Planning of Experiments¶
Cox, D. R. (1958). Planning of Experiments. John Wiley & Sons.
Cited by¶
7 citations across 7 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Blocking (In Experimental Design)
- 6. The matched-pair-as-block-of-two limiting case — paired designs (matched samples, crossover with two periods, twins, siblings) are a special case of blocking where block size is two, achieving maximum within-block homogeneity and variance reduction on the matched dimension at the cost of degrees of freedom and limited heterogeneity detection
This sourceNon-mathematical exposition of design principles including paired/matched and blocked designs, treating the matched pair as the limiting block of size two
- 6. The matched-pair-as-block-of-two limiting case — paired designs (matched samples, crossover with two periods, twins, siblings) are a special case of blocking where block size is two, achieving maximum within-block homogeneity and variance reduction on the matched dimension at the cost of degrees of freedom and limited heterogeneity detection
- Experimental Design
- Unlike passive observation, which records what naturally occurs, experimental design actively intervenes—assigning units (subjects, molecules, software systems, regions) to treatments—and specifies how outcomes will be measured, in order to isolate causal effects from confounding, as Cox (1958) develops in his canonical exposition of experimental planning.
This sourcecanonical nonmathematical exposition of how active intervention — assigning units to treatments and pre-specifying measurement — isolates causal effects from confounding, with the justification and practical difficulties of randomization across scientific fields.
- Unlike passive observation, which records what naturally occurs, experimental design actively intervenes—assigning units (subjects, molecules, software systems, regions) to treatments—and specifies how outcomes will be measured, in order to isolate causal effects from confounding, as Cox (1958) develops in his canonical exposition of experimental planning.
- Hypothesis Testing (Null vs. Alternative)
- FDA and EMA guidance require pre-specification of primary and key secondary endpoints, testing strategy, and multiplicity adjustments
This sourceCanonical exposition of how active intervention—assigning units to treatments and pre-specifying measurement—isolates causal effects from confounding across scientific domains.
- FDA and EMA guidance require pre-specification of primary and key secondary endpoints, testing strategy, and multiplicity adjustments
- Randomization
- When randomization is not feasible, what observational-inference method applies, and what assumptions does it require to identify the causal estimate?*
This sourceCanonical exposition of how active intervention—assigning units to treatments and pre-specifying measurement—isolates causal effects from confounding across scientific domains.
- When randomization is not feasible, what observational-inference method applies, and what assumptions does it require to identify the causal estimate?*
- Statistical Power
- Design efficiency (e.g., paired versus independent designs, blocking, covariate adjustment) can substantially increase power without changing n
This sourceCanonical exposition of how active intervention—assigning units to treatments and pre-specifying measurement—isolates causal effects from confounding across scientific domains.
- Design efficiency (e.g., paired versus independent designs, blocking, covariate adjustment) can substantially increase power without changing n
- Statistical Significance (p-Value)
- A p-value computation exhibits: (a) the null hypothesis as probability model — a well-defined H₀ specifying a parameter value or relationship; (b) the probability model under H₀ — specifying the joint distribution of the data; © the test statistic as data summary — T(X), a function of sample data with a known or derivable distribution under H₀; (d) the null distribution — the sampling distribution of T(X) under H₀, derived from theory (t, F, χ²), randomization (permutation), or simulation (bootstrap); (e) the observed test-statistic value t* computed from realized data; (f) the definition of "at least as extreme" — one-sided or two-sided, aligned with the alternative hypothesis; (g) the p-value computation — p = P(T(X) at least as extreme as t* | H₀ and model), a tail probability of the null distribution; (h) proper handling of multiplicity when multiple tests are conducted—adjusted p-values or FDR-controlled procedures; (i) reporting of the p-value alongside the effect estimate and confidence interval, not the p-value alone
This sourceCanonical exposition of how active intervention—assigning units to treatments and pre-specifying measurement—isolates causal effects from confounding across scientific domains.
- A p-value computation exhibits: (a) the null hypothesis as probability model — a well-defined H₀ specifying a parameter value or relationship; (b) the probability model under H₀ — specifying the joint distribution of the data; © the test statistic as data summary — T(X), a function of sample data with a known or derivable distribution under H₀; (d) the null distribution — the sampling distribution of T(X) under H₀, derived from theory (t, F, χ²), randomization (permutation), or simulation (bootstrap); (e) the observed test-statistic value t* computed from realized data; (f) the definition of "at least as extreme" — one-sided or two-sided, aligned with the alternative hypothesis; (g) the p-value computation — p = P(T(X) at least as extreme as t* | H₀ and model), a tail probability of the null distribution; (h) proper handling of multiplicity when multiple tests are conducted—adjusted p-values or FDR-controlled procedures; (i) reporting of the p-value alongside the effect estimate and confidence interval, not the p-value alone
- Type I & Type II Errors
This sourceCanonical exposition of how active intervention—assigning units to treatments and pre-specifying measurement—isolates causal effects from confounding across scientific domains.
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Links previously used in the corpus¶
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