Concurrences and Quasi‐replication: An alternative approach to precision in designed experiments

Summary

It is shown that precision of estimation in any block design depends entirely upon the frequency with which pair of treatments come together in blocks, the concurrences being weighted by the reciprocal of the block size. It is suggested that the extent to which a treatment participates in a design should be measured not by the number of plots assigned to it but by the quasi‐replication, i. e., the total of weighted concurrences it makes with other treatments, and the size of an experiment should be measured not by the total number of plots it contains but by the total of the weighted concurrences it makes between different treatments.

Beside the general case, design constants are presented for totally balanced designs, those with supplemented balance, group‐divisible designs and for bipartite designs, i. e., multipartite designs with only two groups.