Designs Involving Varying Temporal Environments Under Factorial Treatment Structure

Abstract

In agricultural or animal experiments, when a series of tasks are assigned to the experimental units under different environmental conditions, it is often a tedious job to alter the conditions at the end of each task period. Hence, each unit is put to perform all the assigned tasks under one set of conditions during one session (environment) and then the conditions are altered for the next session for the next series of tasks. The setting is such that there is a gap between each main session and hence it is assumed that no carry over effect transfers from a main session to another. But carry over effects are assumed to be present within main sessions, between sub-sessions. Designs involving sequences of treatment combinations of two factors, one nested within the other, are suitable for such situations. A general method of construction of such designs has been obtained here. The resultant designs are balanced in the sense that each combination is followed by every level of second factor same number of times. The method of construction has been illustrated by two series of designs wherein the second series is a rearrangement of the first one and used for comparative study. It was observed that the precision of estimation of direct and carry over effects is more with the design having more number of levels of the nested factor.