That Alexa isn’t good at giving reliable statistics is well known in IT. Any website like Alexa that tries to estimate traffic to a website in a similar way via indirect measurements will encounter the same issues it has. Those that work in IT often know what those issues are and know what the consequences are for the data that’s gathered via those methods.
The main issue that Alexa has is that it gathers the data it uses via users that installed the Alexa toolbar (or a toolbar that passes information to Alexa). This has as a result that demographic, used browsers, and even the country visitors are from influence the statistics that Alexa gathers about a website. This can introduce serious artefacts and biases into the collected data and basically makes Alexa data worthless. At best it can give you an idea about how well a website is doing, but that doesn’t mean that what you’re seeing matches reality. I’ve already written a far more detailed blog post about how Alexa works and why you never should rely on the data it provides; it’s just too unreliable.
The blog post that I wrote about Alexa were all sparked by Anthony Watts using Alexa data to claim he’s doing better than his competition. His website is certainly big and it could very well be the case that he is outperforming his competitors. But Alexa is not the tool that you can use for determining if you are doing better than your competitor.