Andy Rooney was on the Don Imus radio show last month and seems to have stirred up some buzz when he said that he didn't care for the term "African-American." Some simple-minded people thought this meant he did not care for African-Americans, but one takes that kind of response for granted nowadays. What got my interest was when he said, "I mean, am I an Irish-American?" My response, not surprisingly, was, "I'll check that out."
Turns out Andrew Aitken Rooney was named for a Scottish great-grandfather, Andrew Aitken. One of Andy's grandparents was Scottish. The other three grandparents were all born in England and all of their parents were born in England.
Maybe sometime in the distant past the Rooneys went from Ireland to England. That would make them Irish-British before they came to this country. And so, no, Andy you are not Irish-American. You are Irish-British/English/Scots-American.