I think the dressing well vs badly dichotomy may be misleading here, a better analogy might be with similarity to certain archetypes.
For example neither Barack Obama or Justin Timberlake dress 'badly' but he way they dress is radically different. So if you want to alter your social perceptions dress in a manner similar to the archetype most relevant to your goals.
Applying this, if you are in a university environment your goals might be wanting the professor to treat your work favourably, and possibly be lenient in cases. Hence you can choose similarity to the archetypes "Lazy student" (Stained t-shirt, baggy trousers) or "Academic" (Shirt, neat but non flashy clothes). This can be generalized to other environments and social signalling situations.
Yesterday I attended a meetup where the discussion turned to fashion for a time (because apparently the mini-camp participants were given some instructions on fashion as a useful part of instrumental rationality). (Unfortunately none of us knew much about the topic so the discussion turned into "how can we find an expert to advise us for minimal cost?") It was mentioned that dressing "badly" can be a useful signalling device, and some examples were given. Here's an attempt at a more complete list of possible signals one might be sending by dressing "badly".
The idea here is, if you do decide to start dressing "well", know what you're giving up first. (Of course you're also giving up possibly implying that nobody taught you how to dress and you're not sufficiently strategic to have thought of learning it yourself. Or implying that you don't have the mental, financial, and/or social resources to keep up with fashion. A lot of signaling depends on what your audience already knows about you, or can infer from your other signals.) See also Yvain's related post, Why Real Men Wear Pink and comments there.