proptest_num: Proportion Tests

In exams.forge: Support for Compiling Examination Tasks using the 'exams' Package

Proportion Tests

Description

Computes all results for test on proportion using either stats::binom.test(), or a normal approximation without continuity correction. Either named parameters can be given or an arglist with the following parameters:

• x number of successes

• n sample size (default: sd(x))

• pi0 true value of the proportion (default: 0.5)

• alternative a string specifying the alternative hypothesis (default: "two.sided"), otherwise "greater" or "less" can be used

• alpha significance level (default: 0.05)

• binom2norm can the binomial distribution be approximated by a normal distribution? (default: NA = use binom2norm function)

Usage

proptest_num(..., arglist = NULL)

prop_binomtest_num(..., arglist = NULL)

nbinomtest(..., arglist = NULL)

Arguments

...	named input parameters
arglist	list: named input parameters, if given ... will be ignored

Details

The results of proptest_num may differ from stats::binom.test(). proptest_num is designed to return results when you compute a binomial test by hand. For example, for computing the test statistic the approximation t_n \approx N(0; 1) is used if n>n.tapprox. The p.value is computed by stats::binom.test and may not be reliable, for Details see Note!

Value

A list with the input parameters and the following:

• X distribution of the random sampling function

• Statistic distribution of the test statistics

• statistic test value

• critical critical value(s)

• criticalx critical value(s) in x range

• acceptance0 acceptance interval for H0

• acceptance0x acceptance interval for H0 in x range

• accept1 is H1 accepted?

• p.value p value for test (note: the p-value may not be reliable see Notes!)

• alphaexact exact significance level

• stderr standard error of the proportion used as denominator

Note

The computation of a p-value for non-symmetric distribution is not well defined, see https://stats.stackexchange.com/questions/140107/p-value-in-a-two-tail-test-with-asymmetric-null-distribution.

Examples

n <- 100
x <- sum(runif(n)<0.4)
proptest_num(x=x, n=n)

exams.forge documentation built on Aug. 21, 2025, 5:41 p.m.