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Is it possible to use Google Analytics to determine where my visitors go when they leave my site? For example, is it possible to know how many went straight to example.com from my site?
The answer isn't in front of your face although it is there if you search the G Analytics site, as long as you know what to search FOR.
If the route from your site to example.com goes through a link that's placed on your site, yes it's possible. If the visitors just browse to example.com, there's no way of knowing except for using one of the big services that claims to be able to estimate what sites are visited together .... Compete, Nielsen, Comscore.
The two ways of knowing are:
1) Get example.com to put YOUR Google Analytics tag on their landing page. Of course, you'll pick up a lot of hits going to that page from sources other than your site.
2) Program the link to example.com so that when it experiences an onclick or ondown event, it fires the Google Analytics tag and passes information to the tag about which exit link was clicked on.
For the latter, Google says they have instructions for it, but I haven't looked at them in months. The tag I use (for another tool, WebTrends) automatically senses off-site clicks and records them, so I never needed to learn the reprogram-every-link method. I think you'll find the solution without trouble in the GA help site - try searching on "off-site links" or even "ondown" or "onclick". Or maybe somebody here has the info.
You are correct in that Event Tracking can allow to track some of the things you are mentioning. However in my experience Outbound Links are NOT events ...Plays, downloads, widget loads, etc. are events.
In regards to tracking Outbound Links and inflating "Page Views" I have a couple comments:
These clicks belong to you and after long discussion on our end we decided to treat them as "Page Views" being that they do generate a page view which technical should be "owned" by the site that generated it.
Now in regards to inflating your numbers: I don't know if you are getting the most out of GAnalytics by creating multiple profiles (mobile traffic, social networking traffic, etc) but all we did was just make sure that the Outbound Link information that you passed to Google has something unique in it so that you can exclude it from your main reports via an exclusion filter.
Now..with all said if you wanted to still track them as an event and be able to determine what sites people are visiting I am sure you could do that passing the outboundlink.com as one of the optional values explained in the Event Tracking documentation.
However, my thoughts is that what is explained in the link above should be used for outbound links and mailto links and both I have no problem considering a pageview.