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I understand the meaning of "make a (big) difference", I am a bit confused about the usage of the preposition though.

Ngram Viewer shows that both are common

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From a tutorial (transcript)

When you speak English, do other people find it difficult to understand what you’re saying? If so, you might not be using stress correctly. Pronouncing words with the correct stress can make a big difference to your English ...

While her pronunciation sounds like

... make a big difference in your English ...

Obviously, the speaker is trying to say that pronouncing words with the correct stress can make your English better.

To convey that idea, should I use "in" or "to" there?

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Ngram is useless here because the phrases have different meanings.

Of course it makes a difference to my happiness if my sister marries that lunatic.

Here the effect being discussed is emotional.

Of course it makes a difference in the prognosis whether the biopsy shows cancer or not.

Here the effect being discussed is non-emotional.

In the question you asked, the effect desired is non-emotional and calls for "difference in."

Ngram is a great tool, but it does not distinguish between different meanings.

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