fisher.pvalues.support {DiscreteFDR} R Documentation

## Computing discrete p-values and their support for binomial and Fisher's exact tests

### Description

Computes discrete raw p-values and their support for binomial test or Fisher's exact test applied to 2 x 2 contingency tables summarizing counts coming from two categorical measurements.

### Usage

fisher.pvalues.support(counts, alternative = "greater", input = "noassoc")

### Arguments

 counts a data frame of 2 or 4 columns and any number of lines, each line representing a 2 x 2 contingency table to test. The number of columns and what they must contain depend on the value of the input argument, see Details. alternative same argument as in fisher.test. The three possible values are "greater" (default), "two.sided" or "less" and you can specify just the initial letter. input the format of the input data frame, see Details. The three possible values are "noassoc" (default), "marginal" or "HG2011" and you can specify just the initial letter.

### Details

Assume that each contingency tables compares 2 variables and resumes the counts of association or not with a condition. This can be resumed in the following table:

 Association No association Total Variable 1 X1 Y1 N1 Variable 2 X2 Y2 N2 Total X1 + X2 Y1 + Y2 N1 + N2

If input="noassoc", counts has 4 columns which respectively contain X1, Y1, X2 and Y2. If input="marginal", counts has 4 columns which respectively contain X1, N1, X2 and N2.

If input="HG2011", we are in the situation of the amnesia data set as in Heller & Gur (2011, see References). Each contingency table is obtained from one variable which is compared to all other variables of the study. That is, counts for "second variable" are replaced by the sum of the counts of the other variables:

 Association No association Total Variable j Xj Yj Nj Variables !=j SUM(Xi) - Xj SUM(Yi) - Yj SUM(Ni) - Nj Total SUM(Xi) SUM(Yi) SUM(Ni)

Hence counts needs to have only 2 columns which respectively contain Xj and Yj.

binomial.pvalues.support and fisher.pvalues.support are wrapper functions for pvalues.support, setting test.type = "binomial" and test.type = "fisher", respectively.

The code for the computation of the p-values of Fisher's exact test is inspired by the example in the help page of p.discrete.adjust.

See the Wikipedia article about Fisher's exact test, paragraph Example, for a good depiction of what the code does for each possible value of alternative.

The binomial test simply tests for p = 0.5 by using X1 as the test statistic and N1 as the number of trials.

This version: 2021-05-23.

### Value

A list of two elements:

 raw raw discrete p-values. support a list of the supports of the CDFs of the p-values. Each support is represented by a vector in increasing order.

### References

R. Heller and H. Gur (2011). False discovery rate controlling procedures for discrete tests. arXiv preprint arXiv:1112.4627v2 link.

"Fisher's exact test", Wikipedia, The Free Encyclopedia, accessed 2018-03-20, link.

### Examples

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 support
df.formatted <- fisher.pvalues.support(counts = df, input = "noassoc")
raw.pvalues <- df.formatted$raw pCDFlist <- df.formatted$support

data(amnesia)
#We only keep the first 100 lines to keep the computations fast.
#We also drop the first column to keep only columns of counts, in the Heller & Gur (2011) setting.
amnesia <- amnesia[1:100,2:3]

#Construction of the p-values and their support
amnesia.formatted <- fisher.pvalues.support(counts = amnesia, input = "HG2011")
raw.pvalues <- amnesia.formatted$raw pCDFlist <- amnesia.formatted$support

[Package DiscreteFDR version 1.3.6 Index]