isGYD: Checking Simple Block and Row-Column Designs for Balance

Description

A function to check a simple block or 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 and concurrence matrices are given.

Usage

isGYD(d, tables=FALSE, type=TRUE)

Arguments

A matrix representing the experimental design. The treatments must be numbered 1,…,\(trt\).

tables

Logical flag. If TRUE, incidence matrices are displayed.

type

Logical flag. If TRUE, the type of design is displayed.

Value

A list containing information about balance in rows and columns as well as incidence and concurrence matrices for the design.

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 in the sense that each treatment appears in each block either \(n\) or \(n\)+1 times where \(n\) is an integer. iii) The number of concurrences of treatments \(i\) and \(j\) 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.

Examples

Run this code

# NOT RUN {
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)    
# }