A mathematical test of whether a study’s results could be caused by chance or whether they really show what they seem to show.

Significance is an English word that has been hijacked by statisticians. In general usage the term significant difference means an important difference, but "significant" in this sense is subjective. On the other hand, statistical significance is objective, and is based on the concept "p0.05". In an experiment, a difference is detected by challenging a null hypothesis of "no difference". When p is less than 0.05, the null hypothesis is rejected - when p is greater than 0.05, the null hypothesis is accepted. So what does p0.05 really mean? A p value of less than 0.05 means that there is even less than a 0.05 probability of getting the observed test statistic if the null hypothesis is true. This is an incredibly misunderstood concept, by even experienced users of statistics. See also Probability.

Results of a clinical experiment are said to be "statistically" significant when they are highly unlikely to be attributable to "chance" and arguably more likely due to "psi". The chance probability is reported as 'the significance level'. Generally, to be considered significant, the chance probability must be less than 1 in 20 (5% or 0.05).

comes in 2 varieties: statistical significance is when the p-value is small enough to reject the null hypothesis of no effect; where clinical significance is when the effect size is large enough to be potentially considered worthwhile by patients.

Is achieved when there is a low probability that the results of an experiment occurred by chance alone. In psychology it is conventional that results are said to be significant if the probability of their occurrence by chance is equal to or less than 5 per cent or 0.05

refers to the statistical probability that the result or finding could not have happened by chance.

Statistical significance is the probability that percentages or mean scores observed in the sample are truly different from each other. One way to determine statistical significance is to check whether the confidence intervals around the percentages or scores overlap. (from TalkingQuality.gov)

The degree to which a research finding is meaningful or salient. The level of significance of a test of hypotheses is the probability of rejecting the null hypothesis when it is in fact true.

when a statistical hypothesis is tested, it is declared true if a calculated probability exceeds a given value, referred to generally as the significance level.

A probability measure of how strongly the data support a certain result (usually of a statistical test). If the significance of a result is said to be .05, it means that there is only a .05 probability that the result could have happened by chance alone. Very low significance (less than .05) is usually taken as evidence that the data mining model should be accepted since events with very low probability seldom occur. So if the estimate of a parameter in a model showed a significance of .01 that would be evidence that the parameter must be in the model.