The Bonferroni correction is a multiple-comparison correction used when several dependent or independent statistical tests are being performed
simultaneously (since while a given alpha value 
may be appropriate for each individual
comparison, it is not for the set of all comparisons). In order to avoid a
lot of spurious positives, the alpha value needs to
be lowered to account for the number of comparisons being performed.
The simplest and most conservative approach is the Bonferroni correction, which sets the alpha value for the entire set of 
comparisons equal to 
by taking the alpha value
for each comparison equal to 
. Explicitly, given 
tests 
for hypotheses 
(
) under the assumption 
that all hypotheses 
are false, and if the individual test critical values are
,
then the experiment-wide critical value is 
. In equation form, if
 |
for 
,
then
 |
which follows from the Bonferroni inequalities.
