Mathematical theory of the symmetrical factorial design.¶
Bose, R. C. (1947). Mathematical theory of the symmetrical factorial design. Sankhyā: The Indian Journal of Statistics, 8(2), 107-166.
Cited by¶
2 citations across 2 artifacts.
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Primes¶
- Blocking (In Experimental Design)
- T4 — Block size versus within-block homogeneity. Small blocks (e.g., pairs, triples) maximize within-block homogeneity and thus variance reduction, but cost many degrees of freedom for block effects and can limit the number of treatment arms per block
This sourceDevelops the combinatorial/finite-geometry theory of confounding in symmetrical factorial designs, governing how block size constrains degrees of freedom and treatment arms.
- T4 — Block size versus within-block homogeneity. Small blocks (e.g., pairs, triples) maximize within-block homogeneity and thus variance reduction, but cost many degrees of freedom for block effects and can limit the number of treatment arms per block
- Factorial Design
- 6. The orthogonality property simplifying analysis — balanced factorial designs produce uncorrelated factor columns in the analysis matrix, making main effects and interactions orthogonal (independent) and separable, which simplifies interpretation and protects against multicollinearity bias in effect estimation
This sourceDevelops the mathematical (Galois-field/finite-geometry) theory of symmetrical factorial designs, establishing the orthogonality of balanced factorial structures that makes main effects and interactions separable. (Older Sankhyā paper; no stable open scholarly link located.)
- 6. The orthogonality property simplifying analysis — balanced factorial designs produce uncorrelated factor columns in the analysis matrix, making main effects and interactions orthogonal (independent) and separable, which simplifies interpretation and protects against multicollinearity bias in effect estimation
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