Ask HN: How do you validate assumptions?

Three of us are building a startup and we are trying to validate a bunch of assumptions. We have an MVP in place, set up Mixpanel and have some custom-built tracking set up, so we can measure everything we want based on these assumptions.

However, we are having a hard time stating our goals and expectations that should come from these assumptions. In the Lean Startup, Eric Ries talks about Kodak. They were building an event photo album creator and wanted to validate if people want to create photo albums at all. They concluded that people wanted to do this, but what amount of data did they look at?

In general, how much data do you need to be able to make conclusions out of assumptions? When are you satisfied with the results and how do you decide to pivot or persevere?

I realize this is very subjective, but I was wondering if someone has some insights into this. Thanks!