Statistically significant refers to something that is thought to have sufficient evidence
not to have occured by chance
. This is to say, we assume something to be statistically significant if the likelihood
of it having occured by chance is very low, hence the likelihood of occuring by design
is very high.
Usually, the critical value for statistical significance is p=<.05. This means that if we believe the probability of something having occured by chance is less than or equal to .05, we assume it has not occured by chance.
This critical value is not hard and fast, however. Depending on the issue being analyzed, the probability value may be .10, or lower, say .01, or .001.