Exact Binomial Test

Performs exact binomial test and pairwise comparisons following a significant exact multinomial test. Wrapper around the R base function link[stats]{binom.test}() that returns a data frame as a result.

binom_test(
  x,
  n,
  p = 0.5,
  alternative = "two.sided",
  conf.level = 0.95,
  detailed = FALSE
)

pairwise_binom_test(
  x,
  p.adjust.method = "holm",
  alternative = "two.sided",
  conf.level = 0.95
)

pairwise_binom_test_against_p(
  x,
  p = rep(1/length(x), length(x)),
  p.adjust.method = "holm",
  alternative = "two.sided",
  conf.level = 0.95
)

Arguments

x: numeric vector containing the counts.
n: number of trials; ignored if x has length 2.
p: a vector of probabilities of success. The length of p must be the same as the number of groups specified by x, and its elements must be greater than 0 and less than 1.
alternative: indicates the alternative hypothesis and must be one of "two.sided", "greater" or "less". You can specify just the initial letter.
conf.level: confidence level for the returned confidence interval.
detailed: logical value. Default is FALSE. If TRUE, a detailed result is shown.
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 containing the p-value and its significance. with some the following columns:

group, group1, group2: the categories or groups being compared.
statistic: the number of successes.
parameter: the number of trials.
p: p-value of the test.
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: the estimated probability of success.
alternative: a character string describing the alternative hypothesis.
conf.low,conf.high: Lower and upper bound on a confidence interval for the probability of success.

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

Functions

binom_test(): performs exact binomial test. Wrapper around the R base function binom.test that returns a dataframe as a result.
pairwise_binom_test(): performs pairwise comparisons (binomial test) following a significant exact multinomial test.
pairwise_binom_test_against_p(): performs pairwise comparisons (binomial test) following a significant exact multinomial test for given probabilities.

Examples

# Exact binomial test
#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# Data: 160 mice with cancer including 95 male and 65 female
# Q1: Does cancer affect more males than females?
binom_test(x = 95, n = 160)
#> # A tibble: 1 × 6
#>       n estimate conf.low conf.high      p p.signif
#> * <dbl>    <dbl>    <dbl>     <dbl>  <dbl> <chr>   
#> 1   160    0.594    0.513     0.671 0.0216 *       
# => yes, there are a significant difference


# Q2: compare the observed proportion of males
# to an expected proportion (p = 3/5)
binom_test(x = 95, n = 160, p = 3/5)
#> # A tibble: 1 × 6
#>       n estimate conf.low conf.high     p p.signif
#> * <dbl>    <dbl>    <dbl>     <dbl> <dbl> <chr>   
#> 1   160    0.594    0.513     0.671 0.872 ns      
# => there are no significant difference

# Multinomial test
#%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
# Data
tulip <- c(red = 81, yellow = 50, white = 27)
# Question 1: are the color equally common ?
# this is a test of homogeneity
res <- multinom_test(tulip)
res
#> # A tibble: 1 × 2
#>             p p.signif
#> *       <dbl> <chr>   
#> 1 0.000000711 ****    
attr(res, "descriptives")
#> # A tibble: 3 × 3
#>   group  observed expected
#>   <chr>     <dbl>    <dbl>
#> 1 red          81     52.7
#> 2 yellow       50     52.7
#> 3 white        27     52.7

# Pairwise comparisons between groups
pairwise_binom_test(tulip, p.adjust.method = "bonferroni")
#> # A tibble: 3 × 9
#>   group1 group2     n estimate conf.low conf.high           p      p.adj p.adj…¹
#> * <chr>  <chr>  <dbl>    <dbl>    <dbl>     <dbl>       <dbl>      <dbl> <chr>  
#> 1 red    yellow   131    0.618    0.529     0.702 0.00851        2.55e-2 *      
#> 2 red    white    108    0.75     0.657     0.828 0.000000191    5.72e-7 ****   
#> 3 yellow white     77    0.649    0.532     0.755 0.0117         3.5 e-2 *      
#> # … with abbreviated variable name ¹p.adj.signif


# Question 2: comparing observed to expected proportions
# this is a goodness-of-fit test
expected.p <- c(red = 0.5, yellow = 0.33, white = 0.17)
res <- multinom_test(tulip, expected.p)
res
#> # A tibble: 1 × 2
#>       p p.signif
#> * <dbl> <chr>   
#> 1 0.942 ns      
attr(res, "descriptives")
#> # A tibble: 3 × 3
#>   group  observed expected
#>   <chr>     <dbl>    <dbl>
#> 1 red          81     79  
#> 2 yellow       50     52.1
#> 3 white        27     26.9

# Pairwise comparisons against a given probabilities
pairwise_binom_test_against_p(tulip, expected.p)
#> # A tibble: 3 × 10
#>   group  observed expected     n estimate conf.low conf.high     p p.adj p.adj…¹
#> * <chr>     <dbl>    <dbl> <dbl>    <dbl>    <dbl>     <dbl> <dbl> <dbl> <chr>  
#> 1 red          81     79     158    0.513    0.432     0.593 0.811     1 ns     
#> 2 yellow       50     52.1   158    0.316    0.245     0.395 0.800     1 ns     
#> 3 white        27     26.9   158    0.171    0.116     0.239 1         1 ns     
#> # … with abbreviated variable name ¹p.adj.signif

Arguments

Value

Functions

See also

Examples