aligned.rank.transform: Aligned Rank Transform procedure
In ART: Aligned Rank Transform for Nonparametric Factorial Analysis
Description
Usage
Arguments
Details
Value
Author(s)
References
See Also
Examples
Description
Aligned Rank Transform for Nonparametric Factorial Analysis
Usage
1
2
Arguments
formula
A formula indicating the model to be fitted.
data
A data frame containing the input data. The name of the columns should match the names used in
the user-specified formula of the model that will be fitted.
perform.aov
Optional: whether separate ANOVAs should be run on the Ranked aligned responses or not.
In case it should not, only the ranked aligned responses will be returned. Defaults to TRUE.
SS.type
A string indicating the type of sums of squares to be used in the ANOVA on the aligned responses.
Must be one of "I", "II", "III". If perform.aov was set to FALSE, the value of SS.type will be ignored.
Please note SS types coincide when the design is balanced (equal number of observations per cell) but differ otherwise.
Refer to Shaw and Mitchell-Olds (1993) or Fox (1997) for further reading and recomentations on how to conduct ANOVA analyses with unbalanced designs.
...
Other arguments passed to lm when computing effect estimates via ordinary least squares for the alignment.
Details
The function computes a separate aligned response variable for each effect of an user-specified model,
transform it into a ranking, and applies a separate ANOVA to every resulting ranked aligned response to
check the significance of the corresponding effect.
Value
A tagged list with the following elements:
-
$aligned: a data frame with the input data and additional columns to the right, containing the aligned
and the ranked aligned responses for each model effect.
-
$significance: (only when perform.aov = TRUE) the ANOVA table that collects every unique meaningful row of
each of the separate ANOVA tables obtained from the ranked aligned responses.
Author(s)
Pablo J. Villacorta Iglesias
References
Higgins, J. J., Blair, R. C. and Tashtoush, S. (1990). The aligned rank transform procedure. Proceedings of the Conference on Applied Statistics in Agriculture.
Manhattan, Kansas: Kansas State University, pp. 185-195.
Higgins, J. J. and Tashtoush, S. (1994). An aligned rank transform test for interaction. Nonlinear World 1 (2), pp. 201-211.
Mansouri, H. (1999). Aligned rank transform tests in linear models. Journal of Statistical Planning and Inference 79, pp. 141 - 155.
Wobbrock, J.O., Findlater, L., Gergle, D. and Higgins, J.J. (2011). The Aligned Rank Transform for nonparametric factorial analyses using only ANOVA procedures.
Proceedings of the ACM Conference on Human Factors in Computing Systems (CHI '11). New York: ACM Press, pp. 143-146.
Higgins, J.J. (2003). Introduction to Modern Nonparametric Statistics. Cengage Learning.
Shaw, R.G. and Mitchell-Olds, T. (1993). Anova for Unbalanced Data: An Overview. Ecology 74, 6, pp. 1638 - 1645.
Fox, J. (1997). Applied Regression Analysis, Linear Models, and Related Methods. SAGE Publications.
ARTool R package, for full models only. http://cran.r-project.org/package=ARTool
See Also
lm
Examples
1
2
3
4
5
6
7
# Input data contained in the Higgins1990-Table1.csv file distributed with ARTool
# The data were used in the 1990 paper cited in the References section
data(higgins1990, package = "ART");
# Two-factor full factorial model that will be fitted to the data
art.results = aligned.rank.transform(Response ~ Row * Column, data = data.higgins1990);
print(art.results$aligned, digits = 4);
print(art.results$significance);
Example output
Row Column Response Aligned_Row Aligned_Column Aligned_Row_Column Ranks_Row
1 1 1 11.5 3.35208 -1.2812 2.12500 22.0
2 1 1 10.1 1.95208 -2.6812 0.72500 14.0
3 1 1 9.9 1.75208 -2.8812 0.52500 12.0
4 1 1 10.6 2.45208 -2.1812 1.22500 18.0
5 1 2 9.0 3.49583 -4.1625 2.65000 24.0
6 1 2 7.4 1.89583 -5.7625 1.05000 13.0
7 1 2 8.8 3.29583 -4.3625 2.45000 20.5
8 1 2 8.8 3.29583 -4.3625 2.45000 20.5
9 1 3 3.8 0.93958 -9.7437 0.47500 4.0
10 1 3 6.3 3.43958 -7.2437 2.97500 23.0
11 1 3 4.9 2.03958 -8.6437 1.57500 15.0
12 1 3 5.3 2.43958 -8.2437 1.97500 17.0
13 2 1 9.9 1.37083 -4.8708 -1.08333 7.0
14 2 1 9.8 1.27083 -4.9708 -1.18333 6.0
15 2 1 9.3 0.77083 -5.4708 -1.68333 3.0
16 2 1 9.1 0.57083 -5.6708 -1.88333 2.0
17 2 2 9.3 3.03333 -6.2333 1.34167 19.0
18 2 2 7.4 1.13333 -8.1333 -0.55833 5.0
19 2 2 7.7 1.43333 -7.8333 -0.25833 9.0
20 2 2 7.9 1.63333 -7.6333 -0.05833 11.0
21 2 3 4.1 0.09583 -12.1958 -0.83333 1.0
22 2 3 6.3 2.29583 -9.9958 1.36667 16.0
23 2 3 5.5 1.49583 -10.7958 0.56667 10.0
24 2 3 5.4 1.39583 -10.8958 0.46667 8.0
25 3 1 13.9 4.98958 -2.8604 1.30833 28.0
26 3 1 16.0 7.08958 -0.7604 3.40833 35.0
27 3 1 14.2 5.28958 -2.5604 1.60833 29.0
28 3 1 15.2 6.28958 -1.5604 2.60833 33.0
29 3 2 13.0 5.97083 -4.9042 3.43333 32.0
30 3 2 13.4 6.37083 -4.5042 3.83333 34.0
31 3 2 11.2 4.17083 -6.7042 1.63333 25.0
32 3 2 12.8 5.77083 -5.1042 3.23333 30.0
33 3 3 9.6 4.45208 -9.4479 3.05833 26.5
34 3 3 9.6 4.45208 -9.4479 3.05833 26.5
35 3 3 11.0 5.85208 -8.0479 4.45833 31.0
36 3 3 13.4 8.25208 -5.6479 6.85833 36.0
Ranks_Column Ranks_Row_Column
1 35.0 23.0
2 31.0 13.0
3 29.0 11.0
4 33.0 15.0
5 28.0 27.0
6 17.0 14.0
7 26.5 24.5
8 26.5 24.5
9 5.0 10.0
10 14.0 28.0
11 8.0 19.0
12 9.0 22.0
13 24.0 4.0
14 22.0 3.0
15 20.0 2.0
16 18.0 1.0
17 16.0 17.0
18 10.0 6.0
19 12.0 7.0
20 13.0 8.0
21 1.0 5.0
22 4.0 18.0
23 3.0 12.0
24 2.0 9.0
25 30.0 16.0
26 36.0 32.0
27 32.0 20.0
28 34.0 26.0
29 23.0 33.0
30 25.0 34.0
31 15.0 21.0
32 21.0 31.0
33 6.5 29.5
34 6.5 29.5
35 11.0 35.0
36 19.0 36.0
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
ART documentation built on May 2, 2019, 9:24 a.m.
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Description Usage Arguments Details Value Author(s) References See Also Examples
Description
Aligned Rank Transform for Nonparametric Factorial Analysis
Usage
1 2 |
Arguments
formula |
A formula indicating the model to be fitted. |
data |
A data frame containing the input data. The name of the columns should match the names used in
the user-specified |
perform.aov |
Optional: whether separate ANOVAs should be run on the Ranked aligned responses or not.
In case it should not, only the ranked aligned responses will be returned. Defaults to |
SS.type |
A string indicating the type of sums of squares to be used in the ANOVA on the aligned responses.
Must be one of "I", "II", "III". If |
... |
Other arguments passed to lm when computing effect estimates via ordinary least squares for the alignment. |
Details
The function computes a separate aligned response variable for each effect of an user-specified model, transform it into a ranking, and applies a separate ANOVA to every resulting ranked aligned response to check the significance of the corresponding effect.
Value
A tagged list with the following elements:
-
$aligned: a data frame with the input data and additional columns to the right, containing the aligned and the ranked aligned responses for each model effect. -
$significance: (only whenperform.aov = TRUE) the ANOVA table that collects every unique meaningful row of each of the separate ANOVA tables obtained from the ranked aligned responses.
Author(s)
Pablo J. Villacorta Iglesias
References
Higgins, J. J., Blair, R. C. and Tashtoush, S. (1990). The aligned rank transform procedure. Proceedings of the Conference on Applied Statistics in Agriculture. Manhattan, Kansas: Kansas State University, pp. 185-195.
Higgins, J. J. and Tashtoush, S. (1994). An aligned rank transform test for interaction. Nonlinear World 1 (2), pp. 201-211.
Mansouri, H. (1999). Aligned rank transform tests in linear models. Journal of Statistical Planning and Inference 79, pp. 141 - 155.
Wobbrock, J.O., Findlater, L., Gergle, D. and Higgins, J.J. (2011). The Aligned Rank Transform for nonparametric factorial analyses using only ANOVA procedures. Proceedings of the ACM Conference on Human Factors in Computing Systems (CHI '11). New York: ACM Press, pp. 143-146.
Higgins, J.J. (2003). Introduction to Modern Nonparametric Statistics. Cengage Learning.
Shaw, R.G. and Mitchell-Olds, T. (1993). Anova for Unbalanced Data: An Overview. Ecology 74, 6, pp. 1638 - 1645.
Fox, J. (1997). Applied Regression Analysis, Linear Models, and Related Methods. SAGE Publications.
ARTool R package, for full models only. http://cran.r-project.org/package=ARTool
See Also
lm
Examples
1 2 3 4 5 6 7 | # Input data contained in the Higgins1990-Table1.csv file distributed with ARTool
# The data were used in the 1990 paper cited in the References section
data(higgins1990, package = "ART");
# Two-factor full factorial model that will be fitted to the data
art.results = aligned.rank.transform(Response ~ Row * Column, data = data.higgins1990);
print(art.results$aligned, digits = 4);
print(art.results$significance);
|
Example output
Row Column Response Aligned_Row Aligned_Column Aligned_Row_Column Ranks_Row
1 1 1 11.5 3.35208 -1.2812 2.12500 22.0
2 1 1 10.1 1.95208 -2.6812 0.72500 14.0
3 1 1 9.9 1.75208 -2.8812 0.52500 12.0
4 1 1 10.6 2.45208 -2.1812 1.22500 18.0
5 1 2 9.0 3.49583 -4.1625 2.65000 24.0
6 1 2 7.4 1.89583 -5.7625 1.05000 13.0
7 1 2 8.8 3.29583 -4.3625 2.45000 20.5
8 1 2 8.8 3.29583 -4.3625 2.45000 20.5
9 1 3 3.8 0.93958 -9.7437 0.47500 4.0
10 1 3 6.3 3.43958 -7.2437 2.97500 23.0
11 1 3 4.9 2.03958 -8.6437 1.57500 15.0
12 1 3 5.3 2.43958 -8.2437 1.97500 17.0
13 2 1 9.9 1.37083 -4.8708 -1.08333 7.0
14 2 1 9.8 1.27083 -4.9708 -1.18333 6.0
15 2 1 9.3 0.77083 -5.4708 -1.68333 3.0
16 2 1 9.1 0.57083 -5.6708 -1.88333 2.0
17 2 2 9.3 3.03333 -6.2333 1.34167 19.0
18 2 2 7.4 1.13333 -8.1333 -0.55833 5.0
19 2 2 7.7 1.43333 -7.8333 -0.25833 9.0
20 2 2 7.9 1.63333 -7.6333 -0.05833 11.0
21 2 3 4.1 0.09583 -12.1958 -0.83333 1.0
22 2 3 6.3 2.29583 -9.9958 1.36667 16.0
23 2 3 5.5 1.49583 -10.7958 0.56667 10.0
24 2 3 5.4 1.39583 -10.8958 0.46667 8.0
25 3 1 13.9 4.98958 -2.8604 1.30833 28.0
26 3 1 16.0 7.08958 -0.7604 3.40833 35.0
27 3 1 14.2 5.28958 -2.5604 1.60833 29.0
28 3 1 15.2 6.28958 -1.5604 2.60833 33.0
29 3 2 13.0 5.97083 -4.9042 3.43333 32.0
30 3 2 13.4 6.37083 -4.5042 3.83333 34.0
31 3 2 11.2 4.17083 -6.7042 1.63333 25.0
32 3 2 12.8 5.77083 -5.1042 3.23333 30.0
33 3 3 9.6 4.45208 -9.4479 3.05833 26.5
34 3 3 9.6 4.45208 -9.4479 3.05833 26.5
35 3 3 11.0 5.85208 -8.0479 4.45833 31.0
36 3 3 13.4 8.25208 -5.6479 6.85833 36.0
Ranks_Column Ranks_Row_Column
1 35.0 23.0
2 31.0 13.0
3 29.0 11.0
4 33.0 15.0
5 28.0 27.0
6 17.0 14.0
7 26.5 24.5
8 26.5 24.5
9 5.0 10.0
10 14.0 28.0
11 8.0 19.0
12 9.0 22.0
13 24.0 4.0
14 22.0 3.0
15 20.0 2.0
16 18.0 1.0
17 16.0 17.0
18 10.0 6.0
19 12.0 7.0
20 13.0 8.0
21 1.0 5.0
22 4.0 18.0
23 3.0 12.0
24 2.0 9.0
25 30.0 16.0
26 36.0 32.0
27 32.0 20.0
28 34.0 26.0
29 23.0 33.0
30 25.0 34.0
31 15.0 21.0
32 21.0 31.0
33 6.5 29.5
34 6.5 29.5
35 11.0 35.0
36 19.0 36.0
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
R Package Documentation
Browse R Packages
We want your feedback!
Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Embedding an R snippet on your website
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.