I applied to the Product Analyst position online without knowing anyone at the company and got notification that I'd be having a phone interview within about a week of my application.
The phone interview had all the standard questions (Why IXL?, etc) in addition to a brain teaser. I was also asked to describe my PhD research as I would to a kid in 4th Grade. I was notified at the end of the phone call that I'd be advancing to the next round, the skills test.
They emailed me the skills test with a few questions for me to answer at home over the space of a week. The questions were, apparently, a fairly good representation of the type of work you'd be doing for the company in this position. I did my best but was a little unsure about how I'd done, but it must have been good enough because within a few days I was notified that I would be advancing to the on-site interview round.
The onsite interview lasted about 2 hours. I met with 3 different people; a math product analyst, a science product analyst and a director. You are just left in one room the whole time while the interviewers come to you, but they give you some puzzles and reading material about the company to keep you entertained while you're waiting. The two product analysts were very heavy on skills questions, very similar to the take-home skills test but you are expected to answer on the spot. You're given an example of a problem that might appear on the website then asked how you would vary difficulty on this problem, what other types of questions you might ask and how you'd make it more engaging. The director asked more typical interview questions about past conflicts/resolutions at work, why I want to work at that company, what experience makes me the ideal candidate, etc.
In the end, I was left feeling unsure how I'd done but didn't feel like I'd said anything too stupid. I didn't get an offer so I don't have any useful advice about what they may be looking for.