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There are a lot of people in southern Ohio with a southern accent because, as Ivory Lee Spurlock mentioned, there are a lot of 'immigrants' from the Appalachians who have come up in the last few generations.
But to say that is "the" accent there is way off. There are millions of New Yorkers with a Chinese accent but you wouldn't say that the trademark accent of NYC is a Chinese accent.
That said, southern Ohio is a strong Midland accent (as heard from Philly/So. NJ to St. Louis) which deviates from the General American accent of broadcast television presenters.