t-test for the ratio of two means

Description

Performs t-test for the ratio of means of two independent samples from two gaussian distributions. In case of heterogeneous variances a Satterthwaite approximation of the degrees of freedom is used (Tamhane & Logan, 2004).

Usage

 
## Default S3 method:
t.test.ratio(x, y, alternative = "two.sided",
 rho = 1, var.equal = FALSE, conf.level = 0.95,
 iterativeCI=FALSE, ul=1e+10, ll=-1e+10, ...)
## S3 method for class 'formula'
t.test.ratio(formula, data, base=2, ...)

Arguments

Details

This function implements the t-test for the ratio of two means and Fiellers confidence interval for the ratio of two means assuming mutually independent Gaussian errors with homogeneous variances, e.g. in Hauschke, Kieser, Hothorn (1999), when the argument var.equal=TRUE. With the argument var.equal=FALSE (default), the t-test for the ratio of two means assuming mutually independent Gaussian errors and possibly heterogeneous group variances (Tamhane and Logan, 2004) is implemented. When iterativeCI = FALSE (default) the corresponding confidence limits are obtained by using Fiellers formula with plug-in of the Satterthwaites degree of freedom calculated with the sample estimates for ratio and variances (not published). These bounds perform quite well but do not necessarily exactly coincide with the test decision. Setting iterativeCI = TRUE invokes interatively searching for the confidence limits by inverting Tamhane and Logans test using the function uniroot. If the confidence set is unbounded or gives irregular upper and/or lower bounds, a warning and NAs for the confidence limits are returned.

Note that when the mean of the denominator of the ratio is close to zero, confidence intervals might be degenerated and are not returned.

Value

An object of class "htest"

Author(s)

Frank Schaarschmidt

References

Hauschke, D., Kieser, M., Hothorn, L.A. (1999). Proof of safety in toxicology based on the ratio of two means for normally distributed data. Biometrical Journal 41, 295-304.

Tamhane, A.C., Logan, B.R. (2004). Finding the maximum safe dose level for heteroscedastic data. Journal of Biopharmaceutical Statistics 14, 843-856.

Examples

library(mratios)

####################################################

# ASAT values of female rats in a toxicity study
#     (Hauschke, 1999).

data(ASAT)
ASAT

t.test.ratio(ASAT~group, data=ASAT, alternative="less",
 base=1, rho=1.25, var.equal=TRUE)

######################################################

# Bodyweights of male rats in a toxicity study.
# Objective was to show equivalence between the high
# dose group (Dosis) and the control group (Kon).
# Equivalence margins are set to 0.8 and 1.25. The 
# type-I-error to show equivalence is set to alpha=0.05.

data(rat.weight)

# two one-sided tests:

t.test.ratio(weight~group, data=rat.weight, alternative="less",
 rho=1.25, var.equal=TRUE)

t.test.ratio(weight~group, data=rat.weight, alternative="greater",
 rho=0.8, var.equal=TRUE)



# For rho=1, t.test.ratio corresponds to a simple t.test
# with the difference of means under the null set to zero 
# (,i.e. mu=0).


t.test.ratio(ASAT~group, data=ASAT, alternative="less",
 rho=1, var.equal=TRUE)

t.test(ASAT~group, data=ASAT, alternative="less",
 mu=0, var.equal=TRUE)

# Ratio of means bewtween negative and positive control in the
# mutagenicity data set, allowing heterogeneous variances:

data(Mutagenicity)
DM<-subset(Mutagenicity, Treatment=="Vehicle"|Treatment=="Cyclo25")

# 95%-CI using the Fieller formula, Satterthwaite df with plug-in of 
# ratio estimate 

t.test.ratio(MN~Treatment, data=DM, alternative="two.sided",
 var.equal=FALSE, iterativeCI=FALSE)

# 95%-CI based on directly inverting Tamhane and Logans test 
# (Satterthwaite df, avoiding simple plug-in of the ratio estimate)

t.test.ratio(MN~Treatment, data=DM, alternative="two.sided",
 var.equal=FALSE, iterativeCI=TRUE)

t.test.ratio(MN~Treatment, data=DM, alternative="greater", rho=4.589893)$p.value
t.test.ratio(MN~Treatment, data=DM, alternative="less", rho=18.640143)$p.value

Results