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Encyclopedia > Statistically significant

In statistics, a result is significant if it is unlikely to have occurred by chance, given that a presumed null hypothesis is true, but is not improbable if the null hypothesis is false.


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). The significance of a result is also called its p-value.


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".


If the significance level is smaller, a value will be less likely to be more extreme than the critical value. So a result which is "significant at the 1% level" is more significant than a result which is "significant at the 5% level". However a test at the 1% level is more likely to have a Type II error than a test at the 5% level, and so will have less statistical power. In devising a hypothesis test, the tester will aim to maximize power for a given significance, but ultimately have to recognise that the best which can be achieved is likely to be a balance between significance and power, in other words between the risks of Type I and Type II errors.


  Results from FactBites:
 
Statistical Significance Terms (1108 words)
Statistical methods are used to estimate the probability that chance alone accounts for the differences in outcomes.
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In most clinical trials, a result is statistically significant if the difference between groups could have occurred by chance alone in less than 1 time in 20.
Statistical Significance (1299 words)
The first part simplifies the concept of statistical significance as much as possible; so that non-technical readers can use the concept to help make decisions based on their data.
In contrast the high significance level for type of vehicle (.001 or 99.9%) indicates there is almost certainly a true difference in purchases of Brand X by owners of different vehicles in the population from which the sample was drawn.
While this logic passes the common sense test, the mathematics behind statistical significance do not actually guarantee that 1-p gives the exact probability that there is a difference is the population.
  More results at FactBites »

 
 

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