wBoot (version 1.0.3)

boot.paired.bca: BCa Bootstrap Paired-Samples Test and CI for Two Means

Description

Obtains a paired-samples confidence interval and (optionally) performs a paired-samples hypothesis test for the difference between two population means, using the BCa bootstrap method.

Usage

boot.paired.bca(x, y, variable = NULL, 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.

y

a (non-empty) numeric vector of data values.

variable

an optional character string that gives the name of the variable 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.paired" containing the following components:
• Boot.values
  the point estimates for the differences between the means 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 or NULL
• Pop.1
  the first population.
• Pop.2
  the second population.
• n
  the sample size.
• Statistic
  the name of the statistic, here diff.mean.
• Observed
  the observed point estimate for the difference between the means.
• 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
• Paired-sample inferences
• Confidence interval
• Hypothesis test
• Inferences for two means

Details

Note that x and y must have the same length, as together they represent the paired data. Also note, for instance, that alternative = "greater" is the alternative that x variable has a larger mean than y variable.

Examples

# The number of inappropriate words out of 10 that were identified in the
# Times New Roman (TNR) and Gigi fonts by each of 25 participants.
data("fonts")
str(fonts)
attach(fonts)

# 90% confidence interval for the difference between the mean number of
# inappropriate words out of 10 identified for the TNR and Gigi fonts.
boot.paired.bca(TNR, GIGI, conf.level = 0.90)

# A right-tailed test with null hypothesis 2, and a 95% (default) lower
# confidence bound for the difference between the mean number of
# inappropriate words out of 10 identified for the TNR and Gigi fonts. 
boot.paired.bca(TNR, GIGI, null.hyp = 2, alternative = "greater")
# Not significant at the 5% level.

# A right-tailed test with null hypothesis 1, and a 95% (default) lower
# confidence bound for the difference between the mean number of
# inappropriate words out of 10 identifiedd for the TNR and Gigi fonts.
boot.paired.bca(TNR, GIGI, null.hyp = 1, alternative = "greater")
# Significant at the 5% level.

detach(fonts)   # clean up