia.org/wiki/Statistical_significance). This means it may be difficult to express the same meaning in the same construction without using this term. The meaning of the term "significantly" in this context would need to be expressed in some other way that described further concepts relevant to the statistically "significant" result. – remnant Mar 27 '17 at 12:51
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    @remnant - I guess the question is about the use of "so" rather than "significantly". – user66974 Mar 27 '17 at 12:53
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    If the question is about the use of "so", this definition from Merriam-Webster may help: "in a manner or way indicated or suggested". In the example given, the correlation is described as "strong". The adjective "strong" is then intensified by an adverbial phrase "significantly so" = "significantly in the manner or way indicated" = "significantly strong". – remnant Mar 27 '17 at 13:29
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    @mahmudkoya The sentence can be considered complete, no extra verb is needed. – oerkelens Mar 27 '17 at 13:38
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So here is a predicate adjective, "mirroring" strong. Thus, significantly is an adverb modifying an adjective. (How strong? Significantly strong.)

A similar example:

The loud music is deafeningly so.

It is not necessary that so be an adjective:

The man runs quickly, and astonishingly so. (Used here as an adverb modifier—so is here an adverb)

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