wBoot (version 1.0.3)

boot.two.bca: BCa Bootstrap Independent Two-Samples Test and CI

Description

Obtains an independent-samples confidence interval and (optionally) performs an independent-samples hypothesis test for the difference between two population means, medians, proportions, or some user-defined function, using the BCa bootstrap method.

Usage

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

Arguments

x

a numeric vector of observations of the variable (stacked case) or a numeric vector of data values representing the first of the two samples (unstacked case).

y

a vector of corresponding population identifiers (stacked case) or a numeric vector of data values representing the second of the two samples (unstacked case).

parameter

the parameter under consideration.

stacked

a logical value (default TRUE) indicating whether the data are stacked.

variable

an optional string that gives the name of the variable under consideration; ignored if stacked is TRUE.

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.two" containing the following components:
• Stacked
  a logical indicating whether the data are stacked (TRUE) or not (FALSE).
• Boot.values
  the point estimates for the difference between the parameter values obtained from the bootstrap.
• Confidence.limits
  the confidence limit(s) for the confidence interval.
• Parameter
  the parameter under consideration.
• Header
  the main title for the output.
• Variable
  the name of the variable under consideration or NULL.
• Pop.1
  the first population.
• Pop.2
  the second population.
• n.1
  the sample size for the first population.
• n.2
  the sample size for the second population.
• Statistic
  the name of the statistic.
• Observed.1
  the observed point estimate for the parameter value of the first population.
• Observed.2
  the observed point estimate for the parameter value of the second population.
• Observed
  the observed point estimate for the difference between the parameter values.
• 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
• Independent-samples inferences
• Confidence interval
• Hypothesis test
• Inferences for two means
• Inferences for two standard deviations
• Inferences for two proportions

Details

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

Examples

# Driving distances, in yards, for independent samples of drives off a
# 2-3/4" wooden tee and off a 3" Stinger Competition golf tee.
data("tees")
str(tees)
attach(tees)
# Note that the data are unstacked.

# 99% confidence interval for the difference between the mean driving
# distances of the two types of tees. Name variable DISTANCE.
boot.two.bca(REGULAR, STINGER, mean, stacked = FALSE, variable = "DISTANCE",
conf.level = 0.99)

# 95% (default) upper confidence bound for the difference between the mean
# driving distances of the two types of tees, a left-tailed test with null
# hypothesis -10 (i.e., the difference between the mean driving distances
# is -10 yards), and 99999 bootstrap replications. 
boot.two.bca(REGULAR, STINGER, mean, stacked = FALSE, null.hyp = -10,
alternative = "less", R = 99999)

# 95% (default) confidence interval for the difference between the standard
# deviations of the driving distances, and a two-tailed test with null
# hypothesis 0 (i.e., the standard deviations are equal). Name variable DISTANCE.
boot.two.bca(REGULAR, STINGER, sd, stacked = FALSE, variable = "DISTANCE", null.hyp = 0) 

detach(tees)  # clean up