The efficiency and optimality characterization of certain six-Treatment incomplete-Block designs emanating from some quasi-Semi-Latin squares

Block designs are used when designing experiments in which varieties of a commodity are compared. ‘Designs and geometry’ introduces various types of block design, and then relates them to finite projective planes and orthogonal latin squares. A block design consists of a set of v varieties arranged into b blocks. If each block contains the same number k of varieties, each variety appears in the same number r of blocks, then for every block design we have v × r = b × k. A balanced incomplete-block design is when all pairs of varieties in a design are compared the same number of times. A triple system is when each block has three varieties.

Download Full-text

A uniformity trial on groundnuts

The Journal of Agricultural Science ◽

10.1017/s002185960005749x ◽

1953 ◽

Vol 43 (3) ◽

pp. 323-328 ◽

Cited By ~ 1

Author(s):

G. E. Hodnett

Keyword(s):

Regression Coefficient ◽

Unit Area ◽

Latin Squares ◽

Block Designs ◽

Incomplete Block ◽

Similar Relationship ◽

The Mean ◽

End To End ◽

Logarithmic Relationship

A uniformity trial on groundnuts has been analysed and the results discussed. Plant number is less variable than yield and less sensitive to shape of plot and of block. For yield, long narrow plots are more efficient than shorter and wider plots, in all shapes and sizes of blocks and in Latin squares. The plots should not be arranged end to end along the contours, but side by side, either singly or in pairs, forming compact blocks.The regression of the plot variance of the mean yield per unit area on size of plot approximately follows a linear logarithmic relationship. A similar relationship holds for plant number. The value of the regression coefficient b′ is low and it has been shown that, as expected, there is considerable gain from the use of small blocks. The efficiencies of various confounded and incomplete block designs relative to designs in larger blocks have been determined for some particular layouts, and values for other layouts, ignoring shape of plots and of blocks, have been obtained by interpolation.The field used for this uniformity trial appears equally variable in all directions.

Download Full-text

Sensory analysis. Methodology. Balanced incomplete block designs

10.3403/30196838 ◽

2011 ◽

Keyword(s):

Sensory Analysis ◽

Block Designs ◽

Incomplete Block ◽

Balanced Incomplete Block Designs ◽

Analysis Methodology ◽

Balanced Incomplete Block

Download Full-text

A Unified Method for Constructing PBIB (Partially Balanced Incomplete Block) Designs Based on Triangular and L2 Schemes.

10.21236/ada126802 ◽

1982 ◽

Author(s):

Ching-Shui Cheng ◽

Gregory M. Constantine ◽

A. S. Hedayat

Keyword(s):

Block Designs ◽

Incomplete Block ◽

Balanced Incomplete Block Designs ◽

Balanced Incomplete Block ◽

Unified Method

Download Full-text

Block designs for variety trials

The Journal of Agricultural Science ◽

10.1017/s0021859600055507 ◽

1978 ◽

Vol 90 (2) ◽

pp. 395-400 ◽

Cited By ~ 83

Author(s):

H. D. Patterson ◽

E. R. Williams ◽

E. A. Hunter

Keyword(s):

Block Designs ◽

Incomplete Block ◽

Variety Trials ◽

Rectangular Lattices

SummaryIn this paper we present a series of resolvable incomplete block designs suitable for variety trials with any number of varieties v in the range 20 ≤v ≤ 100. These designs usefully supplement existing square and rectangular lattices. They are not necessarily optimal in the sense of having smallest possible variances but their efficiencies are known to be high.

Download Full-text