K1K2 Design
- Experimental units are grouped into k1 blocks, each containing k2 units.
- Blocks are arranged so every pair of units from different blocks is included together the same number of times, which helps separate block effects from factor effects.
- Common instances include the Latin square (used in agriculture) and the Balanced Incomplete Block design (used in psychology).
Definition
Section titled “Definition”A (k1, k2)-design is a type of combinatorial design used in the design of experiments. The experimental units are divided into k1 groups called blocks, and each block consists of k2 units. The blocks are arranged so that every pair of units from different blocks is included in the same number of blocks.
Explanation
Section titled “Explanation”In a (k1, k2)-design, grouping experimental units into k1 blocks of k2 units provides a structured way to control and distribute block-related variation. The defining property—that every pair of units from different blocks appears together the same number of times—ensures an even distribution of block effects across comparisons, which makes it easier to determine the effect of each experimental factor on the outcome.
Examples
Section titled “Examples”Latin square design
Section titled “Latin square design”The Latin square design, often used in agricultural experiments, arranges experimental units in a k1 x k2 grid. In this arrangement each row and each column represents a different block, and every pair of units from different blocks is included in exactly one block, facilitating determination of factor effects.
Balanced Incomplete Block design (BIB)
Section titled “Balanced Incomplete Block design (BIB)”The Balanced Incomplete Block design, commonly used in psychological experiments, divides experimental units into k1 blocks with each block consisting of k2 units. Unlike the Latin square, units within each block are not arranged in a specific pattern, which allows greater flexibility in design but can make it more difficult to determine the effects of different factors.
Use cases
Section titled “Use cases”- Agriculture (example: Latin square)
- Psychology (example: Balanced Incomplete Block design)
- Other areas of science and engineering
Notes or pitfalls
Section titled “Notes or pitfalls”- Balanced Incomplete Block designs allow greater flexibility because units within each block need not follow a pattern, but this flexibility can make it more difficult to determine the effects of different factors.
Related terms
Section titled “Related terms”- Latin square design
- Balanced Incomplete Block design (BIB)