Valid Randomisation for the First‐difference Analysis

SUMMARY A general method is presented for randomising a block design while preserving the neighbour relationships between treatments. The randomisation possesses validity properties for the first‐difference analysis introduced by Besag & Kempton (1986). The estimators of treatment differences are unbiased, and the paper shows how to calculate quadratic estimators of their variance, which are unbiased if treatment effects and plot effects are additive. Simplifications, which appear when the design is neighbour‐balanced, are described and illustrated.