isGYD                package:crossdes                R Documentation

_C_h_e_c_k_i_n_g _S_i_m_p_l_e _B_l_o_c_k _a_n_d _R_o_w-_C_o_l_u_m_n _D_e_s_i_g_n_s _f_o_r _B_a_l_a_n_c_e

_D_e_s_c_r_i_p_t_i_o_n:

     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.

_U_s_a_g_e:

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

_A_r_g_u_m_e_n_t_s:

       d: 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. 

_D_e_t_a_i_l_s:

     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.

_V_a_l_u_e:

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

_A_u_t_h_o_r(_s):

     Oliver Sailer sailer@statistik.uni-dortmund.de

_S_e_e _A_l_s_o:

     'isCbalanced'

_E_x_a_m_p_l_e_s:

     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)    

