fisher_test {rstatix}

Fisher's Exact Test for Count Data

Description

Performs Fisher's exact test for testing the null of independence of rows and columns in a contingency table.

Wrappers around the R base function fisher.test() but have the advantage of performing pairwise and row-wise fisher tests, the post-hoc tests following a significant chi-square test of homogeneity for 2xc and rx2 contingency tables.

Usage

fisher_test(
  xtab,
  workspace = 2e+05,
  alternative = "two.sided",
  conf.int = TRUE,
  conf.level = 0.95,
  simulate.p.value = FALSE,
  B = 2000,
  detailed = FALSE,
  ...
)

pairwise_fisher_test(xtab, p.adjust.method = "holm", detailed = FALSE, ...)

row_wise_fisher_test(xtab, p.adjust.method = "holm", detailed = FALSE, ...)

Arguments

xtab

a contingency table in a matrix form.

workspace

an integer specifying the size of the workspace used in the network algorithm. In units of 4 bytes. Only used for non-simulated p-values larger than 2 \times 2 tables. Since R version 3.5.0, this also increases the internal stack size which allows larger problems to be solved, however sometimes needing hours. In such cases, simulate.p.values=TRUE may be more reasonable.

alternative

indicates the alternative hypothesis and must be one of "two.sided", "greater" or "less". You can specify just the initial letter. Only used in the 2 \times 2 case.

conf.int

logical indicating if a confidence interval for the odds ratio in a 2 \times 2 table should be computed (and returned).

conf.level

confidence level for the returned confidence interval. Only used in the 2 \times 2 case and if conf.int = TRUE.

simulate.p.value

a logical indicating whether to compute p-values by Monte Carlo simulation, in larger than 2 \times 2 tables.

B

an integer specifying the number of replicates used in the Monte Carlo test.

detailed

logical value. Default is FALSE. If TRUE, a detailed result is shown.

...

Other arguments passed to the function fisher_test().

p.adjust.method

method to adjust p values for multiple comparisons. Used when pairwise comparisons are performed. Allowed values include "holm", "hochberg", "hommel", "bonferroni", "BH", "BY", "fdr", "none". If you don't want to adjust the p value (not recommended), use p.adjust.method = "none".

Value

return a data frame with some the following columns:

• group: the categories in the row-wise proportion tests.

• p: p-value.

• p.adj: the adjusted p-value.

• method: the used statistical test.

• p.signif, p.adj.signif: the significance level of p-values and adjusted p-values, respectively.

• estimate: an estimate of the odds ratio. Only present in the 2 by 2 case.

• alternative: a character string describing the alternative hypothesis.

• conf.low,conf.high: a confidence interval for the odds ratio. Only present in the 2 by 2 case and if argument conf.int = TRUE.

The returned object has an attribute called args, which is a list holding the test arguments.

Functions

• fisher_test(): performs Fisher's exact test for testing the null of independence of rows and columns in a contingency table with fixed marginals. Wrapper around the function fisher.test().

• pairwise_fisher_test(): pairwise comparisons between proportions, a post-hoc tests following a significant Fisher's exact test of homogeneity for 2xc design.

• row_wise_fisher_test(): performs row-wise Fisher's exact test of count data, a post-hoc tests following a significant chi-square test of homogeneity for rx2 contingency table. The test is conducted for each category (row).

Examples

# Comparing two proportions
#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# Data: frequencies of smokers between two groups
xtab <- as.table(rbind(c(490, 10), c(400, 100)))
dimnames(xtab) <- list(
  group = c("grp1", "grp2"),
  smoker = c("yes", "no")
)
xtab
# compare the proportion of smokers
fisher_test(xtab, detailed = TRUE)

# Homogeneity of proportions between groups
#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# H0: the proportion of smokers is similar in the four groups
# Ha:  this proportion is different in at least one of the populations.
#
# Data preparation
grp.size <- c( 106, 113, 156, 102 )
smokers  <- c( 50, 100, 139, 80 )
no.smokers <- grp.size - smokers
xtab <- as.table(rbind(
  smokers,
  no.smokers
))
dimnames(xtab) <- list(
  Smokers = c("Yes", "No"),
  Groups = c("grp1", "grp2", "grp3", "grp4")
)
xtab

# Compare the proportions of smokers between groups
fisher_test(xtab, detailed = TRUE)

# Pairwise comparison between groups
pairwise_fisher_test(xtab)


# Pairwise proportion tests
#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# Data: Titanic
xtab <- as.table(rbind(
  c(122, 167, 528, 673),
  c(203, 118, 178, 212)
))
dimnames(xtab) <- list(
  Survived = c("No", "Yes"),
  Class = c("1st", "2nd", "3rd", "Crew")
)
xtab
# Compare the proportion of survived between groups
pairwise_fisher_test(xtab)

# Row-wise proportion tests
#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# Data: Titanic
xtab <- as.table(rbind(
  c(180, 145), c(179, 106),
  c(510, 196), c(862, 23)
))
dimnames(xtab) <- list(
  Class = c("1st", "2nd", "3rd", "Crew"),
  Gender = c("Male", "Female")
)
xtab
# Compare the proportion of males and females in each category
row_wise_fisher_test(xtab)

# A r x c table  Agresti (2002, p. 57) Job Satisfaction
Job <- matrix(c(1,2,1,0, 3,3,6,1, 10,10,14,9, 6,7,12,11), 4, 4,
              dimnames = list(income = c("< 15k", "15-25k", "25-40k", "> 40k"),
                             satisfaction = c("VeryD", "LittleD", "ModerateS", "VeryS")))
fisher_test(Job)
fisher_test(Job, simulate.p.value = TRUE, B = 1e5)