pairwiseCImethodsCont {pairwiseCI}

Confidence intervals for two sample comparisons of continuous data

Description

Confidence interval methods available for pairwiseCI for comparison of two independent samples. Methods for continuous variables.

Usage

Param.diff(x, y, conf.level=0.95, alternative="two.sided", ...)
Param.ratio(x, y, conf.level=0.95, alternative="two.sided", ...)

Lognorm.diff(x, y, conf.level=0.95, alternative="two.sided", sim=10000, ...)
Lognorm.ratio(x, y, conf.level=0.95, alternative="two.sided", sim=10000, ...)

HL.diff(x, y, conf.level=0.95, alternative="two.sided", ...)
HL.ratio(x, y, conf.level=0.95, alternative="two.sided", ...)

Median.diff(x, y, conf.level=0.95, alternative="two.sided", ...)
Median.ratio(x, y, conf.level=0.95, alternative="two.sided", ...)

Arguments

x

vector of observations in the first sample

y

vector of observations in the second sample

alternative

character string, either "two.sided", "less" or "greater"

conf.level

the comparisonwise confidence level of the intervals, where 0.95 is default

sim

a single integer value, specifying the number of samples to be drawn for calculation of the empirical distribution of the generalized pivotal quantities

...

further arguments to be passed to the individual methods, see details

Details

• Param.diff calculates the confidence interval for the difference in means of two Gaussian samples by calling t.test in package stats, assuming homogeneous variances if var.equal=TRUE, and heterogeneous variances if var.equal=FALSE (default);

• Param.ratio calculates the Fiellers (1954) confidence interval for the ratio of two Gaussian samples by calling ttestratio in package mratios, assuming homogeneous variances if var.equal=TRUE. If heterogeneous variances are assumed (setting var.equal=FALSE, the default), the test by Tamhane and Logan (2004) is inverted by solving a quadratic equation according to Fieller, where the estimated ratio is simply plugged in order to get Satterthwaite approximated degrees of freedom. See Hasler and Vonk (2006) for some simulation results.

• Lognorm.diff calculates the confidence interval for the difference in means of two Lognormal samples, based on general pivotal quantities (Chen and Zhou, 2006); currently, further arguments (\dots) are not used;

• Lognorm.ratio calculates the confidence interval for the ratio in means of two Lognormal samples, based on general pivotal quantities (Chen and Zhou, 2006); currently, further arguments (\dots) are not used;

• HL.diff calculates the Hodges-Lehmann confidence interval for the difference of locations by calling wilcox_test in package coin, further arguments ... are passed to wilcox_test and corresponding methods for Independence problems, for example distribution may be used to switch from exact (default), to approximate or asymptotic versions;

• HL.ratio calculates a Hodges-Lehmann-like confidence interval for the ratio of locations for positive data by calling wilcox_test in package coin on the logarithms of observations and backtransforming (Hothorn and Munzel, 2002), further arguments ... are passed to wilcox_test and corresponding methods for Independence problems, for example distribution may be used to switch from exact (default), to approximate or asymptotic versions;

• Median.diff calculates a percentile bootstrap confidence interval for the difference of Medians using boot.ci in package boot, the number of bootstrap replications can be set via R=999 (default);

• Median.ratio calculates a percentile bootstrap confidence interval for the ratio of Medians using boot.ci in package boot, the number of bootstrap replications can be set via R=999 (default);

Value

A list containing:

conf.int

a vector containing the lower and upper confidence limit

estimate

a single named value

References

• Param.diff uses t.test in stats.

• Fieller EC (1954): Some problems in interval estimation. Journal of the Royal Statistical Society, Series B, 16, 175-185.

• Tamhane, AC, Logan, BR (2004): Finding the maximum safe dose level for heteroscedastic data. Journal of Biopharmaceutical Statistics 14, 843-856.

• Hasler, M, Vonk, R, Hothorn, LA: Assessing non-inferiority of a new treatment in a three arm trial in the presence of heteroscedasticity (submitted).

• Chen, Y-H, Zhou, X-H (2006): Interval estimates for the ratio and the difference of two lognormal means. Statistics in Medicine 25, 4099-4113.

• Hothorn, T, Munzel, U: Exact Nonparametric Confidence Interval for the Ratio of Medians. Technical Report, Universitaet Erlangen-Nuernberg, Institut fuer Medizininformatik, Biometrie und Epidemiologie, 2002; available via: http://www.statistik.uni-muenchen.de/~hothorn/bib/TH_TR_bib.html.

Examples

data(sodium)

iso<-subset(sodium, Treatment=="xisogenic")$Sodiumcontent
trans<-subset(sodium, Treatment=="transgenic")$Sodiumcontent

iso
trans

## CI for the difference of means, 
# assuming normal errors and homogeneous variances :

thomo<-Param.diff(x=iso, y=trans, var.equal=TRUE)

# allowing heterogeneous variances
thetero<-Param.diff(x=iso, y=trans, var.equal=FALSE)


## Fieller CIs for the ratio of means,
# also assuming normal errors:

Fielhomo<-Param.ratio(x=iso, y=trans, var.equal=TRUE)

# allowing heterogeneous variances

Fielhetero<-Param.ratio(x=iso, y=trans, var.equal=FALSE)


HLD<-HL.diff(x=iso, y=trans)

thomo
thetero

Fielhomo
Fielhetero

HLD


# # #

# Lognormal CIs:

x<-rlnorm(n=10, meanlog=0, sdlog=1)
y<-rlnorm(n=10, meanlog=0, sdlog=1)

Lognorm.diff(x=x, y=y)
Lognorm.ratio(x=x, y=y)