The Design of Experiments¶
Fisher, R. A. (1935). The Design of Experiments. Oliver and Boyd.
Cited by¶
19 citations across 19 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Blocking (In Experimental Design)
- 1. The homogeneous experimental-unit grouping — units are stratified ex-ante into blocks where members within each block are similar on known nuisance dimensions (soil fertility, patient age, baseline outcome, location, batch), such that within-block comparisons isolate treatment effects from these nuisance sources
This sourceOliver and Boyd, Edinburgh. Foundational treatise establishing randomization as the 'reasoned basis for inference' and developing the three principles of randomization, replication, and blocking.
SupportedVerified against the work's full text
Fisher grounds blocking: group variable material into relatively homogeneous blocks, apply every treatment within each, and remove between-block differences from comparisons.
“An equally great advantage is obtained, in other fields of research, by a similar subdivision of the material into relatively homogeneous series, to each of which the different experimental treatments are applied in equal proportion.”
- 1. The homogeneous experimental-unit grouping — units are stratified ex-ante into blocks where members within each block are similar on known nuisance dimensions (soil fertility, patient age, baseline outcome, location, batch), such that within-block comparisons isolate treatment effects from these nuisance sources
- Ceteris Paribus
- In controlled experiments it is the discipline of holding all factors fixed except the manipulated variable, with randomization as the device that approximately implements it across unmeasured factors.
This sourceEstablishes the controlled experiment and randomization as the device that holds unmeasured factors equal in expectation across treatment arms, implementing "all else equal," with residual confounding quantified by the analysis.
SupportedVerified against the work's full text
Fisher calls equalising every condition but the tested one an impossible ideal and makes randomisation the safeguard against the uncontrolled causes left over.
“standing as a kind of shorthand symbol for the full procedure of randomisation, by which the validity of the test of significance may be guaranteed against corruption by the causes of disturbance which have not been eliminated.”
- In controlled experiments it is the discipline of holding all factors fixed except the manipulated variable, with randomization as the device that approximately implements it across unmeasured factors.
- Control Sample
- The agricultural design discipline of replicated, randomized, blocked trials with controls, developed for field experiments, ported directly into online experimentation, marketing experiments, and operations testing nearly a century later, the design templates surviving the move intact.
This sourceFounding text of randomized, replicated, blocked agricultural field trials with controls — the design template later ported to industrial and online experimentation.
Supported in partVerified against the work's full text
Fisher sets out the agricultural randomised, replicated, blocked design and says its designs apply to other fields, but cannot show later uptake in online or marketing testing.
“In each block the five plots are assigned one to each of the five varieties under test, and this assign- ment is made at random.”
- The agricultural design discipline of replicated, randomized, blocked trials with controls, developed for field experiments, ported directly into online experimentation, marketing experiments, and operations testing nearly a century later, the design templates surviving the move intact.
- Experimental Design
- Experimental design is the principled architecture of an empirical investigation structured to support causal or comparative inference under resource and ethical constraints, as Fisher (1935) established in his foundational treatment of randomization, blocking, and factorial design.
This sourceFoundational treatise establishing randomization as the "reasoned basis for inference" and developing the principles of randomization, replication, blocking, and factorial design that underpin modern experimental design.
Supported in partVerified against the work's full text
Fisher treats randomisation, randomised blocks and factorial arrangement as the basis of valid inference under limited resources; ethical constraints are not discussed.
“it is an essential characteristic of experimentation that it is carried out with limited resources, and an’ essential part of the subject of experimental design to ascertain how these should be best applied”
- Experimental design is the principled architecture of an empirical investigation structured to support causal or comparative inference under resource and ethical constraints, as Fisher (1935) established in his foundational treatment of randomization, blocking, and factorial design.
- Factorial Design
- 1. The multi-factor combinatorial enumeration — the design explicitly covers all (or balanced subsets of) combinations of factor levels so that each factor is studied not in isolation but across multiple contexts (levels of other factors), enabling detection of context-dependent effects
This sourceFoundational treatise developing factorial design alongside randomization, replication, and blocking; establishes the multi-factor combinatorial enumeration and the principle that systems rarely decompose into additive single-factor effects.
Supported in partVerified against the work's full text
Fisher states the combinatorial condition directly: to conserve "the main effects and the interactions between pairs", the treatments sharing a block must take the three levels of each ingredient and the nine combinations of each pair of factors. Covering every pair of levels in a balanced subset is the enumeration the sentence describes, and conserving pairwise interactions is what keeps a factor estimable across the levels of the others. The passage works through one three-ingredient, three-level case rather than stating the requirement as a general principle about factorial designs.
“If, for example, an increase in ingredient A were advantageous in the presence of B, but were ineffective or disadvantageous in its absence, we could only hope to learn this fact by carrying out our test of A both in the presence and in the absence of B ; and this, in fact, is what the factorial experiment is designed to do”
- 1. The multi-factor combinatorial enumeration — the design explicitly covers all (or balanced subsets of) combinations of factor levels so that each factor is studied not in isolation but across multiple contexts (levels of other factors), enabling detection of context-dependent effects
- Falsifiability
- Statistics: A null hypothesis can be rejected by sufficiently improbable data but never accepted — only "failed to reject" — a directional asymmetry Fisher (1935) built into the logic of significance testing.
This sourceStates the directional asymmetry of significance testing directly: 'the null hypothesis is never proved or established, but is possibly disproved, in the course of experimentation' (p. 18); every experiment exists to give the facts a chance of disproving the null.
SupportedVerified against the work's full text
Fisher states that the null hypothesis is never proved or established but may be disproved, and ties this to the test of significance.
“the null hypothesis is never proved or established, but is possibly disproved, in the course of experimentation.”
- Statistics: A null hypothesis can be rejected by sufficiently improbable data but never accepted — only "failed to reject" — a directional asymmetry Fisher (1935) built into the logic of significance testing.
- Intervention
- Randomization is the physical realization of \(\mathrm{do}\): assigning \(X\) by coin flip severs every incoming edge at once — including confounders nobody named — which is why it sits at the apex of identification.
This sourceFoundational argument that randomization severs treatment from all pre-existing common causes — known and unknown — placing it at the apex of causal identification.
Supported in partVerified against the work's full text
Fisher shows randomisation guards the test against disturbing causes including unknown ones, but uses no causal-graph or do-operator language and does not rank randomisation as the apex of identification.
“Randomisation properly carried out, in which each pair of plants is assigned their positions independently at random, ensures that the estimates of error will take proper care of all such causes of different growth rates”
- Randomization is the physical realization of \(\mathrm{do}\): assigning \(X\) by coin flip severs every incoming edge at once — including confounders nobody named — which is why it sits at the apex of identification.
- Nonparametric Methods
This sourceOliver and Boyd, Edinburgh. (Foundational treatise on experimental design; establishes randomization as the "reasoned basis for inference" and develops the principles of randomization, replication, and blocking that underpin modern randomization-based causal inference.)
- Randomization
- 1. The random treatment-assignment mechanism — a stochastic procedure with pre-specified, known allocation probabilities that assigns units independent of measured or unmeasured characteristics, ensuring exchangeability ex-ante
This sourceOliver and Boyd, Edinburgh. (Foundational treatise on experimental design; establishes randomization as the "reasoned basis for inference" and develops the principles of randomization, replication, and blocking that underpin modern randomization-based causal inference.)
SupportedVerified against the work's full text
Fisher shows that assigning treatments strictly at random gives every allocation an exactly known probability regardless of uncontrolled disturbing causes, guaranteeing a valid test.
“we assign, strictly at random, 4 out of the 8 cups to each of our experimental treatments, then every set of 4, whatever its probability of being so classified, will certainly have a probability of exactly 1 in”
- 1. The random treatment-assignment mechanism — a stochastic procedure with pre-specified, known allocation probabilities that assigns units independent of measured or unmeasured characteristics, ensuring exchangeability ex-ante
- Randomness
- . Statistics and experimental design use randomness as the foundation of causal inference, formalized by Fisher (1935)
This sourceOliver and Boyd, Edinburgh. (Foundational treatise on experimental design; establishes randomization as the "reasoned basis for inference" and develops the principles of randomization, replication, and blocking that underpin modern randomization-based causal inference.)
SupportedVerified against the work's full text
Fisher presents randomisation as the essential safeguard that guarantees valid experimental tests against uncontrolled causes of disturbance.
“the simple precaution of randomisation will suffice to guarantee the validity of the test of significance”
- . Statistics and experimental design use randomness as the foundation of causal inference, formalized by Fisher (1935)
- Reproducibility & Replicability
- The
multi_origin_equalflag is warrantedThis sourceOliver and Boyd, Edinburgh. (Foundational treatise on experimental design; establishes randomization as the "reasoned basis for inference" and develops the principles of randomization, replication, and blocking that underpin modern randomization-based causal inference.)
Supported in partVerified against the work's full text
Fisher makes replication essential to inference as the only source of the error estimate for significance tests; he says nothing on disciplinary origins.
“its main purpose, which there is no alternative method of achieving, is to supply an estimate of error by which the significance of these comparisons is to be judged.”
- The
- Statistical Inference
- A core function of statistical inference, as Fisher (1935) made central in his treatise on experimental design, is to name the gap between what we observe (a finite, noisy sample) and what we want to know (the true population parameter, causal effect, or mechanism).
This sourceOliver and Boyd, Edinburgh. (Foundational treatise on experimental design; establishes randomization as the "reasoned basis for inference" and develops the principles of randomization, replication, and blocking that underpin modern randomization-based causal inference.)
Supported in partVerified against the work's full text
Fisher's preface frames experimentation as inference from sample to population and says the uncertainty of such inference can be expressed rigorously; it does not speak of a 'gap' as such.
“from a sample to the population from which the sample was drawn, or, as a logician might put it, from the particular to the general.”
- A core function of statistical inference, as Fisher (1935) made central in his treatise on experimental design, is to name the gap between what we observe (a finite, noisy sample) and what we want to know (the true population parameter, causal effect, or mechanism).
Domain-specific¶
- Null distribution
- For a composite null, valid calibration may require a nuisance-parameter adjustment, conditioning argument, pivotal statistic, or supremum over null parameter values rather than substitution of one convenient point.
This sourceOliver and Boyd, foundational treatment of randomization and significance testing.
- For a composite null, valid calibration may require a nuisance-parameter adjustment, conditioning argument, pivotal statistic, or supremum over null parameter values rather than substitution of one convenient point.
Mechanisms¶
- Blocking or Stratification
- The discipline that guards against this is to pre-specify the blocks
This sourceDevelops randomized-block designs that form blocks before treatment allocation to control known nuisance variation.
- The discipline that guards against this is to pre-specify the blocks
- Paired Comparison Experiment
- Because each block's soil quality cancels out of its own difference, the paired design detects a real varietal effect that an unpaired comparison of the same size would have drowned in field-to-field noise.
This sourceShows how blocking removes field heterogeneity from within-block varietal contrasts, increasing the precision with which a treatment effect can be detected.
- Because each block's soil quality cancels out of its own difference, the paired design detects a real varietal effect that an unpaired comparison of the same size would have drowned in field-to-field noise.
- Permutation Tests
- This is the logic of R. A. Fisher's randomization test, the Lady Tasting Tea, where the physical act of random assignment is what makes the probability statement true.
This sourceUses the Lady Tasting Tea experiment to ground a randomization test in the physical random assignment of treatments.
- This is the logic of R. A. Fisher's randomization test, the Lady Tasting Tea, where the physical act of random assignment is what makes the probability statement true.
- Randomized Assignment
- Its strength is manufacturing comparability: in expectation it strips out confounding — measured and unmeasured — so a difference in outcome is attributable to the condition, which is the foundation of credible causal comparison.
This sourceEstablishes random allocation as the basis for comparable treatment groups and valid attribution of systematic outcome differences under an experimental design.
- Its strength is manufacturing comparability: in expectation it strips out confounding — measured and unmeasured — so a difference in outcome is attributable to the condition, which is the foundation of credible causal comparison.
- Randomized or Staggered Assignment
- Its strength is decisive: when assignment is random and intact, both arms regress equally, so no reversion benchmark, simulation, or shrinkage is even needed — the comparison identifies the effect directly.
This sourceEstablishes randomization as the basis for a valid experimental comparison of treatment effects.
- Its strength is decisive: when assignment is random and intact, both arms regress equally, so no reversion benchmark, simulation, or shrinkage is even needed — the comparison identifies the effect directly.
- Within-Block Randomization Inference
- This design-based approach is the modern form of Fisher's randomization test.
This sourceDescribes Fisher's randomization test as comparing an observed statistic with its distribution under treatment-label permutations.
- This design-based approach is the modern form of Fisher's randomization test.
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