wBoot (version 1.0.3)

boot.one.bca: BCa Bootstrap One-Sample Test and CI

Description

Obtains a confidence interval and (optionally) performs a hypothesis test for one population mean, median, proportion, standard deviation, or user-defined function such as a trimmed mean, using the BCa bootstrap method.

Usage

boot.one.bca(x, parameter, null.hyp = NULL,
             alternative = c("two.sided", "less", "greater"),
             conf.level = 0.95, type = NULL, R = 9999)

Arguments

x

a (non-empty) numeric vector of data values.

parameter

the parameter under consideration.

null.hyp

the null-hypothesis value; if omitted, no hypothesis test is performed.

alternative

a character string specifying the alternative hypothesis; must be one of "two.sided" (default), "greater", or "less".

conf.level

the confidence level (between 0 and 1); default is 0.95.

type

a character string specifying the type of CI; if user-supplied, must be one of "two-sided", "upper-bound", or "lower-bound"; defaults to "two-sided" if alternative is "two.sided", "upper-bound" if alternative is "less", and "lower-bound" if alternative

R

the number of bootstrap replications; default is 9999.

Value

• A list with class "boot.one" containing the following components:
• Boot.values
  the point estimates for the parameter obtained from the bootstrap.
• Confidence.limits
  the confidence limit(s) for the confidence interval.
• Header
  the main title for the output.
• Variable
  the name of the variable under consideration.
• n
  the sample size.
• Statistic
  the name of the statistic.
• Observed
  the observed point estimate for the parameter.
• Replications
  the number of bootstrap replications.
• Mean
  the mean of the bootstrap values.
• SE
  the standard deviation of the bootstrap values.
• Bias
  the difference between the mean of the bootstrap values and the observed value.
• Percent.bias
  the percentage bias: 100*|Bias/Observed|.
• Null
  the null-hypothesis value or NULL.
• Alternative
  the alternative hypothesis or NULL.
• P.value
  the P-value or a statement like P < 0.001 or NULL.
• p.value
  the P-value or NULL.
• Level
  the confidence level.
• Type
  the type of confidence interval.
• Confidence.interval
  the confidence interval.

concept

• Bootstrap
• BCa bootstrap
• One-sample inferences
• Confidence interval
• Hypothesis test
• Inferences for one mean
• Inferences for one standard deviation
• Inferences for one proportion

Details

For a proportion, the data must consist of 1s and 0s, with 1 corresponding to a success.

Examples

# Losses ($) for a sample of 25 pickpocket offenses.
data("loss")
str(loss)

# 95% (default) confidence interval for the mean loss of all pickpocket offenses.
boot.one.bca(loss, mean)

# 95% (default) lower confidence bound for the mean loss of all pickpocket
# offenses, and a right-tailed test with null hypothesis 500.
boot.one.bca(loss, mean, null.hyp = 500, alternative = "greater")

# 90% two-sided confidence interval for the mean loss of all pickpocket
# offenses, and a right-tailed test with null hypothesis 500.
boot.one.bca(loss, mean, null.hyp = 500, alternative = "greater", conf.level = 0.90,
type = "two-sided")

# 95% (default) confidence interval for the standard deviation of losses of all
# pickpocket offenses.
boot.one.bca(loss, sd)

# 95% (default) confidence interval for the 20% trimmed mean.
twen.tm <- function(x) mean(x, trim = 0.20)
boot.one.bca(loss, twen.tm)