aligned.rank.transform: Aligned Rank Transform procedure

Description Usage Arguments Details Value Author(s) References See Also Examples

Description

Aligned Rank Transform for Nonparametric Factorial Analysis

Usage

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aligned.rank.transform(formula, data, perform.aov = TRUE, SS.type = c("III",
  "II", "I"), ...)

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:

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

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# 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.