Contrast Matrices

Computes contrast matrices for several multiple comparison procedures.

contrMat(n, type = c("Dunnett", "Tukey", "Sequen", "AVE", 
                     "Changepoint", "Williams", "Marcus", 
                     "McDermott", "UmbrellaWilliams", "GrandMean"), 
         base = 1)

Arguments

n

a (possibly named) vector of sample sizes for each group.

type

type of contrast.

base

an integer specifying which group is considered the baseline group for Dunnett contrasts.

Details

Computes the requested matrix of contrasts for comparisons of mean levels.

Value

The matrix of contrasts with appropriate row names is returned.

References

Frank Bretz, Torsten Hothorn and Peter Westfall (2010), Multiple Comparisons Using R, CRC Press, Boca Raton.

Frank Bretz, Alan Genz and Ludwig A. Hothorn (2001), On the numerical availability of multiple comparison procedures. Biometrical Journal, 43(5), 645–656.

Examples

 n <- c(10,20,30,40)
 names(n) <- paste("group", 1:4, sep="")
 contrMat(n)  # Dunnett is default
#> 
#> 	 Multiple Comparisons of Means: Dunnett Contrasts
#> 
#>                 group1 group2 group3 group4
#> group2 - group1     -1      1      0      0
#> group3 - group1     -1      0      1      0
#> group4 - group1     -1      0      0      1
 contrMat(n, base = 2)  # use second level as baseline
#> 
#> 	 Multiple Comparisons of Means: Dunnett Contrasts
#> 
#>                 group1 group2 group3 group4
#> group1 - group2      1     -1      0      0
#> group3 - group2      0     -1      1      0
#> group4 - group2      0     -1      0      1
 contrMat(n, type = "Tukey")
#> 
#> 	 Multiple Comparisons of Means: Tukey Contrasts
#> 
#>                 group1 group2 group3 group4
#> group2 - group1     -1      1      0      0
#> group3 - group1     -1      0      1      0
#> group4 - group1     -1      0      0      1
#> group3 - group2      0     -1      1      0
#> group4 - group2      0     -1      0      1
#> group4 - group3      0      0     -1      1
 contrMat(n, type = "Sequen")
#> 
#> 	 Multiple Comparisons of Means: Sequen Contrasts
#> 
#>                 group1 group2 group3 group4
#> group2 - group1     -1      1      0      0
#> group3 - group2      0     -1      1      0
#> group4 - group3      0      0     -1      1
 contrMat(n, type = "AVE")
#> 
#> 	 Multiple Comparisons of Means: AVE Contrasts
#> 
#>      group1  group2  group3  group4
#> C 1  1.0000 -0.2222 -0.3333 -0.4444
#> C 2 -0.1250  1.0000 -0.3750 -0.5000
#> C 3 -0.1429 -0.2857  1.0000 -0.5714
#> C 4 -0.1667 -0.3333 -0.5000  1.0000
 contrMat(n, type = "Changepoint")
#> 
#> 	 Multiple Comparisons of Means: Changepoint Contrasts
#> 
#>      group1  group2  group3 group4
#> C 1 -1.0000  0.2222  0.3333 0.4444
#> C 2 -0.3333 -0.6667  0.4286 0.5714
#> C 3 -0.1667 -0.3333 -0.5000 1.0000
 contrMat(n, type = "Williams")
#> 
#> 	 Multiple Comparisons of Means: Williams Contrasts
#> 
#>     group1 group2 group3 group4
#> C 1     -1 0.0000 0.0000 1.0000
#> C 2     -1 0.0000 0.4286 0.5714
#> C 3     -1 0.2222 0.3333 0.4444
 contrMat(n, type = "Marcus")
#> 
#> 	 Multiple Comparisons of Means: Marcus Contrasts
#> 
#>      group1  group2  group3 group4
#> C 1 -1.0000  0.2222  0.3333 0.4444
#> C 2 -1.0000  0.0000  0.4286 0.5714
#> C 3 -0.3333 -0.6667  0.4286 0.5714
#> C 4 -1.0000  0.0000  0.0000 1.0000
#> C 5 -0.3333 -0.6667  0.0000 1.0000
#> C 6 -0.1667 -0.3333 -0.5000 1.0000
 contrMat(n, type = "McDermott")
#> 
#> 	 Multiple Comparisons of Means: McDermott Contrasts
#> 
#>      group1  group2 group3 group4
#> C 1 -1.0000  1.0000    0.0      0
#> C 2 -0.3333 -0.6667    1.0      0
#> C 3 -0.1667 -0.3333   -0.5      1
 ### Umbrella-protected Williams contrasts, i.e. a sequence of 
 ### Williams-type contrasts with groups of higher order 
 ### stepwise omitted
 contrMat(n, type = "UmbrellaWilliams")
#> 
#> 	 Multiple Comparisons of Means: UmbrellaWilliams Contrasts
#> 
#>     group1 group2 group3 group4
#> C 1     -1 0.0000 0.0000 1.0000
#> C 2     -1 0.0000 0.4286 0.5714
#> C 3     -1 0.2222 0.3333 0.4444
#> C 4     -1 0.0000 1.0000 0.0000
#> C 5     -1 0.4000 0.6000 0.0000
#> C 6     -1 1.0000 0.0000 0.0000
 ### comparison of each group with grand mean of all groups
 contrMat(n, type = "GrandMean")
#> 
#> 	 Multiple Comparisons of Means: GrandMean Contrasts
#> 
#>        group1 group2 group3 group4
#> group1    0.9   -0.2   -0.3   -0.4
#> group2   -0.1    0.8   -0.3   -0.4
#> group3   -0.1   -0.2    0.7   -0.4
#> group4   -0.1   -0.2   -0.3    0.6