Statistical significance and p=0.05?

Gets tricky with those double negatives. In plain words what it means is that there is MORE than a 5% chance that differences you may have observed are just by chance. For example, say you were comparing the survival of two groups of fruit flies, one exposed to low level radiation, the other not. If you compare survivorship and the result is not significant at p=0.05, then you'd be inclined to say that there's no evidence that the radiation exposure is affecting survival.