Final answer:
The two key principles of a BIBD are uniformity, which ensures each treatment appears equally throughout the design, and balance, which requires each pair of treatments to co-occur in the same number of blocks.
Step-by-step explanation:
The two key principles of a Balanced Incomplete Block Design (BIBD) with regards to treatments are uniformity and balance. The concept of uniformity states that every treatment must appear the same number of times in the entire design. On the other hand, the balance principle indicates that every pair of treatments must co-occur in the same number of blocks. These principles ensure that in the analysis of variance, the effects of the treatments can be estimated with the same precision. BIBD is an important tool in the field of experimental design, particularly in agricultural and industrial experiments where the objective is to study the effects of various treatments under controlled conditions.