Not that any huge difference exists between a paper for anthropology and one for English, but students often exaggerate the differences that do exist and cause themselves and their teachers unnecessary grief. The social sciences, by their very use of that word "science," like to imagine themselves as somehow more objective and disciplined than those wackos in the English department. The word "science" comes from the Latin scio, which means "I know." Science takes its claims to knowledge seriously and has little patience with the kind of relativistic solipsism that runs rampant in English departments. There is a truth and they know it. They did build that bomb, didn't they? But the hard sciences look down on the soft social sciences as much as the social sciences look down on the literary types. We thus have a continuum with the hard sciences like biology and physics on one end, the relativists in the English department on the other end, and the many branches of the social sciences defensively in the middle.
"Real" Marxists from the sociology or economics department can barely break bread with their literary cousins across the hall. And all of the social sciences believe their work to be based in strict adherence to certain methodological principles and their precise terminology. Partly because of this sneer, the professors in the English department adopted French postmodern theory so that they too could have certain methodological principles and an incomprehensible vocabulary to go with them. In the end, the two groups all roughly do pretty much the same thing in the same way, alas.
Students still have to deal with those perceptions. Therefore, a paper for sociology or anthropology needs to adopt science's arrogant "we know," that assumption of a common body of knowledge backed up by scholarly studies. You can make almost any claim you want if you can find a journal article somewhere, or a scholarly book, that can be footnoted as a reference for your "fact." You need to spell out carefully near the beginning of the paper which or whose methodology the paper is based upon. And you absolutely must have studies from reputable journals to back up any claims. Subjective color is appropriate in an English paper, but a social science paper also requires a vigorous and engaging voice. Use anecdotes as you would analogies to illustrate your points, but do not depend upon them to substantiate your points. The crucial difference is that a paper for a social science class must state its objectives clearly and use evidence that will stand up to critical scrutiny. In short, cover your ass.
Statistics are also important. They are the data upon which the paper's generalities are based. No human trait is absolute, so generalities are a necessary evil. We look for generalities but distrusting them. Hence, a study of any group of people has to determine at what point the repetition of a certain trait becomes "statistically significant." If one out of five African Americans is lactose intolerant, is that significant? Or must the statistic be three out of five before we start making generalities about whether African Americans have difficulty digesting milk? Such statistical questions need to be addressed as part of the discussion of methodology.