It is easy to see "experimental evidence" as "the truth" but the truth is not a fruit so easily reached. More often than not, the data gained from an experiment is tainted by the experimenter himself. This is called the "experimenter effect" or "confirmation bias". In some cases, a better nomenclature might be "the accidental illusionist" effect; especially when it comes to Special Relativity.
An excellent example is an anti-relativist (Herbert Ives) who set out to prove relativity false and, by the end of the experiment, believed he had proven relativity correct. This experiment is called the Ives-Stilwell experiment. He used a particle accelerator to measure the light emitted by hydrogen particles from the front and rear simultaneously by viewing the particles directly and from a mirror placed behind the moving particles.
The intent was to determine what, if any, was the difference between classical transverse doppler effect and relativistic or lorentzian transverse doppler effect. Much to the consternation of Ives, the results matched the predictions of relativity.
Ives never realized that the particle accelerator was not using classical calculations to determine particle speed, but relativistic calculations...
Garbage in - Garbage out ...and the error has never been publicly recognized to this day.