Introductory concepts - Practical Biomedical Signal Analysis Using MATLAB - page 18

The number of cases V , T , U , S ,and R are treated as random variables, but only R
can be observed. The family wise error rate FWER is the probability of falsely re-
jecting one or more true null hypotheses among all the hypotheses when performing
multiple tests:

FW ER = P ( V ≥ 1 )= 1 − P ( V = 0 ) (1.44)

In studies where one specifies a finite number of a priori inferences, families of hy-
potheses are defined for which conclusions need to be jointly accurate or by which
hypotheses are similar in content or purpose. If these inferences are unrelated in
terms of their content or intended use (although they may be statistically depen-
dent), then they should be treated separately and not jointly [Hochberg and Tamhane,
1987].
Sometimes it is not necessary to control the FWER and it is sufficient to con-
trol the number of falsely rejected null hypotheses—the false discoveries. The false
discovery rate (FDR) is defined as expected proportion of incorrectly rejected null
hypotheses:

E E V

R

V

FDR = = (1.45)

V + S

TABLE 1.1:

Outcomes of m hypothesis tests.

# declared non-
significant ( H 0 accepted)

# declared significant To tal

( H 0 rejected)

# true null hy-
potheses

U V m 0

# false null
hypotheses

T S m − m 0

−

To tal m R R m

Below we briefly describe three approaches to MCP: correction of the significance
level α, statistical maps, and false discovery rate (FDR).

1.5.3.1 Correcting the significance level

The most straightforward approach is known as Bonferroni correction, which
states that if one performs n hypotheses tests on a set of data, then the statistical
significance level that should be used for each hypothesis separately should be re-
duced n times in respect to the value that would be used if only one hypothesis were
tested. For example, when testing two hypotheses, instead of an α value of 0

. 05,

one should use α value of 0 025. The Bonferroni correction is a safeguard against

multiple tests of statistical significance on the same data. On the other hand this cor-
rection is conservative in case of correlated tests, which means that the significance

.