# continuous.GR: Continuous Guo-Romano procedure In FDX: False Discovery Exceedance Controlling Multiple Testing Procedures

## Description

Apply the usual continuous [GR] procedure, with or without computing the critical values, to a set of p-values. A non-adaptive version is available as well.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```continuous.GR( raw.pvalues, alpha = 0.05, zeta = 0.5, adaptive = TRUE, critical.values = FALSE ) GR(raw.pvalues, alpha = 0.05, zeta = 0.5, critical.values = FALSE) NGR(raw.pvalues, alpha = 0.05, zeta = 0.5, critical.values = FALSE) ```

## Arguments

 `raw.pvalues` vector of the raw observed p-values, as provided by the end user and before matching with their nearest neighbor in the CDFs supports. `alpha` the target FDP, a number strictly between 0 and 1. For `*.fast` kernels, it is only necessary, if `stepUp = TRUE`. `zeta` the target probability of not exceeding the desired FDP, a number strictly between 0 and 1. If `zeta=NULL` (the default), then `zeta` is chosen equal to `alpha`. `adaptive` a boolean specifying whether to conduct an adaptive procedure or not. `critical.values` a boolean. If `TRUE`, critical constants are computed and returned (this is computationally intensive).

## Details

`GR` and `NGR` are wrapper functions for `continuous.GR`. The first one simply passes all its parameters to `continuous.GR` with `adaptive = TRUE` and `NGR` does the same with `adaptive = FALSE`.

## Value

A `FDX` S3 class object whose elements are:

 `Rejected` Rejected raw p-values. `Indices` Indices of rejected hypotheses. `Num.rejected` Number of rejections. `Adjusted` Adjusted p-values (only for step-down direction). `Critical.values` Critical values (if requested). `Method` A character string describing the used algorithm, e.g. 'Discrete Lehmann-Romano procedure (step-up)'. `FDP.threshold` FDP threshold `alpha`. `Exceedance.probability` Probability `zeta` of FDP exceeding `alpha`; thus, FDP is being controlled at level `alpha` with confidence `1 - zeta`. `Adaptive` A boolean specifying whether an adaptive procedure was conducted or not. `Data\$raw.pvalues` The values of `raw.pvalues`. `Data\$data.name` The respective variable names of `raw.pvalues` and `pCDFlist`.

`kernel`, `FDX-package`, `continuous.LR`, `discrete.LR`, `discrete.GR`, `discrete.PB`, `weighted.LR`, `weighted.GR`, `weighted.PB`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26``` ```X1 <- c(4, 2, 2, 14, 6, 9, 4, 0, 1) X2 <- c(0, 0, 1, 3, 2, 1, 2, 2, 2) N1 <- rep(148, 9) N2 <- rep(132, 9) Y1 <- N1 - X1 Y2 <- N2 - X2 df <- data.frame(X1, Y1, X2, Y2) df # Construction of the p-values and their supports (fisher.pvalues.support # is from 'DiscreteFDR' package!) df.formatted <- fisher.pvalues.support(counts = df, input = "noassoc") raw.pvalues <- df.formatted\$raw pCDFlist <- df.formatted\$support GR.fast <- GR(raw.pvalues) summary(GR.fast) GR.crit <- GR(raw.pvalues, critical.values = TRUE) summary(GR.crit) NGR.fast <- NGR(raw.pvalues) summary(NGR.fast) NGR.crit <- NGR(raw.pvalues, critical.values = TRUE) summary(NGR.crit) ```