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I suggest the best way to test is try a trial period of whatever they are offering if it involves any sort of referral (referrals in your logs from their site to yours; click through tracking etc). Bottom line is not how popular or hits they get, but the number of referrals YOU get.
There are various organizations that measure web site traffic for major sites through the various Netratings and Media matrix type things, but only good for major site "players" with major traffic. Usually based on surveys and user tracking. There are other attempts being developed that aim to provide some sort of "audited" figures like the mainstream press "audited circulation" figures.
If sites are serious about providing data about their traffic they would provide access to their live logs and results. They would not be happy about providing referral data, but this can be filtered out. But all you would need i think is some sort of unique user count, with maybe the limited demographic info that logs can provide such as country and type of domain (country domains as we know are very unreliable as we know), pages ranked by popularity and browser type.
I would tend not to belive any claims about traffic unless it can be backed up by independent auditing, valid logs, or referral tracking. Webmasters can easily go blur on what the difference bwteen a hit and a unqiue user is, and how they define a unqiue user. "Oh sorry... those are our total hits" or "Those monthly figures were based on our daily uniques, not our monthly uniques (A BIG difference!)
you could also try [stats.domain.com...] sometimes it works
As well as that try the "obvious" directory extensions.
In addition try the source code to see if there are any commercial trackers in place. Then read those
The guy probably just had the Alexa toolbar installed on his own PC and looked at his own site a lot, which skewed the Alexa rankings in his favor.
I installed the Alexa toolbar on my browser for fun, and within weeks my site went from 243,000 to 163,000 in popularity, and I have a thousand plus unique visitors a day.
And I only click on my site once or twice a day.
Obviously Alexa has to thin of a market share to provide usefull results.
What I mean to say is that I have a site with good traffic, with no visible change in that traffic, the 80,000 jump in popularity is artificial, due to the installing of a alexa toolbar that hardly nobody uses.
Now if Google added this feature to its toolbar, then we have something, we can measure.
If you really want to find out how your competitors is doing. Pull the companies credit file, and see how much they are purchasing from there suppliers. And yes this is perfectly legal (in Canada at least).