Efficient block designs for settings with spatially correlated errors

SUMMARY Two-dimensional block designs, with block size p x 2 for v treatments, are studied for situations in which the errors are spatially correlated. Conditions for universal optimality are given for two different error covariance structures, the doubly geometric, for which the correlations decay rapidly, and the autonormal, which exhibits a slower rate of decay. In the special cases of p = v for even v to obtain complete blocks, and p = 1(v - 1) for odd v for nearly complete blocks, numerical calculations establish that much smaller designs, using only a fraction of the blocks required by universal optimality, are also reasonably efficient. A table of designs with v < 30 is included.

[1]  J. Morgan.  Some series constructions for two-dimensional neighbor designs , 1990 .

[2]  C. Radhakrishna Rao.  Some Combinatorial Problems of Arrays and Applications to Design of Experiments††Paper read at the International Symposium on Combinatorial Mathematics and its Applications, Fort Collins, Colorado, September 1971. , 1973 .

[3]  R. J. Martin.  On the design of experiments under spatial correlation , 1986 .

[4]  J. Morgan,et al.  On the class of 22 balanced incomplete block designs with nested rows and columns , 1996 .

[5]  J. Morgan,et al.  Two-Dimensional Design for Correlated Errors , 1991 .

[6]  R. J. Martin.  Some aspects of experimental design and analysis when errors are correlated , 1982 .

[7]  J. Kiefer.  Construction and optimality of generalized Youden designs II , 1975 .

[8]  R. J. Martin.  A subclass of lattice processes applied to a problem in planar sampling , 1979 .

[9]  C. Radhakrishna Rao,et al.  Combinatorial arrangements analogous to orthogonal arrays , 1961 .

[10]  D. V. Gokhale,et al.  A Survey of Statistical Design and Linear Models. , 1976 .

[11]  Murari Singh,et al.  Block designs with nested rows and columns , 1979 .

[12]  I. Chakravarti,et al.  Block Designs for First and Second Order Neighbor Correlations , 1988 .

[13]  R. J. Martin,et al.  Optimal incomplete block designs for general dependence structures , 1991 .

[14]  R. J. Martin,et al.  15 Spatial experimental design , 1996, Design and analysis of experiments.

[15]  R. J. Martin,et al.  Incomplete block designs with spatial layouts when observations are dependent , 1993 .

[16]  N. Uddin.  Optimal and near optimal sets of Latin squares for correlated errors , 1991 .