ChristianKl comments on Outside the Laboratory - Less Wrong
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I wouldn't. Two studies opens the door to publication bias concerns and muddles the 'replication': rarely do people do a straight replication.
From Nickerson in http://lesswrong.com/lw/g13/against_nhst/
If you put the general significance standard at P<0.005 you will even further decrease the amount of straight replications. We need more straight replication instead of less.
A single study can wrong due to systematic bias. One researcher could engage in fraud and therefore get a P<0.005 result. He could also simply be bad at blinding his subjects properly. There are many possible ways to get a P<0.005 result by messing up the underlying science in a way that you can't see by reading a paper.
Having a second researcher reproduce the effects is vital to know that the first result is not due to some error in the experiment setup of the first study.