Stephen Jay Gould famously argued in his book, The Mismeasure of Man, that Samuel George Morton's skull size measurements were biased by Morton's a priori beliefs, and that this is inherent to scientific investigations into culturally or politically sensitive areas.
Turns out Gould was projecting. He never bothered to remeasure Morton's skulls, he just assumed Morton's measurements must be wrong. Now a group has actually gone back and remeasured the skulls, and it turns out Morton's measurements were correct, and Gould was wrong:
Summary by an anthropologist here: