isGYD {crossdes}R Documentation

Checking Row-Column Designs for Balance

Description

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.

Usage

isGYD(d, invis = FALSE, tables = FALSE, coded = FALSE)

Arguments

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.

Details

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.

Value

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.

Author(s)

Oliver Sailer sailer@statistik.uni-dortmund.de

See Also

isCbalanced

Examples

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)    

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