# Input data contained in the Higgins1990-Table1.csv file distributed with ARTool
# The data were used in the 1990 paper cited in the References section
data(higgins1990, package = "ART")
library(ARTool)
## Warning: package 'ARTool' was built under R version 3.4.4
library(ART)
## Warning: package 'ART' was built under R version 3.4.4
# Two-factor full factorial model that will be fitted to the data
art.results = aligned.rank.transform(Response ~ Row * Column, data = data.higgins1990)
print(art.results$aligned, digits = 4)
## Row Column Response Aligned_Row Aligned_Column Aligned_Row_Column
## 1 1 1 11.5 3.35208 -1.2812 2.12500
## 2 1 1 10.1 1.95208 -2.6812 0.72500
## 3 1 1 9.9 1.75208 -2.8812 0.52500
## 4 1 1 10.6 2.45208 -2.1812 1.22500
## 5 1 2 9.0 3.49583 -4.1625 2.65000
## 6 1 2 7.4 1.89583 -5.7625 1.05000
## 7 1 2 8.8 3.29583 -4.3625 2.45000
## 8 1 2 8.8 3.29583 -4.3625 2.45000
## 9 1 3 3.8 0.93958 -9.7437 0.47500
## 10 1 3 6.3 3.43958 -7.2437 2.97500
## 11 1 3 4.9 2.03958 -8.6437 1.57500
## 12 1 3 5.3 2.43958 -8.2437 1.97500
## 13 2 1 9.9 1.37083 -4.8708 -1.08333
## 14 2 1 9.8 1.27083 -4.9708 -1.18333
## 15 2 1 9.3 0.77083 -5.4708 -1.68333
## 16 2 1 9.1 0.57083 -5.6708 -1.88333
## 17 2 2 9.3 3.03333 -6.2333 1.34167
## 18 2 2 7.4 1.13333 -8.1333 -0.55833
## 19 2 2 7.7 1.43333 -7.8333 -0.25833
## 20 2 2 7.9 1.63333 -7.6333 -0.05833
## 21 2 3 4.1 0.09583 -12.1958 -0.83333
## 22 2 3 6.3 2.29583 -9.9958 1.36667
## 23 2 3 5.5 1.49583 -10.7958 0.56667
## 24 2 3 5.4 1.39583 -10.8958 0.46667
## 25 3 1 13.9 4.98958 -2.8604 1.30833
## 26 3 1 16.0 7.08958 -0.7604 3.40833
## 27 3 1 14.2 5.28958 -2.5604 1.60833
## 28 3 1 15.2 6.28958 -1.5604 2.60833
## 29 3 2 13.0 5.97083 -4.9042 3.43333
## 30 3 2 13.4 6.37083 -4.5042 3.83333
## 31 3 2 11.2 4.17083 -6.7042 1.63333
## 32 3 2 12.8 5.77083 -5.1042 3.23333
## 33 3 3 9.6 4.45208 -9.4479 3.05833
## 34 3 3 9.6 4.45208 -9.4479 3.05833
## 35 3 3 11.0 5.85208 -8.0479 4.45833
## 36 3 3 13.4 8.25208 -5.6479 6.85833
## Ranks_Row Ranks_Column Ranks_Row_Column
## 1 22.0 35.0 23.0
## 2 14.0 31.0 13.0
## 3 12.0 29.0 11.0
## 4 18.0 33.0 15.0
## 5 24.0 28.0 27.0
## 6 13.0 17.0 14.0
## 7 20.5 26.5 24.5
## 8 20.5 26.5 24.5
## 9 4.0 5.0 10.0
## 10 23.0 14.0 28.0
## 11 15.0 8.0 19.0
## 12 17.0 9.0 22.0
## 13 7.0 24.0 4.0
## 14 6.0 22.0 3.0
## 15 3.0 20.0 2.0
## 16 2.0 18.0 1.0
## 17 19.0 16.0 17.0
## 18 5.0 10.0 6.0
## 19 9.0 12.0 7.0
## 20 11.0 13.0 8.0
## 21 1.0 1.0 5.0
## 22 16.0 4.0 18.0
## 23 10.0 3.0 12.0
## 24 8.0 2.0 9.0
## 25 28.0 30.0 16.0
## 26 35.0 36.0 32.0
## 27 29.0 32.0 20.0
## 28 33.0 34.0 26.0
## 29 32.0 23.0 33.0
## 30 34.0 25.0 34.0
## 31 25.0 15.0 21.0
## 32 30.0 21.0 31.0
## 33 26.5 6.5 29.5
## 34 26.5 6.5 29.5
## 35 31.0 11.0 35.0
## 36 36.0 19.0 36.0
print(art.results$significance)
## Sum Sq Df F value Pr(>F)
## Row 146.7202 1 1.6915027 0.202691776
## Column 414.8571 1 11.3108716 0.002011463
## Row:Column 22.5625 1 0.2388043 0.628403463