wBoot (version 1.0.3)

boot.ratio.sd.bca: BCa Bootstrap Independent-Samples Test and CI for Two Standard Deviations

Description

Obtains an independent-samples confidence interval and (optionally) performs an independent-samples hypothesis test for the ratio of two population standard deviations, using the BCa bootstrap method.

Usage

boot.ratio.sd.bca(x, y, 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).

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 ratio of the standard deviations obtained from the bootstrap.
• Confidence.limits
  the confidence limit(s) for the confidence interval.
• Parameter
  the parameter under consideration, here standard deviation.
• 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, here ratio.sd.
• Observed.1
  the observed point estimate for the standard deviation of the first population.
• Observed.2
  the observed point estimate for the standard deviation of the second population.
• Observed
  the observed point estimate for the ratio of the two standard deviations.
• 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 standard deviations

Examples

# Elmendorf tear strengths, in grams, for independent samples of
# Brand A and Brand B vinyl floor coverings.
data("elmendorf")
str(elmendorf)
attach(elmendorf)
# Note that the data are stacked.

# 90% confidence interval for the ratio of the population standard
# deviations of tear strength for Brands A and B.
boot.ratio.sd.bca(STRENGTH, BRAND, conf.level = 0.90)

# 95% (default) confidence interval for the ratio of the population
# standard deviations of tear strength for Brands A and B, and a
# two-tailed hypothesis test with null hypothesis 1 (i.e., the
# population standard deviations are equal).
boot.ratio.sd.bca(STRENGTH, BRAND, null.hyp = 1)

detach(elmendorf)  # clean up