MKmisc (version 1.9)

mi.t.test: Multiple Imputation Student's t-Test

Description

Performs one and two sample t-tests on multiple imputed datasets.

Usage

mi.t.test(miData, ...)
# S3 method for default
mi.t.test(miData, x, y = NULL,
        alternative = c("two.sided", "less", "greater"), mu = 0,
        paired = FALSE, var.equal = FALSE, conf.level = 0.95,
        subset = NULL, ...)

Value

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

statistic

the value of the t-statistic.

parameter

the degrees of freedom for the t-statistic.

p.value

the p-value for the test.

conf.int

a confidence interval for the mean appropriate to the specified alternative hypothesis.

estimate

the estimated mean (one-sample test), difference in means (paired test), or estimated means (two-sample test) as well as the respective standard deviations.

null.value

the specified hypothesized value of the mean or mean difference depending on whether it was a one-sample test or a two-sample test.

alternative

a character string describing the alternative hypothesis.

method

a character string indicating what type of t-test was performed.

data.name

a character string giving the name(s) of the data.

Arguments

miData

list of multiple imputed datasets.

x

name of a variable that shall be tested.

y

an optional name of a variable that shall be tested (paired test) or a variable that shall be used to split into groups (unpaired test).

alternative

a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less". You can specify just the initial letter.

mu

a number indicating the true value of the mean (or difference in means if you are performing a two sample test).

paired

a logical indicating whether you want a paired t-test.

var.equal

a logical variable indicating whether to treat the two variances as being equal. If TRUE then the pooled variance is used to estimate the variance otherwise the Welch (or Satterthwaite) approximation to the degrees of freedom is used.

conf.level

confidence level of the interval.

subset

an optional vector specifying a subset of observations to be used.

...

further arguments to be passed to or from methods.

Author

Matthias Kohl

Details

alternative = "greater" is the alternative that x has a larger mean than y.

If paired is TRUE then both x and y must be specified and they must be the same length. Missing values are not allowed as they should have been imputed. If var.equal is TRUE then the pooled estimate of the variance is used. By default, if var.equal is FALSE then the variance is estimated separately for both groups and the Welch modification to the degrees of freedom is used.

We use the approach of Rubin (1987) in combination with the adjustment of Barnard and Rubin (1999).

References

Rubin, D. (1987). Multiple Imputation for Nonresponse in Surveys. John Wiley & Sons, New York.

Barnard, J. and Rubin, D. (1999). Small-Sample Degrees of Freedom with Multiple Imputation. Biometrika, 86(4), 948-955.

See Also

t.test

Examples

## Generate some data
set.seed(123)
x <- rnorm(25, mean = 1)
x[sample(1:25, 5)] <- NA
y <- rnorm(20, mean = -1)
y[sample(1:20, 4)] <- NA
pair <- c(rnorm(25, mean = 1), rnorm(20, mean = -1))
g <- factor(c(rep("yes", 25), rep("no", 20)))
D <- data.frame(ID = 1:45, variable = c(x, y), pair = pair, group = g)

## Use Amelia to impute missing values
library(Amelia)
res <- amelia(D, m = 10, p2s = 0, idvars = "ID", noms = "group")

## Per protocol analysis (Welch two-sample t-test)
t.test(variable ~ group, data = D)
## Intention to treat analysis (Multiple Imputation Welch two-sample t-test)
mi.t.test(res$imputations, x = "variable", y = "group")

## Per protocol analysis (Two-sample t-test)
t.test(variable ~ group, data = D, var.equal = TRUE)
## Intention to treat analysis (Multiple Imputation two-sample t-test)
mi.t.test(res$imputations, x = "variable", y = "group", var.equal = TRUE)

## Specifying alternatives
mi.t.test(res$imputations, x = "variable", y = "group", alternative = "less")
mi.t.test(res$imputations, x = "variable", y = "group", alternative = "greater")

## One sample test
t.test(D$variable[D$group == "yes"])
mi.t.test(res$imputations, x = "variable", subset = D$group == "yes")
mi.t.test(res$imputations, x = "variable", mu = -1, subset = D$group == "yes",
          alternative = "less")
mi.t.test(res$imputations, x = "variable", mu = -1, subset = D$group == "yes",
          alternative = "greater")

## paired test
t.test(D$variable, D$pair, paired = TRUE)
mi.t.test(res$imputations, x = "variable", y = "pair", paired = TRUE)