There's an interesting NYT's article from this past week called "Do College Admissions Interviews Matter?" Although the article makes a convincing argument that undergraduate interviews may not matter in many cases, it does point out that many graduate school interviews do. It also recommends doing mock interviews.
The NRMP Program Directors' Survey makes it quite clear that residency interviews matter a lot, which was also my experience as Assistant Residency Director at Harvard. I remember very robust conversations about even small comments that candidates had made in their interviews that adversely affected their ranking on our Match list.
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