meldtTest: Meld t Test

Description

Tests for a difference in parameters, when the parameter estimates are independent and both have t distributions.

Usage

meldtTest(x, y, alternative = c("two.sided", "less", "greater"), delta = 0, 
    conf.level = 0.95, control = bfControl(), ...)

Value

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

statistic: the value of the t-statistic.
parameter: R = atan(x$stderr/y$stderr) used in Behrens-Fisher distribution, see pbf
p.value: the p-value for the test.
conf.int: a confidence interval for the difference in means appropriate to the specified alternative hypothesis.
estimate: means and difference in means estimates
null.value: the specified hypothesized value of the difference in parameters
alternative: a character string describing the alternative hypothesis.
method: a character string describing the test.
data.name: a character string giving the name(s) of the data.

Arguments

x: a list from the first group with objects: estimate (estimate of parameter), stderr (standard error of the estimate), and df (degrees of freedom associated with t distribution)
y: a list from the second group with objects: estimate, stderr, and df
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.
delta: a number indicating the null hypothesis value of the difference in parameters when alternative="two.sided". See details for one-sided hypotheses
conf.level: confidence level of the interval.
control: a list of arguments used for determining the calculation algorithm, see bfControl
...: further arguments to be passed to or from methods (currently not used)

Warning

If the two estimates are not independent, this function may give invalid p-values and confidence intervals!

Author

Michael P. Fay

Details

Suppose x$estimate and y$estimate estimate the parameters xParm and yParm. Let Delta=yParm-xParm. This function tests hypotheses of the form,

alternative="two.sided" tests H0: Delta=delta versus H1: Delta != delta
alternative="less" tests H0: Delta >= delta versus H1: Delta< delta
alternative="greater" tests H0: Delta <= delta versus H1: Delta> delta

The test uses the theory of melding (Fay, Proschan and Brittain, 2015). The idea is to use confidence distribution random variables (CD-RVs). It is easiest to understand the melding confidence intervals by looking at the Monte Carlo implementation. Let nmc be the number of Monte Carlo replicates, then the simulated CD-RV associated with x are Bx = x$estimate + x$stderr * rt(nmc,df=x$df). Similarly define By. Then the 95 percent melded confidence interval for Delta=yParm-xParm is estimated by quantile(By-Bx, probs=c(0.025,0.975)).

When the estimates are means from normal distributions, then the meldtTest reduces to the Behrens-Fisher solution (see bfTest).

Only one of x$stderr or y$stderr may be zero.

References

Fay, MP, Proschan, MA, Brittain, E (2015). Combining One-sample confidence procedures for inference in the two-sample case. Biometrics. 71: 146-156.

Examples

Run this code

## Classical example: Student's sleep data
## Compare to bfTest
xValues<- sleep$extra[sleep$group==1]
yValues<- sleep$extra[sleep$group==2]


x<-list(estimate=mean(xValues),
    stderr=sd(xValues)/sqrt(length(xValues)),
    df=length(xValues)-1)
y<-list(estimate=mean(yValues),
    stderr=sd(yValues)/sqrt(length(yValues)),
    df=length(yValues)-1)
bfTest(xValues,yValues)
# by convention the meldtTest does mean(y)-mean(x)
meldtTest(x,y)
meldtTest(y,x)

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