Ask HN: Will Google penalize my site if I don't use Google Analytics?

I'm starting a new niche site, and would like to preserve my visitors' privacy for those to whom that's an important issue. For that reason, I'd like to leave out as many third-party tracking links as possible.

According to one of the big SEO firms[1], the top three ranking factors that Google uses are:

1) direct website visits 2) time on site 3) pages per session

To measure these, it seems to me a site would either have to ping back to Google on every page hit, or else the user's browser (i.e., Chrome) would have to do it for them.

Chrome stores it's users browser history on Google's servers[2], so they know this data for all logged-in users. But it can't track non-logged-in users, nor users of other web browsers.

If I leave off my GA code, Google won't be able to measure these three metrics for many visitors. Won't that hurt my web site ranking?

[1] - https://www.semrush.com/ranking-factors [2] - https://www.google.com/chrome/browser/privacy/index.html#browser-modes