casallas/artr

Aligned Rank TransformR: An R port of Jacob Wobbrock's ARTool (https://depts.washington.edu/aimgroup/proj/art/)

artR

Aligned Rank TransformR: An R port of Jacob Wobbrock's (C#) ARTool (https://depts.washington.edu/aimgroup/proj/art/)

Ported to R by Juan Sebastián Casallas in 2013

The Aligned Rank Transform (ART) allows using parametric tests on nonparametric data. The ARTool is a C# program that does this transformation on an input dataset, and generates a new dataset with extra aligned and ranked columns. Its main limitation is that it's only available for Windows (or, if you're courageous to Unix via Mono), and it involves an external step in the data analysis worflow. Thus, I've created this R port to integrate the ART in my usual *nix–R workflow. More details about ARTool and ART are presented in the ARTool website and in [2].

Installation

This package can be installed using devtools: devtools::install_github("casallas/artR")

Usage

As with ARTool, input for the ART function should be a "long format" data frame, whose first column corresponds to the subject number and whose last column corresponds to the Y, or dependent variable; all the columns in between correspond to the X, or independent variables.

The following example uses Table 1 from [1] provided in ARTool (https://depts.washington.edu/aimgroup/proj/art/ARTool.zip)

library(compare) # Compare equal
library(artR) # ART

higgins1 <- within(read.csv("Higgins1990-Table1.csv"), {
	Subject <- factor(Subject)
	Row <- factor(Row)
	Column <- factor(Column)
})
higgins1.art <- ART(higgins1)

# Results given by ARTool
higgins1.artool <- within(read.csv("Higgins1990-Table1.art.csv"), {
  Subject <- factor(Subject)
  Row <- factor(Row)
  Column <- factor(Column)
})
# Both results are the same
compareEqual(higgins1.artool, higgins1.art)$detailedResult # All columns have the same values

The following ANOVA coincides with that of Table 4 in [1] (Row*Column interaction)

library(ez) # ezANOVA
ezANOVA(data=higgins1.art, dv=ART.Response.Row.x.Column, wid=Subject, between=.(Row, Column))
#       Effect DFn DFd          F         p p<.05
# 1        Row   2  27 0.11058723 0.8957116      
# 2     Column   2  27 0.08551222 0.9182895      
# 3 Row:Column   4  27 0.64166309 0.6374203      

ANOVA for individual Row and Column can also be computed

ezANOVA(data=higgins1.art, dv=ART.Response.Row, wid=Subject, between=.(Row, Column))
ezANOVA(data=higgins1.art, dv=ART.Response.Column, wid=Subject, between=.(Row, Column))

Differences with ARTool

ARTool and artR give very similar results in terms of number of columns and values. One minor difference is the name of the columns:

Columns	ARTool	artR
aligned	"aligned(Y) for X"	"aligned.Y.X"

    |"aligned(Y) for X1*X2"|"aligned.Y.X1.x.X2"

ART |"ART(Y) for X" |"ART.Y.X" |"ART(Y) for X1*X2" |"ART.Y.X1.x.X2"

artR's column notation is shorter and allows using aligned and ART column names in R formulae, e.g. in lmer or lm. For example Table 4 in [1] can also be generated using:

summary(aov(ART.Response.Row.x.Column ~ Row*Column, data=higgins1.art))
#             Df Sum Sq Mean Sq F value Pr(>F)
# Row          2     29   14.33   0.111  0.896
# Column       2     22   11.08   0.086  0.918
# Row:Column   4    333   83.17   0.642  0.637
# Residuals   27   3500  129.61

Even though the expected data frame's header should have the form "Subject", "X1", "X2", ..., "Xn", "Y", it's easy to transform any data frame to this format before calling ART:

df <- data.frame(X1=(1:100)^2, subj=1:100, Y=log(1:100), X2=sqrt(1:100))
ART(df[c("subj", "X1", "X2", "Y")])

References

[1] Higgins, J. J., Blair, R. C. and Tashtoush, S. (1990). The aligned rank transform procedure. Proceedings of the Conference on Applied Statistics in Agriculture. Manhattan, Kansas: Kansas State University, pp. 185-195.

[2] Wobbrock, J. O., Findlater, L., Gergle, D., & Higgins, J. J. (2011, May). The aligned rank transform for nonparametric factorial analyses using only anova procedures. In Proceedings of the SIGCHI Conference on Human Factors in Computing Systems (pp. 143-146). ACM.