isGYD {crossdes} | R Documentation |
A function to check a row-column design for balance. The rows and columns of the design are blocking variables. It is checked, which type of balance the design fulfills. Optionally, incidence matrices are given.
isGYD(d, invis = FALSE, tables = FALSE, coded = FALSE)
d |
A matrix representing the experimental design. The treatments must be numbered 1,...,trt. |
invis |
Logical flag. If TRUE, the type of design is displayed. |
tables |
Logical flag. If TRUE, incidence matrices are given. |
coded |
Logical flag. If TRUE, a logical vector representing the type of design is displayed. |
A design is said to be a balanced block design if the following three conditions hold: i) Each treatment appears equally often in the design. ii) The design is binary, i.e. each treatment appears in each block either n or n+1 times where n is an integer. iii) The number of blocks where treatments i and j each occur n+1 times is the same for all pairs of distinct treatments (i,j). Here the blocks are either rows or columns.
A design that has less columns (rows) than treatments is said to be incomplete with respect to rows (columns). A design that is balanced with respect to both rows and columns is called a generalized Youden design (GYD). A GYD for which each treatment occurs equally often in each row (column) is called uniform on the rows (columns). If both conditions hold, it is called a generalized latin square. A design where each treatment occurs exactly once in each row and column is called a latin square.
If coded
is TRUE, a logical vector of length 8 is retured. The type of design is coded by this vector.
If coded
is FALSE, no value is returned.
If invis
is FALSE, the type of design is displayed on the screen.
If tables
is TRUE, additional incidence tables (occurences of treatments and pairs of treatments) are displayed.
Oliver Sailer sailer@statistik.uni-dortmund.de
d1 <- matrix( c(1,2,3,4,1,1,1,1), 4,2) # d1 is not balanced d2 <- matrix( c(1:4,2:4,1,4,1:3,3,4,1,2),ncol=4) # d2 is a latin square d3 <- matrix( rep(1:3,each=2), ncol=2) # d3 is a balanced incomplete block design. d1 isGYD(d1,tables=TRUE) d2 isGYD(d2,tables=TRUE) d3 isGYD(d3,tables=TRUE)