Design and Analysis of Experiments¶
Montgomery, D. C. (2017). Design and Analysis of Experiments. Wiley.
Cited by¶
6 citations across 5 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Blocking (In Experimental Design)
- Blocking makes the sources of variability in an experiment explicit and auditable
This sourceStandard DOE textbook showing how explicit block terms make sources of variability auditable and conditional on block
- Blocking makes the sources of variability in an experiment explicit and auditable
- Cartesian Product
- Experimental design. A full factorial design is the Cartesian product of factor-level sets; \(n\) factors at \(k\) levels yields \(k^n\) cells, each a distinct experimental condition.
This sourceStandard reference defining full factorial designs as the Cartesian product of factor-level sets (k^n cells), with main-effects-versus-interactions and fractional designs.
- Three dimensions of three levels yield 27 cells; four dimensions of four levels yield 256; the growth is multiplicative, and the prime forces the analyst to confront multiplicativity rather than mistake it for additivity.
This sourceConfirms the multiplicative growth of factorial cell counts (k levels across n factors gives k^n cells), forcing the analyst to confront multiplicativity rather than additivity.
- Experimental design. A full factorial design is the Cartesian product of factor-level sets; \(n\) factors at \(k\) levels yields \(k^n\) cells, each a distinct experimental condition.
- Experimental Design
- The discipline spans classical statistics (Fisher's randomization, blocking, factorial designs), clinical medicine (RCTs, blinding, stratification), drug development (dose-finding, crossover designs), engineering (Design of Experiments, Taguchi methods, robust design), social science (field experiments, natural experiments, regression discontinuity, instrumental variables), machine learning (A/B testing, multi-armed bandits, holdout sets), and policy evaluation (quasi-experimental methods, difference-in-differences); Montgomery (2017) surveys this breadth in the standard DOE textbook.
This sourcethe standard DOE textbook surveying the breadth of experimental design across statistics, engineering, manufacturing, agriculture, and the biological and social sciences.
- The discipline spans classical statistics (Fisher's randomization, blocking, factorial designs), clinical medicine (RCTs, blinding, stratification), drug development (dose-finding, crossover designs), engineering (Design of Experiments, Taguchi methods, robust design), social science (field experiments, natural experiments, regression discontinuity, instrumental variables), machine learning (A/B testing, multi-armed bandits, holdout sets), and policy evaluation (quasi-experimental methods, difference-in-differences); Montgomery (2017) surveys this breadth in the standard DOE textbook.
- Factorial Design
- T1 — Interaction discovery versus run-count growth. Full factorials estimate all interactions but grow combinatorially: 2^7 = 128 runs, 2^10 = 1024 runs
This sourcethe standard DOE textbook documenting how factorials make interaction structure explicit and how full factorials grow combinatorially (2^7 = 128, 2^10 = 1024 runs), motivating fractional designs.
- T1 — Interaction discovery versus run-count growth. Full factorials estimate all interactions but grow combinatorially: 2^7 = 128 runs, 2^10 = 1024 runs
- Linear Independence
- In experimental design it is the orthogonality of factor combinations that keeps each factor's effect identifiable, where confounded factors are dependent and their effects cannot be separated.
This sourceOrthogonality of factor combinations keeping each factor's effect identifiable; confounded factors as dependence.
- In experimental design it is the orthogonality of factor combinations that keeps each factor's effect identifiable, where confounded factors are dependent and their effects cannot be separated.
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