wBoot (version 1.0.3)

boot.one.per: Percentile 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 percentile bootstrap method.

Usage

boot.one.per(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.

Warning

This routine should be used only when bias is small and the sampling distribution is roughly symmetric, as indicated by the output of the bootstrap. Otherwise, use the BCa version.

concept

• Bootstrap
• Percentile 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.per(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.per(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.per(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.per(loss, sd)
# See the preceeding warning!

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