The multiple comparisons problem is the increase in the probability of false-positive conclusions when many statistical tests or confidence
statements are considered together. If 
independent tests each have significance level 
, the probability of at least one false rejection when
all null hypotheses are true is
 |
which exceeds 
for 
.
Procedures such as the Bonferroni correction control the probability of making at least one false rejection in a specified family of tests. False-discovery-rate procedures instead control an expected proportion of false rejections among all rejections. The appropriate adjustment depends on which family of conclusions is being made and which error criterion is to be controlled.
