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In [[statistics]], the '''Bonferroni correction''' states that if an experimenter is testing ''n'' dependent or independent [[statistical hypothesis testing|hypotheses]] on a set of data, then one way of maintaining the [[familywise error rate]] is to test each individual hypothesis at a [[statistical significance]] level of 1/''n'' times what it would be if only one hypothesis were tested. ''Statistically significant'' simply means that a given result is unlikely to have occurred by chance.
'''1 - (1 - α)<sup>1/n</sup>
For example, to test two independent hypotheses on the same data at 0.05 significance level, instead of using a [[p-value|''p'' value]] threshold of 0.05, one would use a stricter threshold equal to the square root of 0.05. Notably one can derive valid [[confidence intervals]] matching the test decision using the '''Bonferroni correction''' by using ''100*(1-α<sup>1/n</sup>)%'' confidence intervals.
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