Design and Analysis of Experiments, 9th Edition¶
Montgomery, D. C. (2017). Design and Analysis of Experiments, 9th Edition. John Wiley & Sons.
Cited by¶
15 citations across 14 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
- 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.
Mechanisms¶
- Ablation and Sensitivity Test
- Its central failure mode is specific to emergent systems: when behavior lives in the interaction rather than the parts, removing factors one at a time can wrongly declare each inert, because the effect only shows up in combination — the exact case a purely one-factor-at-a-time design is built to miss.
This sourceExplains that one-factor-at-a-time testing can miss effects that appear only through interactions among factors.
- Its central failure mode is specific to emergent systems: when behavior lives in the interaction rather than the parts, removing factors one at a time can wrongly declare each inert, because the effect only shows up in combination — the exact case a purely one-factor-at-a-time design is built to miss.
- Bandwidth, Stability, and Sensitivity Sweep
- First, a one-factor-at-a-time sweep — the tempting, cheap version — systematically misses interactions, so two conditions that are each survivable alone but fatal together slip through.
This sourceExplains that one-factor-at-a-time sweeps systematically miss interactions, including conditions that are survivable alone but fatal together.
- First, a one-factor-at-a-time sweep — the tempting, cheap version — systematically misses interactions, so two conditions that are each survivable alone but fatal together slip through.
- Factorial Experiment
- Its failure mode is combinatorial explosion: cells grow as the product of every factor's levels, so a handful of many-level factors becomes thousands of runs, and powering the interaction term needs still more.
This sourceExplains that full factorial designs require the product of factor levels and that interaction estimation increases design and sample-size demands.
- Its failure mode is combinatorial explosion: cells grow as the product of every factor's levels, so a handful of many-level factors becomes thousands of runs, and powering the interaction term needs still more.
- Full Factorial Matrix
- Its failure mode is that the same completeness becomes a trap the instant the space grows: the curse of dimensionality
This sourceShows that the run count in a full factorial design grows multiplicatively with each added factor, quickly creating a combinatorial burden.
- Its failure mode is that the same completeness becomes a trap the instant the space grows: the curse of dimensionality
- Pairwise Interaction Probe
- Interactions are not additive: three components can conspire in ways no two of them do, so a suite of green pairwise checks can still sit atop a lethal three-way interaction
This sourceExplains that interactions are nonadditive and that a three-way interaction can escape pairwise checks.
- Interactions are not additive: three components can conspire in ways no two of them do, so a suite of green pairwise checks can still sit atop a lethal three-way interaction
- Parameter Sweep and Sensitivity Grid
- Its failure mode is the one-factor-at-a-time blind spot: varying dials singly can completely miss interactions where two inputs together produce a cliff that neither shows alone.
This sourceExplains that one-factor-at-a-time experimentation cannot detect interactions in which one factor's effect depends on another factor's level.
- Its failure mode is the one-factor-at-a-time blind spot: varying dials singly can completely miss interactions where two inputs together produce a cliff that neither shows alone.
- Pilot Bundle Comparison
- The factorial design is the classic instrument here — by crossing factors it isolates each interaction term, letting the analyst see whether the combined effect exceeds, matches, or falls short of the sum of the parts.
This sourceFactorial designs cross factors so that main effects and interactions, including departures from additivity, can be estimated.
- The factorial design is the classic instrument here — by crossing factors it isolates each interaction term, letting the analyst see whether the combined effect exceeds, matches, or falls short of the sum of the parts.
- Selectivity Curve Sweep
- Its failure mode is under-sampling: a grid too coarse or too narrow can miss a thin window entirely, and a one-factor-at-a-time sweep is blind to the interactions that a response-surface design would surface.
This sourceExplains that one-factor-at-a-time experiments can miss interactions that factorial and response-surface designs are intended to reveal.
- Its failure mode is under-sampling: a grid too coarse or too narrow can miss a thin window entirely, and a one-factor-at-a-time sweep is blind to the interactions that a response-surface design would surface.
- Time, Batch, Run, or Location Block
- It misleads catastrophically when a treatment is aliased with a batch — all of one arm in one run — because the block effect and the treatment effect can no longer be separated, and this cannot be repaired after the fact.
This sourceShows that assigning treatments by batch confounds treatment and block effects, preventing their separate estimation from the collected design.
- It misleads catastrophically when a treatment is aliased with a batch — all of one arm in one run — because the block effect and the treatment effect can no longer be separated, and this cannot be repaired after the fact.
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- https://www.wiley.com/en-us/Design+and+Analysis+of+Experiments%2C+9th+Edition-p-9781119113478 ×6
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