Firstly, what is meant by the term approaching significance? It is basically a term used by psychologists who’s results fractionally miss out on being significant. For example, if you received a significance of .058 then it is technically un-significant but by such a small margin that it may well have been significant with just one other participant or without a measuring error. But the question is, is using this phrase cheating?
Well there are reasons why this phrase might be used. For example an experiment that receives results this close to the significance line it only takes a few more results your way to be able to state that your experimental results are significant. With such a minimal difference between the significance line and the received significance then the experimental results must surely be effective (in the case of testing a new drug or treatment.)
However the point still stands that it is not significant. If you bend the level given for significance, where do you stop it. This science needs an immobile line that psychologists need to aim for, if they can move that line one way or the other then many more experiments may be given as significant or insignificant, thus leading to type one and two errors on the researchers behalf.
Also, ‘approaching significance’ leads the idea that the more you test the more likely it is that it will be proved as significant, but this can go both ways, it is always possible that this person received a biased sample for some reason (un-be known to the researcher) and that the more people are experimented on the less and less significant this result is going to become.
In conclusion, this phrase should not be deemed as cheating or as not cheating, if this phrase is needed, surely it is vital that this experiment be replicated? Or keep going with more participants in the same experiment until you reach a significant effect, or the significance gets worse.