How can I compare "The New Dress" with "Where Are You Going, Where Have You Been" in terms of the two main characters' obsession with...

Of the two short stories, Virginia Woolf's "The New Dress" has a more straight-forward message about appearances and their power over us. Mabel Waring opens the story by worrying about the appropriateness of her dress and overall aesthetic from the very first line. Her nearly debilitating terror is that the old-fashioned dress she attempted to cleverly remake for the party is hideous and everyone is secretly making fun of it. This fear not only eats away at her internally but also colors the reality she lives in:

"all were thinking– 'What's Mabel wearing? What a fright she looks! What a hideous new dress!'" 

The reader sees no evidence that anyone is acting judgmentally or mocking Mabel, but she is so caught up in her fear at not fitting in with the upper-middle class people at the party that she confuses appearances with reality. Mabel also thinks the housemaid gestures too emphatically at the hairbrush and mirror at the front door and that Rose Shaw (whose style she admires) is mocking her when she compliments her dress. Though readers can see this is all (or at least mostly) in Mabel's head, her anxiety and heightened sense of how she doesn't "look right" make her imagine a very different reality. 

This same take on perceptions versus reality is a key factor in Joyce Carol Oates' story "Where Are You Going, Where Have You Been?" and its protagonist, teenage Connie. Throughout the story, Connie has been focused on appearances and how they form her identity and opinions of others. The first thing we learn about Connie, after her name and age, is that

"...she had a quick, nervous giggling habit of craning her neck to glance into mirrors or checking other people's faces to make sure her own was all right."

Though her mother criticizes her for this, Connie knows she is pretty and her mother is not anymore and that this is the most important thing. For contrast, she considers her sister, whose chunky, plain looks seem to seal her fate of living at home at age 24 and working as a secretary at the high school. 

Connie's reliance on appearances to navigate the world is tested, though, when Arnold Friend pulls up in her driveway and tries to get her to come on a ride with him. As he flirts with her and tries to persuade her to come outside, Connie notices the way he is dressed,

"which was the way all of them dressed: tight faded jeans stuffed into black, scuffed boots, a belt that pulled his waist in and showed how lean he was, and a white pull-over shirt that was a little soiled and showed the hard small muscles of his arms and shoulders. He looked as if he probably did hard work, lifting and carrying things."

Connie is drawn in by the illusion of his clothing, car, and music, which allow him to imitate a teenager. Though she begins to suspect aspects of his looks aren't authentic (his hair is a wig, his boots are stuffed, etc.), it isn't until she gets close and sees his age that she senses the danger she's in, and by then it's too late. Connie's over-reliance on appearances seals her fate.