Statistics are generated using computers, and people rarely (in most cases) have any opportunities to corrupt them. This kind of data contains the lowest number of errors possible, and clearly shows things like how a visitor made it to your site or what display resolution their monitor has.
In other words, statistics are incapable of telling a lie.
Perhaps you want to tweak the numbers so they can prove you were right about something, but don't give in to this urge! Statistics must always remain objective.
Statistics do not take into account context
However, statistics never have anything to say about a situation's context. It's, therefore, important to always be careful when interpreting this data. After all, designers are people too, and people can make mistakes.
Don't assume that the statistics you gather will go perfectly with every situation. Behind every statistic, there is a real person, and people's lives are infinitely varied.
Quantity equals quality
If you track the clicks of only ten people, it's possible they're all just wasted from a night out =) So you won't get any real data from them.
But if you track the clicks of 10,000 people, you'd have to be seriously unlucky for all of them to have been drunk that day (that is, of course, if you're looking at any day other than New Year's Eve).
It's imperative that you try and collect as much data as possible before making any decisions. This way the quality can be assured by the quantity.
How to gather statistics
There are several ways to gather statistics:
Web analytics — Google, Yandex and lots of other companies offer free tools to gather anonymous statistics from your site. With just a little help from some programmers, you can create your personal metrics, so there's really no ceiling to how much you can learn.
A/B testing — come up with two design options and try both of them out at once! This way you can find out which one works better because real people will be testing them out in real circumstances.
WebVisor — this is just one example of an entire family of services and software. WebVisor let you anonymously record actual visitor behavior as they interact with your interface. Find out things like mouse movements, how and what kind of information visitors type in, how far down they scroll, and how they travel to and from different pages. This is super helpful!
Site logs — Lots of people don't realize that a site's input form can store every word a visitor types in. If visitors are constantly doing the same searches, this might mean that they don't have direct access to what they're looking for. Logs are really helpful when it comes to optimizing your information architecture and site layout.
Eye-Tracking — see how people's eyes move as they look at your design. Users don't have control over their unconscious eye movements, making data gathered with Eye-Tracking perfectly objective. But getting this type of information, of course, requires special software and equipment.