[cftm]

There's a lot of intuition and experience that is required to be a talented statistician; once the test has begun things are pretty much locked down (ie, if you know the math there is only one "right" answer from the data). The intuition and experience side of things comes with how the test itself is setup. Are things properly controlled, are you collecting the right data for what you're testing, is the data distributed properly for the test statistic you're using...the list goes on and on and on and on and on.

There are plenty of places that require intuition and these are the places that errors are often introduced. Statistics is an art.