However, if you are invited to an interview, that is very good news! The admissions committee liked your application and wants to learn more about you. While an interview offer is not a guarantee of admission, most programs accept a large fraction of the students who are interviewed.
I attended four interviews when I applied to graduate schools for fall 2008. I was very nervous on my first one, but after attending several of them I began to fall into the routine. Here I will share my experiences so you'll know what to expect from the interview, and give a few pieces of advice to help you succeed.
One of the most important parts of the interview involves meeting with various faculty to talk about your own work, their work, and the program and institution overall. You may be asked to provide a list of faculty that you would like to meet when the program is organizing your interview. Now is a good time to review the program website again and come up with a list of 8-12 names. You probably won't have that many interviews, but some professors may be unavailable so they usually ask you to list more than you'll be able to meet. Your meetings may also involve the director of graduate studies for the program, the admissions chair, or some other figure with decision-making power in the admissions process. These meetings are usually considered the "formal" part of the interview, so bring something business-appropriate to wear. Many people wear suits, but anything involving a tie for men or a nice blouse plus slacks or skirt for women should be acceptable. Wear something comfortable, since you'll be running around in your interview clothes all day. Comfortable shoes (NOT heels, ladies... don't make my mistake) are a must. Also, almost everyone wore black to my interviews! Choosing a bright colored tie or blouse will make you more memorable.
The faculty meetings may seem intimidating, but try not to worry too much about them. They usually last only 20-30 minutes, and you should only worry about talking for half of that time. I didn't experience any interviews in which the professor tried to give me "gotcha" questions or test my intelligence; most of them are an easy back-and-forth about your research and the professor's research, or your interests and the graduate program's focus. If you have any nice data figures from your previous research projects, it is very helpful to print out one or two pages of figures so that you'll have something to point to during your conversation. This makes you seem well-prepared for the meeting, and will help remind you of the important points to cover when you discuss your projects. If you don't have a lot of research background, it's fine to ask the professor, "Can you tell me about your lab and what you study?" This usually fills plenty of time! At the end of the interview you'll probably be asked if you have questions about the lab or the program. It's perfectly fine to ask the same questions of each professor. I liked asking them about their current and previous grad students and what they're up to -- you can get a sense of what it would be like to work for the professor, and what kind of jobs you could expect to get after doing a dissertation with them. General questions about the program curriculum, university, or even living in the city where the school is located are also fine. And then you're done! Next interview!
In addition to faculty interviews, you'll probably be shuttled to a bunch of events designed to show off the campus, woo you with free food, and give you the opportunity to interact with current students. These current grad students should be your allies. Pay attention to how they interact with you and with each other. Are they happy? Do they seem to actually be friends? Are they welcoming and inclusive? You should take advantage of your chance to pepper the students with questions. Ask about classes, choosing a mentor, finding an apartment, cost of living in the city where they're located, fun things to do in your free time, and anything else you can think of. Try to get a sense of the program's climate and attitude, to see if you'll fit in. Remember, this interview is not just about you impressing the university; it's about the university impressing you! If you're going on multiple interviews, you'll want to pay careful attention as you'll likely be forced to choose between multiple admissions offers. I recommend bringing a journal (or a laptop...) to write down your impressions of the interview at the end of each day. This will help you remember your impressions later on -- the interviews can be very busy and sometimes everything runs together in your memory, so I found it helpful to refer to my own journal entries.
Despite your best efforts, interview mishaps can occur, either through your own fault or the university's. During my interview at Emory, I was sent to a seafood restaurant for a nice dinner with students and faculty. This occurred in spite of my written notification to the interview organizers that I am deathly allergic to seafood! That really upset me (it was one more stressor added to long interview days and anxiety over making a good impression) and I had a minor melt-down in the ladies' room. Despite all the angst, I was well taken care of, and several different people apologized to me and made me feel much better. In the end, despite freaking out and having to go back to my hotel in the middle of a scheduled event, I was still offered admission. And I accepted! Try to take this anecdote to heart and remain calm during your interview. Even if things go wrong, it will work out in the end; you don't have to obsess about being absolutely perfect.