The African American adolescents had a lower birth weight, a lower verbal IQ, and a higher number of sexual partners than did White adolescents. For each characteristic, the mixed race mean fell between the means of the two parental populations.
Races are extended families. People in a race are genetically and genealogically closer to each other than to people outside of it. This racial clustering of relatedness is empirically testable. Race is not a social construct.
You're conflating two distinct concepts. By the genetic definition, a 3/4 European 1/4 African would be white. By the social definition, a 3/4 European 1/4 African would be black.
My roommate in college was half-Haitian half-Portugese and identified more as European. My near 100% African-American buddy I played cards with identified himself as fully black. A half-Carib half-French (black skin tone) girl I knew identified as French. In London, a good friend who is half-Arabic half-Indian identifies equally as Arabic and Indian. My three-quarters Chinese one-quarter Japanese friend raised in Beijing identifies as pure Chinese. I think a 1/4th African 3/4ths European blood person raised in a predominantly black community would identify as black, and raised in a non-black community would identify as European.
All my data is from people who live in international coastal cities though, so maybe it's different in various provinces and less affluent middle-of-country areas.
Popular perception of race among Americans. The "one-drop rule" is widely attested, and for the most part is still true.
This can and does vary from country to country--mixed-race Brazilians are considered white in Brazil, but black if they immigrate to the United States.
You're using a fairly prescriptive definition of race. Race, as commonly used, is a social construct. Ancestry functions the way you describe, but as the example given above shows, "race" and ancestry are not directly related.
Ancestry is objective. Race is subjective. There is a many-to-many relationship between the two. If people say you're black, then you're black. Different groups may come to different conclusions on what your race is depending on varying social norms. If you disagree with this, then you're not using "race" in the same way that the rest of country is.
PS: It's been a few years since I read that finding so it's going to take me a while to find it again.
Edit: Americans that are 1/4 "African" tend to identify themselves as African. This seems odd to me but it's actually the case.