Tests for General Factorial Designs
Description
The GFD function calculates the Waldtype statistic (WTS), the ANOVAtype statistic (ATS) as well as a permutation version of the WTS for general factorial designs.
Usage
1 
Arguments
formula 
A model 
data 
A data.frame, list or environment containing the variables in

nperm 
The number of permutations used for calculating the permuted Waldtype statistic. The default option is 10000. 
alpha 
A number specifying the significance level; the default is 0.05. 
Details
The package provides the Waldtype statistic, a permuted version
thereof as well as the ANOVAtype statistic for general factorial designs,
even with nonnormal error terms and/or heteroscedastic variances. It is
implemented for both crossed and hierarchically nested designs and allows
for an arbitrary number of factor combinations as well as different sample
sizes in the crossed design.
The GFD
function returns three pvalues: One for the ATS based on an Fquantile and
two for the WTS, one based on the χ^2
distribution and one based on the permutation procedure.
Since the ATS is only an approximation and the WTS based on the χ^2
distribution is known
to be very liberal for small sample sizes, we recommend to use the WTPS in these situations.
Value
A GFD
object containing the following components:
Descriptive 
Some descriptive statistics of the data for all factor level combinations. Displayed are the number of individuals per factor level combination, the mean, variance and 100*(1alpha)% confidence intervals. 
WTS 
The value of the WTS along with degrees of freedom of the central chisquare distribution and pvalue, as well as the pvalue of the permutation procedure. 
ATS 
The value of the ATS, degrees of freedom of the central F distribution and the corresponding pvalue. 
References
Friedrich, S., Konietschke, F., Pauly, M.(2015). GFD  An Rpackage for the Analysis of General Factorial Designs. Submitted to Journal of Statistical Software.
Pauly, M., Brunner, E., Konietschke, F.(2015). Asymptotic Permutation Tests in General Factorial Designs. Journal of the Royal Statistical Society  Series B 77, 461473.
Examples
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