Dear Mr. Clarke,
If you have a subscription to Genealogy.com,and the U.S. CENSUS portion, you can click on My Genealogy.com tab at top of page, on the next page click on "US. Census", in one of the options on that page. You would need to type in the Surname you are looking for and then click 1820, can't recall the exact order of pages, then click "ohio" and it will bring up all the people with that name indexed from the criteria you entered -- I tried it out but I believe I entered the wrong spelling of "clarke" I put in "clark" and on the second page of listings, found a Clark, Birdseye from Nelson, in Portage county then I had the option of going to that census page and saw it there. I hope this helps a little.