| Line 53... |
Line 53... |
| 53 |
\I{Hochberg}'s, but the difference is usually small and the \I{Hochberg}
|
53 |
\I{Hochberg}'s, but the difference is usually small and the \I{Hochberg}
|
| 54 |
p-values are faster to compute.
|
54 |
p-values are faster to compute.
|
| 55 |
|
55 |
|
| 56 |
The \code{"BH"} (aka \code{"fdr"}) and \code{"BY"} methods of
|
56 |
The \code{"BH"} (aka \code{"fdr"}) and \code{"BY"} methods of
|
| 57 |
\I{Benjamini}, \I{Hochberg}, and \I{Yekutieli} control the false discovery rate,
|
57 |
\I{Benjamini}, \I{Hochberg}, and \I{Yekutieli} control the false discovery rate,
|
| 58 |
\I{FDR}, the expected proportion of false discoveries amongst the
|
58 |
\acronym{FDR}, the expected proportion of false discoveries amongst the
|
| 59 |
rejected hypotheses.
|
59 |
rejected hypotheses.
|
| 60 |
|
60 |
|
| 61 |
The \code{"BY"} correction modifies the \I{BH} procedure by replacing the
|
61 |
The \code{"BY"} correction modifies the \acronym{BH} procedure by replacing the
|
| 62 |
target level \eqn{q} with \eqn{q / \sum_{i=1}^{m} 1/i}, where \eqn{m} is
|
62 |
target level \eqn{q} with \eqn{q / \sum_{i=1}^{m} 1/i}, where \eqn{m} is
|
| 63 |
the number of tests (Theorem 1.3 in the reference), which controls the
|
63 |
the number of tests (Theorem 1.3 in the reference), which controls the
|
| 64 |
\I{FDR} under the most general form of dependence structure. This will
|
64 |
\acronym{FDR} under the most general form of dependence structure. This will
|
| 65 |
be more conservative than \code{"BH"}, for small \code{p} even more than
|
65 |
be more conservative than \code{"BH"}, for small \code{p} even more than
|
| 66 |
\I{Bonferroni}, see the example.
|
66 |
\I{Bonferroni}, see the example.
|
| 67 |
The \I{FDR} as implemented by the \code{"BH"} method is a less stringent
|
67 |
The \acronym{FDR} as implemented by the \code{"BH"} method is a less stringent
|
| 68 |
condition than the family-wise error rate, so it is typically more
|
68 |
condition than the family-wise error rate, so it is typically more
|
| 69 |
powerful than the others.
|
69 |
powerful than the others.
|
| 70 |
|
70 |
|
| 71 |
Note that you can set \code{n} larger than \code{length(p)} which
|
71 |
Note that you can set \code{n} larger than \code{length(p)} which
|
| 72 |
means the unobserved p-values are assumed to be greater than all the
|
72 |
means the unobserved p-values are assumed to be greater than all the
|