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
)
```

- 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".

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.

`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.

```
# 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
```