Last updated: 2024-11-28
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Knit directory: muse/
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| File | Version | Author | Date | Message |
|---|---|---|---|---|
| Rmd | 989fe1c | Dave Tang | 2024-11-28 | Benjamini-Hochberg correction |
Testing \(m\) = 10 hypotheses, where:
The p-values are:
pvalues <- c(0.001,0.004,0.020,0.030,0.050,0.060,0.070,0.100,0.150,0.200)
pvalues [1] 0.001 0.004 0.020 0.030 0.050 0.060 0.070 0.100 0.150 0.200Apply the Benjamini-Hochberg (BH) procedure to control the FDR.
p.adjust(pvalues, method = 'BH') [1] 0.01000000 0.02000000 0.06666667 0.07500000 0.10000000 0.10000000
[7] 0.10000000 0.12500000 0.16666667 0.20000000Perform the calculations manually.
\[ p_i^{adjusted} = \min_{j > i} \left( \frac{m}{j} \cdot p_{(j)} \right) \]
where:
bh <- function(pvalues) {
# Number of hypotheses
m <- length(pvalues)
# Sort the p-values and keep track of the original indices
sorted_indices <- order(pvalues)
sorted_pvalues <- pvalues[sorted_indices]
# Compute the adjusted p-values
adjusted_pvalues <- numeric(m)
for (i in m:1) {
if (i == m) {
adjusted_pvalues[i] <- sorted_pvalues[i]
} else {
adjusted_pvalues[i] <- min(adjusted_pvalues[i + 1], m / i * sorted_pvalues[i])
}
}
# Return adjusted p-values in the original order
adjusted_pvalues[order(sorted_indices)]
}
all(bh(pvalues) == p.adjust(pvalues, method = "BH"))[1] TRUETest.
set.seed(1984)
p <- runif(n = 1000, min = 0, max = 1)
all(bh(p) == p.adjust(p, method = "BH"))[1] TRUE
sessionInfo()R version 4.4.1 (2024-06-14)
Platform: x86_64-pc-linux-gnu
Running under: Ubuntu 22.04.5 LTS
Matrix products: default
BLAS: /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3
LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.20.so; LAPACK version 3.10.0
locale:
[1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
[3] LC_TIME=en_US.UTF-8 LC_COLLATE=en_US.UTF-8
[5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
[7] LC_PAPER=en_US.UTF-8 LC_NAME=C
[9] LC_ADDRESS=C LC_TELEPHONE=C
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
time zone: Etc/UTC
tzcode source: system (glibc)
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] lubridate_1.9.3 forcats_1.0.0 stringr_1.5.1 dplyr_1.1.4
[5] purrr_1.0.2 readr_2.1.5 tidyr_1.3.1 tibble_3.2.1
[9] ggplot2_3.5.1 tidyverse_2.0.0 workflowr_1.7.1
loaded via a namespace (and not attached):
[1] sass_0.4.9 utf8_1.2.4 generics_0.1.3 stringi_1.8.4
[5] hms_1.1.3 digest_0.6.37 magrittr_2.0.3 timechange_0.3.0
[9] evaluate_1.0.1 grid_4.4.1 fastmap_1.2.0 rprojroot_2.0.4
[13] jsonlite_1.8.9 processx_3.8.4 whisker_0.4.1 ps_1.8.1
[17] promises_1.3.0 httr_1.4.7 fansi_1.0.6 scales_1.3.0
[21] jquerylib_0.1.4 cli_3.6.3 rlang_1.1.4 munsell_0.5.1
[25] withr_3.0.2 cachem_1.1.0 yaml_2.3.10 tools_4.4.1
[29] tzdb_0.4.0 colorspace_2.1-1 httpuv_1.6.15 vctrs_0.6.5
[33] R6_2.5.1 lifecycle_1.0.4 git2r_0.35.0 fs_1.6.4
[37] pkgconfig_2.0.3 callr_3.7.6 pillar_1.9.0 bslib_0.8.0
[41] later_1.3.2 gtable_0.3.6 glue_1.8.0 Rcpp_1.0.13
[45] xfun_0.48 tidyselect_1.2.1 rstudioapi_0.17.1 knitr_1.48
[49] htmltools_0.5.8.1 rmarkdown_2.28 compiler_4.4.1 getPass_0.2-4