No, statistical analysis cannot demonstrate whether Anita has X-ray vision, but it can ultimately all but rule out whether she just got lucky. At this point, that cannot be ruled out, nor can it be ruled out that she benefited from a flawed test. However, to dismiss her results as a dismal failure shows a bias against her.
Extraordinary claims require extraordinary evidence. Her claim has no basis in known science. Proper weight is being given to the likelihood that she is either the first human out of many billions to possess a unique, unknown, unexplainable ability supported only by anecdotes or merely one of many millions of people who have mistakenly believed or deliberately asserted falsely that they have special abilities.
If you want to call that bias, and I'm sure you do, go right ahead. I call it perspective.