pairwiseCImethodsCont function

Confidence intervals for two sample comparisons of continuous data

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

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);

Returns

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)