Do Google Know What People Are Doing On My Site?
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I run an ecommerce site and am keep to increase the time on site and reduce bounce rate. I have had some good results from writing good articles and advertising them on Outbrain and Twitter; both of these metrics have improved. However, I am wondering if Google will see this. Clearly if people land on the pages from the SERPS and return there they will know what is happening but will they know if people get there from an advert?
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Google owns the Chrome browser and if they wanted to get information about the behavior of visitors on websites, they would have designed a way to collect that data. Also, if you are running Google analytics on your site, you have no idea what bounty they are reaping about what your visitors are doing. You can bet that these two tools, at minimum, are a pipline sending lots of data into their databases.
I've not heard anyone from Google say exactly what info they get from the Chrome browser or from analytics or what they do with it but Google is well known not to say stuff about how they get their info. They are also well-known for putting out bad info about what they are doing.

It's best not to worry about what Google is doin' or thinkin' and just work your ass off making a better website.
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I honestly believe that Google probably knows what users are doing on your website with or without GA, and that GA is just a way for them to show it to you.