meldtTest {asht}

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(), ...)

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)

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.

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.

Warning

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

Author(s)

Michael P. Fay

References

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

See Also

bfTest and pbf

Examples

## 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)