# Calculate p-values from a set of observed test statistics and simulated null test statistics

### Description

Calculates p-values from a set of observed test statistics and simulated null test statistics

### Usage

1 |

### Arguments

`stat` |
A vector of calculated test statistics. |

`stat0` |
A vector or matrix of simulated or data-resampled null test statistics. |

`pool` |
If FALSE, stat0 must be a matrix with the number of rows equal to
the length of |

### Details

The argument `stat`

must be such that the larger the value is
the more deviated (i.e., "more extreme") from the null hypothesis it is.
Examples include an F-statistic or the absolute value of a t-statistic. The
argument `stat0`

should be calculated analogously on data that
represents observations from the null hypothesis distribution. The p-values
are calculated as the proportion of values from `stat0`

that are
greater than or equal to that from `stat`

. If `pool=TRUE`

is
selected, then all of `stat0`

is used in calculating the p-value for a
given entry of `stat`

. If `pool=FALSE`

, then it is assumed that
`stat0`

is a matrix, where `stat0[i,]`

is used to calculate the
p-value for `stat[i]`

. The function `empPvals`

calculates
"pooled" p-values faster than using a for-loop.

See page 18 of the Supporting Information in Storey et al. (2005) PNAS (http://www.pnas.org/content/suppl/2005/08/26/0504609102.DC1/04609SuppAppendix.pdf) for an explanation as to why calculating p-values from pooled empirical null statistics and then estimating FDR on these p-values is equivalent to directly thresholding the test statistics themselves and utilizing an analogous FDR estimator.

### Value

A vector of p-values calculated as described above.

### Author(s)

John D. Storey

### References

Storey JD and Tibshirani R. (2003) Statistical significance for
genome-wide experiments. Proceedings of the National Academy of Sciences,
100: 9440-9445.

http://www.pnas.org/content/100/16/9440.full

Storey JD, Xiao W, Leek JT, Tompkins RG, Davis RW. (2005) Significance
analysis of time course microarray experiments. Proceedings of the
National Academy of Sciences, 102 (36), 12837-12842.

http://www.pnas.org/content/102/36/12837.full.pdf?with-ds=yes

### See Also

`qvalue`

### Examples

1 2 3 4 5 6 7 8 9 10 11 | ```
# import data
data(hedenfalk)
stat <- hedenfalk$stat
stat0 <- hedenfalk$stat0 #vector from null distribution
# calculate p-values
p.pooled <- empPvals(stat=stat, stat0=stat0)
p.testspecific <- empPvals(stat=stat, stat0=stat0, pool=FALSE)
# compare pooled to test-specific p-values
qqplot(p.pooled, p.testspecific); abline(0,1)
``` |