test_binomial: Power and Sample Size Analysis for a Binomial Test

In nutterb/StudyPlanning: Evaluating Sample Size, Power, and Assumptions in Study Planning

Description

Determines the sample size, power, null proportion, alternative proportion, or significance level for a binomial test. The results also return the actual power and significance.

Usage

test_binomial(n = NULL, p0 = NULL, p1 = NULL, power = NULL,
  alpha = 0.05, alternative = "two.tailed", conservative = FALSE,
  n_limits = c(2L, 200L))

Arguments

n	The sample size, or number of trials
p0	The value of the probability of a success under the null hypothesis
p1	The value of the probability of a success under the alternative hypothesis
power	The power of the test
alpha	Significance level for the test
alternative	A character vector giving the alternative to the test. Multiple values may be given, but the values must be "two.tailed", "left.tailed", or "right.tailed".
conservative	A logical vector. This determines if the sample size selected is conservative (larger). This decision is required because the power as a function of sample size is non-montonic in the binomial distribution. In practice, it is usually better to look at both and select the sample size where alpha_actual is closest to alpha.
n_limits	The limits of the search for when n=NULL. The sample size is determined in a manner similar to uniroot, but uniroot doesn't handle discrete values.

Details

Exactly one of the parameters n, p0, p1, alpha, and power must be passed as NULL. The only exception is that delta may be passed as a second NULL when mu0 and mu1 are specified.

The parameters are combined via expand.grid, so all combinations of the inputs are evaluated.

Author(s)

Benjamin Nutter

References

O'Brien R, Castelloe J, "Sample-Size Analysis in Study Planning," American Statistical Association Continuing Education Program: Section on Teaching Statistics in the Health Sciences, Joint Statistical Meetings, San Francisco, CA; 5 August 2003 (Short Course Manual)

Some design choices were obtained from the r-help question at: http://r.789695.n4.nabble.com/Sample-size-calculations-for-one-sided-binomial-exact-test-td3964313.html

Examples

#* Julia Chill's Frozen Sensations Example from O'Brien and Castelloe
test_binomial(n=c(20, 40), p0=.5, p1=.8, alpha=c(.01, .05),
              alternative='right.tailed')

#* Plot the sample size for a range of n
library(ggplot2)
Chill <- test_binomial(n=20:40, p0=.5, p1=.8, alpha=c(.01, .05),
              alternative='right.tailed')

ggplot(Chill, aes(x=n, y=power, colour=factor(alpha))) + geom_line()

nutterb/StudyPlanning documentation built on May 24, 2019, 10:51 a.m.