<P> In statistical hypothesis testing, a result has statistical significance when it is very unlikely to have occurred given the null hypothesis . More precisely, the significance level defined for a study, α, is the probability of the study rejecting the null hypothesis, given that it were true; and the p - value of a result, p, is the probability of obtaining a result at least as extreme, given that the null hypothesis were true . The result is statistically significant, by the standards of the study, when p <α . </P> <P> The significance level for a study is chosen before data collection, and typically set to 5% or much lower, depending on the field of study . In any experiment or observation that involves drawing a sample from a population, there is always the possibility that an observed effect would have occurred due to sampling error alone . But if the p - value of an observed effect is less than the significance level, an investigator may conclude that the effect reflects the characteristics of the whole population, thereby rejecting the null hypothesis . This technique for testing the significance of results was developed in the early 20th century . </P>

When the results of a hypothesis test are statistically significant it means