Question

What is a key difference between a BIBD and RCBD?

1) BIBD and RCBD are completely unrelated
2) BIBD has equal number of treatments and blocks, while RCBD has unequal number of treatments and blocks
3) In BIBD, every treatment is used exactly once in each block, while in RCBD, every treatment is used at least once in each block
4) BIBD always has a factorial treatment design, while RCBD does not necessarily have a factorial treatment design

Answer 1

A key difference between a BIBD and RCBD is the equal number of treatments and blocks in BIBD compared to the unequal number in RCBD. BIBD ensures that every treatment is used exactly once in each block, while RCBD only requires each treatment to be used at least once in each block. Additionally, BIBD always has a factorial treatment design, while RCBD does not necessarily have this design.

Step-by-step explanation:

A key difference between a Balanced Incomplete Block Design (BIBD) and a Randomized Complete Block Design (RCBD) is that BIBD has an equal number of treatments and blocks, while RCBD has an unequal number. In BIBD, every treatment is used exactly once in each block, ensuring each treatment is compared to each other treatment an equal number of times. In contrast, RCBD only requires each treatment to be used at least once in each block, which means some treatments may be used more than others within a block.

Another difference is that BIBD always has a factorial treatment design, which means it includes all possible combinations of treatment levels. On the other hand, RCBD does not necessarily have a factorial treatment design and can have fewer treatments or fewer levels of each treatment.