Restricted Randomization and Quasi-Latin Squares

One-Way Blocks in Two-Way Layouts

“…26) onwards, have observed that the usual analysis for complete blocks of v treatments is validated, in the strong sense of Grundy & Healy (1950), by any randomization scheme with the following property: the probability, over the randomization, that any given pair of distinct plots P1 and P2 be allocated any given pair of treatments T1 and T2 respectively is Then randomization of b complete blocks of v treatments according to the following scheme validates the usual complete-block analysis. 26) onwards, have observed that the usual analysis for complete blocks of v treatments is validated, in the strong sense of Grundy & Healy (1950), by any randomization scheme with the following property: the probability, over the randomization, that any given pair of distinct plots P1 and P2 be allocated any given pair of treatments T1 and T2 respectively is Then randomization of b complete blocks of v treatments according to the following scheme validates the usual complete-block analysis.…”

“…Yates (1948) and Grundy & Healy (1950) introduced restricted randomization to deal with such situations. Yates (1948) and Grundy & Healy (1950) introduced restricted randomization to deal with such situations.…”

The Randomization Theory of Experimental Inference*

“…It is of interest to note in the past few years some explicit recognition of the situation, for example by Grundy and Healy [13], Barnard [2], and Tukey [20]. The author's book [14] contains descriptions of both normal law analyses and randomization analyses for the basic designs.…”

“…Denote the conceptual yield with treatment k ( = 1, 2 (13) or, using (12) -x".). (14) We observe the yield from treatment k on a random plot v of each block u.…”

Fisher's Contributions to Agricultural Statistics

“…It allows us to preserve the structure in a design like a quasi-complete Latin square design (or a nearest-neighbour design) and to avoid losing degrees of freedom by blocking. Subsequent work includes that by Grundy and Healy (1950), Dyke (1964), Youden (1972), several papers by Bailey (especially 1985, 1987), and Bailey and Rowley (1987). Bailey (1986) provides a nice summary of the work and the issues involved.…”