wBoot (version 1.0.3)

boot.ratio.sd.per: Percentile 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 percentile bootstrap method.

Usage

boot.ratio.sd.per(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.

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
• 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.per(STRENGTH, BRAND, conf.level = 0.90)
# See the preceeding warning!

# 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.per(STRENGTH, BRAND, null.hyp = 1)
# See the preceeding warning!

detach(elmendorf)  # clean up