# normDiffCI: Confidence Intervals for Difference of Means In MKmisc: Miscellaneous Functions from M. Kohl

## Description

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

## Usage

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

## 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.

## 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).

## 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.

## Author(s)

Matthias Kohl Matthias.Kohl@stamats.de

## 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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34``` ```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") ## 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 ```

MKmisc documentation built on Aug. 8, 2021, 5:06 p.m.