It is a statistics question, and relates to the topic of hypothesis testing, which generally asserts that there is no significance (the null hypothesis), and the researcher must find sufficient evidence to refute the null hypothesis, leading to support for what is called the alternative hypothesis (presence of significance).

In general, if the results of the study have an associated probability or likelihood that is less than what the researcher is willing to attribute to random chance, then there is evidence to refute the null, lending support for the alternative hypothesis.

If you Google "hypothesis testing" you'll probably get many hits.

A good place to go is Hyperstat:

http://davidmlane.com/hyperstat/logic_hypothesis.html