wBoot (version 1.0.3)

boot.cor.per: Percentile Bootstrap Correlation Test and CI

Description

Obtains a confidence interval and (optionally) performs a hypothesis test for the Pearson correlation, using the percentile bootstrap method.

Usage

boot.cor.per(x, y, 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.

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.regcor" containing the following components:
• Boot.values
  the point estimates (correlations) obtained from the bootstrap.
• Confidence.limits
  the confidence limit(s) for the confidence interval.
• Header
  the main title for the output.
• Variable.1
  the first variable.
• Variable.2
  the second variable.
• n
  the sample size.
• Statistic
  the name of the statistic, here correlation.
• Observed
  the observed point estimate (correlation).
• 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.
• cor.ana
  a logical; always TRUE for this function.

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
• Simple linear regression
• Confidence interval
• Hypothesis test
• Pearson correlation

Examples

# NOTE: See the preceding warning!

# Lot size, house size, and value for a sample of homes in a particular area.
data("homes")
str(homes)
attach(homes)

# 95% (default) confidence interval for the correlation between lot size and value.
boot.cor.per(LOT.SIZE, VALUE)

# 95% (default) lower confidence bound for the correlation between house size
# and value, and a right-tailed test with null hypothesis 0.5.
boot.cor.per(HOUSE.SIZE, VALUE, null.hyp = 0.5, alternative = "greater")

# 90% two-sided confidence interval for the correlation between house size and value,
# a right-tailed test with null hypothesis 0.5, and 999 bootstrap replications.
boot.cor.per(HOUSE.SIZE, VALUE, null.hyp = 0.5, alternative = "greater",
conf.level = 0.90, type = "two-sided", R = 999)

detach(homes) # clean up