In statistics, a result is significant if it is unlikely to have occurred by chance.
More precisely, in traditional frequentist statistical hypothesis testing, the significance level of a test is the maximum probability of accidentally rejecting a true null hypothesis (a decision known as a Type I error).
For example, one may choose a significance level of, say, 5%, and calculate a critical value of a statistic (such as the mean) so that the probability of it exceeding that value, given the truth of the null hypothesis, would be 5%. If the actual, calculated statistic value exceeds the critical value, then it is significant "at the 5% level".
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