f1.ld.f1 {nparLD}R Documentation

Nonparametric Tests for the F1-LD-F1 Design

Description

This function performs several tests for the relative treatment effects with global or patterned alternatives for the F1-LD-F1 design (see Details for the definition). For the experiments with F1-LD-F1 design, the Wald-type statistic (WTS), the ANOVA-type statistic (ATS), and the modified ANOVA-type statistic with Box (1954) approximation are calculated for testing group and time effects, and interaction. The hypothesis can also be tested against patterned alternatives to detect various trends. Moreover, pairwise comparisons of the groups, patterned interactions, and patterned group effects can be tested using this function.

Usage

f1.ld.f1(var, time, group, subject, w.pat=NULL, w.t=NULL, w.g=NULL, 
time.name="Time", group.name="Group", description=TRUE)

Arguments

var a vector of variable of interest; missing values should be specified as NA.
time a vector of the sub-plot factor variable. See Details for more explanation.
group a vector of the whole-plot factor variable. See Details for more explanation.
subject a vector of individual subjects.
w.pat an A-by-T matrix specifying the pattern for the pattern alternatives where A is the group level and T is the time level; the default option is NULL.
w.t a vector of time pattern for the pattern alternatives; the default option is NULL. The length, if specified, must be equal to the number of time levels.
w.g a vector of group pattern for the pattern alternatives; the default option is NULL. The length, if specified, must be equal to the number of group levels.
time.name name of the time vector; the default option is "Time".
group.name name of the group vector; the default option is "Group".
description indicator for whether a short description of the output should be shown; the default option is TRUE.

Details

The F1-LD-F1 design refers to the experimental design with one whole-plot factor and one sub-plot factor. A whole-plot factor refers to a factor effective for each subject at all times. A sub-plot factor refers to a factor effective at a single time point for all time curves and all subjects. See Brunner et al. (2002) for more examples.

Value

A list with the following numeric components.

RTE Summary of the relative treatment effect (RTE) in a n-by-3 matrix form, where n is the total number of time points, group levels, and group-time interactions. The summary includes the mean of the ranks (RankMeans) in the 1st column, number of observations without counting the repeated measurements within the cell (Nobs) in the 2nd column, and the relative treatment effect (RTE) in the 3rd column.
case2x2 the test statistic, corresponding p-value (approximated by standard normal distribution), degrees of freedom (df) for Student's t distribution, and corresponding p-value (approximated by Student's t distribution with the degrees of freedom in the previous column) for the 2-by-2 design with no missing observations. For the cases which do not use the 2-by-2 design, or when there is a missing value in the 2-by-2 design, case2x2 returns NULL.
Wald.test the test statistic, degrees of freedom (df), and corresponding p-value of the Wald-type test.
ANOVA.test the test statistic, degrees of freedom (df), and corresponding p-value of the ANOVA-type test.
ANOVA.test.mod.Box the test statistic, degrees of freedom (df1, df2), and corresponding p-value of the ANOVA-type test for the whole-plot factor.
Wald.test.time the test statistic and corresponding p-value of the Wald-type test with the hypothesis of no simple time effects.
ANOVA.test.time the test statistic and corresponding p-value of the ANOVA-type test with the hypothesis of no simple time effects.
pattern.time the test statistic, corresponding p-value (approximated by standard normal distribution), degrees of freedom (df) for Student's t distribution, and corresponding p-value (approximated by Student's t distribution with the degrees of freedom in the previous column) to test for patterned simple time effects. If the pattern (w.pat) is not specified, pattern.time returns NULL.
pair.comparison the test statistic, degrees of freedom (df), and the corresponding p-value of the pairwise comparisons.
pattern.pair.comparison the test statistic, corresponding p-value (approximated by standard normal distribution), degrees of freedom (df) for Student's t distribution, and corresponding p-value (approximated by Student's t distribution with the degrees of freedom in the previous column) to test for patterned interactions.
pattern.group the test statistic, corresponding p-value (approximated by standard normal distribution), degrees of freedom (df) for Student's t distribution, and corresponding p-value (approximated by Student's t distribution with the degrees of freedom in the previous column) to test for patterned group effects.
covariance the covariance matrix.

Note

Although the function is designed to work for any kind of input (either in charactor or numeric vector) for the factor parameter(s), we recommend inputting them as numeric vector(s) after assigning each group of factors a number (i.e., 1 = first group, 2 = second group, etc.).

Author(s)

Kimihiro Noguchi, Mahbub Latif, Frank Konietschke, Yulia Gel, Edgar Brunner

References

Box, G.E.P. (1954). Some theorems on quadratic forms applied in the study of analysis of variance problems, I. Effect of inequality of variance in the one-way classification. Annals of Mathematical Statistics, 25, 290-302.

Brunner, E., Domhof, S., and Langer, F. (2002). Nonparametric Analysis of Longitudinal Data in Factorial Experiments, Wiley, New York.

Brunner, E. and Langer, F. (1999). Nichtparametrische Analyse longitudinaler Daten, R. Oldenbourg Verlag, Munchen Wien.

See Also

ld.f1, ld.f2, f1.ld.f2, f2.ld.f1, ld.ci, tree

Examples

## Example with the "Vitality of treetops" data ##
data(tree)
var<-c(tree[,"T1"],tree[,"T2"],tree[,"T3"],tree[,"T4"])
time<-c(rep(1,72),rep(2,72),rep(3,72),rep(4,72))
group<-rep(tree[,"Area"],4)
subject<-rep(tree[,"Tree"],4)
w.t<-c(1:4)
w.g<-c(1:3)
w.pat <- rbind(c(1:4), c(1:4), c(1:4))
ex.f1f1<-f1.ld.f1(var,time,group,subject,w.pat,w.t,w.g,
time.name="Year",group.name="Area",description=FALSE)

## Wald-type statistic 
ex.f1f1$Wald.test

#Area       4.510037  2 1.048716e-01
#Year      58.061097  3 1.525335e-12
#Area:Year 14.819966  6 2.170415e-02

## ANOVA-type statistic
ex.f1f1$ANOVA.test

#          Statistic       df      p-value
#Area       2.352854 1.968147 9.601181e-02
#Year      21.389142 2.729147 8.211209e-13
#Area:Year  3.113632 5.346834 6.768732e-03

[Package nparLD version 1.1 Index]