Benjamini-Hochberg (1995) false discovery rate correction

Thin wrapper around stats::p.adjust() with method = "BH" – base R already implements this correctly, so it is not reimplemented.

Usage

fdr_bh(p, q = 0.05)

Arguments

p: Numeric vector of raw p-values in [0, 1] (may contain NA).
q: Numeric. Target FDR level.

Value

A list with q_value (BH-adjusted p-values) and reject (logical).

Details

Function type: Support function – computes the BH procedure used internally by fdr_correction(). Not exported; call fdr_correction(p, method = "BH") for a BH-only result.

Typical use

Supply one family of raw p-values to fdr_correction() with method = "BH"; this internal helper returns the corresponding adjusted values and rejection decisions.

Methodological details

Methods and method selection

Original publication: Benjamini & Hochberg (1995), the paper that introduced false discovery rate control itself.
Main references: Benjamini & Hochberg (1995) for the procedure; Benjamini & Yekutieli (2001) for why it remains valid under the positive dependence typical of gridded spatial data. Full citations appear under "References" below.
Typical applications: correcting for multiple testing when many hypotheses are tested at once (e.g. one Mann-Kendall test per pixel in a raster) and a fixed, non-adaptive guarantee is preferred over fdr_bky()'s adaptive one – see workflow_rta() for a workflow that defaults to this method specifically for that reason.

Statistical assumptions and limitations

BH controls FDR under independence and recognised positive-dependence conditions such as PRDS. Spatial autocorrelation diagnostics can be compatible with those conditions but do not prove them. Use fdr_by() when control under arbitrary dependence is required.

Quality assurance

Adjusted values are generated directly by stats::p.adjust() and are also checked through the package's automated FDR tests.

References

Primary method reference:

Benjamini, Y., & Hochberg, Y. (1995). Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing. Journal of the Royal Statistical Society: Series B, 57, 289-300. doi:10.1111/j.2517-6161.1995.tb02031.x

Theoretical justification for why BH remains valid under the positive spatial dependence typical of gridded data (for which spatial_autocorrelation() or moran_check can provide a diagnostic):

Benjamini, Y., & Yekutieli, D. (2001). The control of the false discovery rate in multiple testing under dependency. Annals of Statistics, 29(4), 1165-1188. doi:10.1214/aos/1013699998

On why multiple testing must be addressed at all in gridded remote sensing data (general problem statement):

Gutiérrez-Hernández, O. and García, L.V. (2025, September 17) Multiple Testing in Remote Sensing: Addressing the Elephant in the Room. Available at SSRN: https://ssrn.com/abstract=4891512. doi:10.2139/ssrn.4891512

On FDR estimation and control specifically under the spatial dependence structure of gridded data (directly motivates this function):

Gutiérrez-Hernández, O., & García, L.V. (2025). False discovery rate estimation and control in remote sensing: reliable statistical significance in spatially dependent gridded data. Remote Sensing Letters, 16(5), 537-548. doi:10.1080/2150704X.2025.2478664

This function is used (not authored) by workflow_rta(), this package's own non-prewhitened workflow (workflow_tst() instead defaults to the adaptive fdr_bky()):

Gutiérrez-Hernández, O. and García, L.V. (2024) Robust Trend Analysis in Environmental Remote Sensing: A Case Study of Cork Oak Forest Decline. Remote Sensing, 16(20), 3886. doi:10.3390/rs16203886

Examples

# Five p-values, ranked from most to least significant. Called
# internally by fdr_correction() -- the public entry point is:
# fdr_correction(c(0.001, 0.01, 0.02, 0.5, 0.8), method = "BH")