Is measuring of web site visitors an exact science?

How do you know how many visitors come to your web site every day (and also how did they find your site)

Well there are two main ways the average site can find out

Plenty of counter you can get for free on the Internet. They vary from mere "number counters" to the very sophisticated ones from Extreme or HitBox that record not just numbers, but also the search engine used, keywords used, referral page, country of browser, operating system used, etc
The owner of the counter will give you a special code to paste into your web site coding (easy to do). Every time a visit is made to your web site it will/should advance the counter by one, and also send information about the visitor to the counter company's web site, where they analyse it and it is available for you to view.
So nothing could be simpler or more accurate - Wrong. It is virtually impossible to know who a unique viewer is.
For example most ISP's (Internet Service Providers) give their surfers a "dynamic" identity. This means that each time a surfer sets out to surf the web, they effectively have a different identity. Further the "dynamic" identity changes every, say, ten minutes - so a visitor to your front page arrives for the first time, gets counted, goes to a second page on the site, dynamic identity changes, and same surfer arrives back at the front page with a different identity and gets counted again. An example of a counter overcounting
Or another example that leads to undercounting is what is called "caching". Let us say that a user from a big ISP like AOL or Compuserve goes to your site and downloads the front page. It gets temporally stored (or cached) on the computer at AOL. Another AOL customer tries to access your site a few minutes later, but they never get to your site, the data is fed directly to them from AOL's cache, so your counter never records the visit. The counter undercounts
In addition the counter will only record visits to the page that it is actually on. It does not count visits to other web pages. So if the visitor never gets to the page with the counter on, the counter obviously never records them. Web sites are complex places. Often they have things called "doorway" pages, not everyone enters by the front page, many come via "doorway" pages that are rich in individual keywords. For example you may have a hotel in Cheltenham, and gain visitors to your web site via two different pages, one targeted at "Cotswolds" another at "Cheltenham". Unless you have counters on each you may only record half the visits to your site
Log File Analysis
Your ISP should have equipment to record all visits and then they should make these so called "raw log files" available to you for you to analyse yourself. Log files are a more accurate measure of visits, in that they record data for all pages.
However you do need a special software program (I use Web Trends) that is not cheap and it does take time to download the compressed log files at the end of every week
The resultant analysis is a series of well presented three dimensional graphs plus back up charts, that tell you how many "unique", where they came from, what keywords they used, how many pages they looked at, which pages they looked at, and much much more.
However the same provisos about problems with counting remain. On top of the problems given under counters above, there are company web sites, where the visitor to your site is behind what is called a "firewall" to protect their site from hackers, and the net result is they use a thing called a "proxy server" which strips out all data from the browser and gives your log files no data to use (about 17% of all browsers are using a proxy server)

If you are sufficiently interested in more information on this subject, I have a more detailed analysis comparing the results of 4 different methods of counting on this page. Briefly a fairly typical hotel web site accumulated visits over time. A counter on the front page recorded around 2200 visits and different log analysis software recorded anywhere from 2350 to 2550 visits. While the log analysis for the whole site recorded a range of 5250 to 5850 visits.

What does it mean - it means a straight counter appears to have underscored visits to the front page by about 10%, and misses altogether another 150% of visits that do not get to the front page. On a complex site the disparity is obviously greater as there are lots more ways the visitor can enter the site and the multiplier becomes around 300% between the front page counter and the whole site

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