BCa Bootstrap One-Sample Test and CI

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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

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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 is "greater".

R

the number of bootstrap replications; default is 9999.

Details

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

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.

Author(s)

Neil A. Weiss

Examples

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# 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)

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