Multiple testing corrections adjust p-values derived from
multiple statistical tests to

correct for occurrence of false positives. In microarray data
analysis, false positives

are genes that are found to be statistically different between
conditions, but are not in

reality.

方法：

A. Bonferroni correction

The p-value of each gene is multiplied by the number of genes in
the gene list. If the

corrected p-value is still below the error rate, the gene will be
significant:

Corrected P-value= p-value * n (number of genes in test)
<0.05

As a consequence, if testing 1000 genes at a time, the highest
accepted individual pvalue

is 0.00005, making the correction very stringent. With a
Family-wise error rate

of 0.05 (i.e., the probability of at least one error in the
family), the expected number

of false positives will be 0.05.

B. Bonferroni Step-down (Holm) correction

This correction is very similar to the Bonferroni, but a little
less stringent:

1) The p-value of each gene is ranked from the smallest to the
largest.

2) The first p-value is multiplied by the number of genes present
in the gene list:

if the end value is less than 0.05, the gene is significant:

Corrected P-value= p-value * n < 0.05

3) The second p-value is multiplied by the number of genes less
1:

Corrected P-value= p-value * n-1 < 0.05

4) The third p-value is multiplied by the number of genes less
2:

Corrected P-value= p-value * n-2 < 0.05

It follows that sequence until no gene is found to be
significant.

Example:

Let n=1000, error rate=0.05

Gene

name

p-value before

correction

Rank Correction Is gene significant

after correction?

A 0.00002 1 0.00002 * 1000=0.02 0.02<0.05 => Yes

B 0.00004 2 0.00004*999=0.039 0.039<0.05 => Yes

C 0.00009 3 0.00009*998=0.0898 0.0898>0.05 => No

Because it is a little less corrective as the p-value increases,
this correction is less

conservative. However the Family-wise error rate is very similar to
the Bonferroni

correction (see table in section IV).

C. Westfall and Young Permutation

Both Bonferroni and Holm methods are called single-step procedures,
where each pvalue

is corrected independently. The Westfall and Young permutation
method takes

advantage of the dependence structure between genes, by permuting
all the genes

at the same time.

The Westfall and Young permutation follows a step-down procedure
similar to the

Holm method, combined with a bootstrapping method to compute the
p-value

distribution:

1) P-values are calculated for each gene based on the original data
set and

ranked.

2) The permutation method creates a pseudo-data set by dividing the
data into

artificial treatment and control groups.

3) P-values for all genes are computed on the pseudo-data
set.

4) The successive minima of the new p-values are retained and
compared to

the original ones.

5) This process is repeated a large number of times, and the
proportion of

resampled data sets where the minimum pseudo-p-value is less than
the

original p-value is the adjusted p-value.

Because of the permutations, the method is very slow. The Westfall
and Young

permutation method has a similar Family-wise error rate as the
Bonferroni and Holm

corrections.

D. Benjamini and Hochberg False Discovery Rate

This correction is the least stringent of all 4 options, and
therefore tolerates more

false positives. There will be also less false negative genes. Here
is how it works:

1) The p-values of each gene are ranked from the smallest to the
largest.

2) The largest p-value remains as it is.

3) The second largest p-value is multiplied by the total number of
genes in gene

list divided by its rank. If less than 0.05, it is
significant.

Corrected p-value = p-value*(n/n-1) < 0.05, if so, gene is
significant.

4) The third p-value is multiplied as in step 3:

Corrected p-value = p-value*(n/n-2) < 0.05, if so, gene is
significant.

And so on.

见：http://yixf.name/2011/01/11/【文献推荐】多重假设检验中的p值校正/

http://fhqdddddd.blog.163.com/blog/static/18699154201093171158444/

http://en.wikipedia.org/wiki/Multiple_comparisons

http://www.silicongenetics.com/Support/GeneSpring/GSnotes/analysis_guides/mtc.pdf

目前这些校正方法用于gene ontology的enrichment analysis