DuckDuckGo conducted a study in June 2018, in which it took a close look at how Google processes search results for logged-in, logged-out, and anonymous users.

Although DuckDuckGo's study may seem quite biased, given that it is a direct competitor to Google, their findings are interesting for anyone who wants to take a closer look at Google's inner workings.
According to the study's findings, Google's personalized results appear based on personal information previously collected for specific users (e.g. search, browsing, and purchase history), automatically adding each of them to a so-called "filter bubble."
Google uses this filter bubble to tailor search results that appear to a user searching for a specific term or phrase, so that most of the study participants see results that are unique to them.
Furthermore, although Google claims to have worked to remove the “filter” feature that showed the results users would want, DuckDuckGo discovered, with the help of the 87 volunteers who participated in the study, that users saw results that were unique to each one, even when they were logged out or in private browsing mode.
Users are trapped in Google’s “filter bubble” even after they log out and browse incognito.
Google also showed some of the study participants search results that other users were unable to see even though they were searching for them, even though they were incognito or logged out. This in itself means that if Google had removed the filter bubble bias, everyone should see the same results, but this is not the case and instead, when a user logs in, Google’s search engine uses the information it already knows to provide personalized results.
According to DuckDuckGo, using private browsing mode or being logged out of your Google account shouldn't give you the anonymity most people imagine. In fact, it's not possible to use Google search and avoid its bubble filter.
This is because fingerprinting techniques, as well as IP addresses, can be used to track people even when they think they are browsing the web anonymously. At this point, it might be worth giving it a try yourself. Log in to a Google account normally, search for a random English term, and see the first 5 search results. Log out, switch to incognito mode in your browser, and search for the same term. And finally, open Tor or an Opera proxy and do the same search again. Compare the first 5 results for these 3 searches.
All of the DuckDuckGo data collected during the study, as well as the search instructions and results achieved, along with the code used to analyze the information, are freely available on its website and ready to be examined by anyone interested in verifying their findings.
