MKmisc (version 1.9)

normDiffCI: Confidence Intervals for Difference of Means

Description

This function can be used to compute confidence intervals for difference of means assuming normal distributions.

Usage

normDiffCI(x, y, conf.level = 0.95, paired = FALSE, method = "welch", na.rm = TRUE)

Value

A list with class "confint" containing the following components:

estimate

point estimate (mean of differences or difference in means).

conf.int

confidence interval.

Infos

additional information.

Arguments

x

numeric vector of data values of group 1.

y

numeric vector of data values of group 2.

conf.level

confidence level.

paired

a logical value indicating whether the two groups are paired.

method

a character string specifing which method to use in the unpaired case; see details.

na.rm

a logical value indicating whether NA values should be stripped before the computation proceeds.

Author

Matthias Kohl

Details

The standard confidence intervals for the difference of means are computed that can be found in many textbooks, e.g. Chapter 4 in Altman et al. (2000).

The method "classical" assumes equal variances whereas methods "welch" and "hsu" allow for unequal variances. The latter two methods use different formulas for computing the degrees of freedom of the respective t-distribution providing the quantiles in the confidence interval. Instead of the Welch-Satterhwaite equation the method of Hsu uses the minimum of the group sample sizes minus 1; see Section 6.8.3 of Hedderich and Sachs (2016).

References

D. Altman, D. Machin, T. Bryant, M. Gardner (eds). Statistics with Confidence: Confidence Intervals and Statistical Guidelines, 2nd edition. John Wiley and Sons 2000.

J. Hedderich, L. Sachs. Angewandte Statistik: Methodensammlung mit R. Springer 2016.

Examples

x <- rnorm(20)
y <- rnorm(20, sd = 2)
## paired
normDiffCI(x, y, paired = TRUE)
## compare
normCI(x-y)

## unpaired
y <- rnorm(10, mean = 1, sd = 2)
## classical
normDiffCI(x, y, method = "classical")
## Welch (default is in case of function t.test)
normDiffCI(x, y, method = "welch")
## Hsu
normDiffCI(x, y, method = "hsu")

# \donttest{
## Monte-Carlo simulation: coverage probability
M <- 10000
CIhsu <- CIwelch <- CIclass <- matrix(NA, nrow = M, ncol = 2)
for(i in 1:M){
  x <- rnorm(10)
  y <- rnorm(30, sd = 0.1)
  CIclass[i,] <- normDiffCI(x, y, method = "classical")$conf.int
  CIwelch[i,] <- normDiffCI(x, y, method = "welch")$conf.int
  CIhsu[i,] <- normDiffCI(x, y, method = "hsu")$conf.int
}
## coverage probabilies
## classical
sum(CIclass[,1] < 0 & 0 < CIclass[,2])/M
## Welch
sum(CIwelch[,1] < 0 & 0 < CIwelch[,2])/M
## Hsu
sum(CIhsu[,1] < 0 & 0 < CIhsu[,2])/M
# }