BCa Bootstrap Independent-Samples Test and CI for Two Standard Deviations

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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

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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 is "greater".

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.

Author(s)

Neil A. Weiss

Examples

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# 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

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