CALM can take existing coding patterns and decode them to determine the hypotheses being tested. The examples below use the built-in codes in R (treatment, SAS, sum, helmert, and poly) and extract the hypotheses implied by each code vector.
The package takes matrix input of the coding pattern (columns represent coded vectors, rows represent the groups being represented) and outputs the linear contrasts hypotheses being represented (the rows represent the weights for the contrast, the columns represent the groups being compared).
Specify that we wish to examine the existing contr.treatment and then
use CALM to decode it into hypotheses.
ex_contr.treatment <- cbind(Int=1,contr.treatment(3))
ex_contr.treatment
## Int 2 3
## 1 1 0 0
## 2 1 1 0
## 3 1 0 1
calm.decode(ex_contr.treatment)
## 1 2 3
## Int 1 0 0
## 2 -1 1 0
## 3 -1 0 1
This shows that the intercept is equivalent to the mean of the first group. The additional parameters represent the difference between each group and the first group.
Specify that we wish to examine the existing contr.SAS and then use
CALM to decode it into hypotheses.
ex_contr.SAS <- cbind(Int=1,contr.SAS(3))
ex_contr.SAS
## Int 1 2
## 1 1 1 0
## 2 1 0 1
## 3 1 0 0
calm.decode(ex_contr.SAS)
## 1 2 3
## Int 0 0 1
## 1 1 0 -1
## 2 0 1 -1
This shows that the intercept is equivalent to the mean of the last group. The additional parameters represent the difference between each group and the last group.
Specify that we wish to examine the existing contr.sum and then use
CALM to decode it into hypotheses.
ex_contr.sum <- cbind(Int=1,contr.sum(3))
ex_contr.sum
## Int
## 1 1 1 0
## 2 1 0 1
## 3 1 -1 -1
calm.decode(ex_contr.sum)
## 1 2 3
## Int 0.3333 0.3333 0.3333
## 0.6667 -0.3333 -0.3333
## -0.3333 0.6667 -0.3333
This shows that the intercept is equivalent to the mean of the group means. The additional parameters represent the difference between each group and the grand mean. The last group is not compared.
Specify that we wish to examine the existing contr.herlmert and then
use CALM to decode it into hypotheses.
ex_contr.helmert <- cbind(Int=1,contr.helmert(3))
ex_contr.helmert
## Int
## 1 1 -1 -1
## 2 1 1 -1
## 3 1 0 2
calm.decode(ex_contr.helmert)
## 1 2 3
## Int 0.3333 0.3333 0.3333
## -0.5000 0.5000 0.0000
## -0.1667 -0.1667 0.3333
This shows that the intercept is equivalent to the mean of the group means. The additional parameters represent the difference between each group and the mean of the subsequent groups.
Specify that we wish to examine the existing contr.poly and then use
CALM to decode it into hypotheses.
ex_contr.poly <- cbind(Int=1,contr.poly(3))
ex_contr.poly
## Int .L .Q
## [1,] 1 -7.071068e-01 0.4082483
## [2,] 1 -7.850462e-17 -0.8164966
## [3,] 1 7.071068e-01 0.4082483
calm.decode(ex_contr.poly)
## GROUP 1 GROUP 2 GROUP 3
## Int 0.3333 0.3333 0.3333
## .L -0.7071 0.0000 0.7071
## .Q 0.4082 -0.8165 0.4082
THis shows that the intercept is equivalent to the mean of the group means. The additional parameters represent polynomial trends (linear, quadratic, etc.).