{ "id": "epbywgbktm", "slug": "screening-design", "title": "Screening design", "updated": "2026-10-15", "topic_path": [ { "id": "physical", "label": "Physical world and mathematics", "api_url": "https://www.edgepedia.org/api/v1/topics/physical" }, { "id": "physical.math", "label": "Mathematics and statistics", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.math" }, { "id": "physical.math.statistics", "label": "Statistics and probability", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.math.statistics" }, { "id": "physical.math.statistics.stats_statistical_inference", "label": "Statistical inference, estimation, sampling, and testing", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.math.statistics.stats_statistical_inference" } ], "geo": [ { "id": "geo.nongeo.t1946.physical.math.statistics.stats_statistical_inference", "label": "Non-geographic · 1946 to 2000: Statistical inference, estimation, sampling, and testing", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.math.statistics.stats_statistical_inference", "path": [ { "id": "geo.nongeo", "label": "Non-geographic", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo" }, { "id": "geo.nongeo.t1946", "label": "Non-geographic · 1946 to 2000", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946" }, { "id": "geo.nongeo.t1946.physical", "label": "Physical world and mathematics", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical" }, { "id": "geo.nongeo.t1946.physical.math", "label": "Mathematics and statistics", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.math" }, { "id": "geo.nongeo.t1946.physical.math.statistics", "label": "Statistics and probability", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.math.statistics" }, { "id": "geo.nongeo.t1946.physical.math.statistics.stats_statistical_inference", "label": "Statistical inference, estimation, sampling, and testing", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.math.statistics.stats_statistical_inference" } ] } ], "excerpt": "A screening design is a statistical experimental plan that identifies the few significant factors among many candidates, emphasizing main effects, and typically opens a sequence of experiments.", "snippet": "A screening design is a statistical experimental plan that identifies the few significant factors among many candidates, emphasizing main effects, and typically opens a sequence of experiments.", "node": "physical.math.statistics.stats_statistical_inference", "markdown": "# Screening design\n\nA screening design is an experimental plan in statistics intended to find the few significant factors from a list of many potential ones, concentrating on main effects rather than interactions. The desired output is a ranked list of factors by importance, the best settings for each factor, a good model, and insight into the process under study.[1](https://www.itl.nist.gov/div898/handbook/pri/section3/pri3346.htm) • [2](https://www.itl.nist.gov/div898/handbook/pri/section5/pri59.htm) Screening is typically the first stage of a sequential program: it narrows many candidate variables to a shortlist that later, more detailed experiments can refine.\n\n| Key fact | Detail |\n|---|---|\n| Purpose | Identify the few active factors among many, with emphasis on main effects[1](https://www.itl.nist.gov/div898/handbook/pri/section3/pri3346.htm) |\n| Output | Ranked factor list, best settings, a model, and insight[2](https://www.itl.nist.gov/div898/handbook/pri/section5/pri59.htm) |\n| Typical run sizes | Fractional factorials use a power of two runs; Plackett–Burman designs use a multiple of four and handle \\( n - 1 \\) factors in \\( n \\) runs[3](https://williamghunter.net/george-box-articles/finding-the-active-factors-in-fractionated-screening-experiment) |\n| Common resolution | Resolution III, because it explores many factors with few runs; resolution IV keeps main effects free of two-factor interaction aliasing at the cost of more runs[1](https://www.itl.nist.gov/div898/handbook/pri/section3/pri3346.htm) |\n| Definitive screening design | Three levels, minimum \\( 2m + 1 \\) runs for \\( m \\) continuous factors and \\( 2m + 2 \\) when a categorical factor is involved, main effects unbiased by any second-order effect[4](https://www.jmp.com/content/dam/jmp/documents/en/white-papers/definitive-screening.pdf) |\n| Supersaturated design | Fewer runs than factors plus one (\\( n < d + 1 \\)), so main-effect estimators are necessarily biased[5](https://ar5iv.labs.arxiv.org/html/1510.05248) |\n| Analysis tools | Lenth's pseudo standard error, half-normal plots, Bayesian and shrinkage model-selection methods[6](https://www.jmp.com/en/statistics-knowledge-portal/design-of-experiments/screening-designs/fractional-factorial-designs) • [7](https://asq.org/quality-resources/articles/using-definitive-screening-designs-to-identify-active-first-and-second-order-factor-effects?id=1ea39098244341969ef1ff7eea6638e5) |\n\n## How it works\n\nScreening many factors in few runs rests on the sparsity-of-effects assumption: of k candidate factors, only two or three are likely to matter, so the remaining effects can be treated as noise.[8](https://online.stat.psu.edu/stat503/book/export/html/673) A two-level fractional factorial is denoted \\( 2^{k-r} \\): r generators, which are higher-order interaction terms, specify which fraction of the full factorial runs is selected and thereby fix the aliasing pattern, the set of effects that share each estimated contrast.[6](https://www.jmp.com/en/statistics-knowledge-portal/design-of-experiments/screening-designs/fractional-factorial-designs) A design of resolution R is one in which no p-factor effect is confounded with any other effect containing fewer than R − p factors.[9](https://www.stat.cmu.edu/technometrics/59-69/VOL-03-03/v0303311.pdf)\n\nResolution determines what a small design can deliver. A resolution III design aliases at least one main effect with a two-factor interaction; a resolution IV design keeps main effects free of aliasing with other main effects and two-factor interactions, but can alias them with three-factor interactions and aliases some pairs of two-factor interactions; resolution V separates main effects and all two-factor interactions but typically requires too many runs for screening.[5](https://ar5iv.labs.arxiv.org/html/1510.05248) • [31](https://www.itl.nist.gov/div898/handbook/pri/section3/pri3324.htm) Regular fractional factorials correspond to subspaces of a finite geometry, so their run size must be a power of a prime; Hadamard-based (nonregular) designs such as the Plackett–Burman family allow run sizes that are any multiple of four.[10](https://www.stat.berkeley.edu/~cheng/Handout13.pdf) The price of nonregular designs is complex aliasing: in the 12-run [Plackett–Burman design](https://www.edgepedia.org/plackett-burman-design), each main-effect contrast has in its alias all two-factor interactions not involving that factor, each with coefficient \\( \\pm 1/3 \\).[3](https://williamghunter.net/george-box-articles/finding-the-active-factors-in-fractionated-screening-experiment)\n\n## How it is done\n\nThe practitioner first fixes the factor list, the run budget, and whether second-order effects matter. With a saturated two-level design there are no degrees of freedom for a standard error, so significance is judged using Lenth's pseudo standard error, which treats inactive effects as noise, together with half-normal probability and ordered-data plots.[6](https://www.jmp.com/en/statistics-knowledge-portal/design-of-experiments/screening-designs/fractional-factorial-designs) • [2](https://www.itl.nist.gov/div898/handbook/pri/section5/pri59.htm) For definitive screening designs, adding at least four extra runs, created by introducing fictitious inactive factors, improves detection of two-factor interactions and quadratic curvature; each fake factor adds two runs.[11](https://www.jmp.com/en/statistics-knowledge-portal/design-of-experiments/screening-designs/definitive-screening-designs) • [12](https://community.jmp.com/kvoqx44227/attachments/kvoqx44227/discovery-2016-content/80/2/Lessons%20from%20Definitive%20Screening%20Designs%20Document.pdf) When effects may be aliased, Bayesian methods compute marginal posterior probabilities that each factor is active, and shrinkage selectors such as [Lasso](https://www.edgepedia.org/lasso-statistics) and the Gauss–Dantzig selector (both AICc-based) identify active terms in unrestricted models, with the SHIM method preferred for strong-heredity models.[3](https://williamghunter.net/george-box-articles/finding-the-active-factors-in-fractionated-screening-experiment) • [7](https://asq.org/quality-resources/articles/using-definitive-screening-designs-to-identify-active-first-and-second-order-factor-effects?id=1ea39098244341969ef1ff7eea6638e5)\n\n## Origin\n\nThe main families trace to a sequence of published papers. R. L. Plackett and J. P. Burman's 1946 [Biometrika](https://www.edgepedia.org/biometrika) paper on the design of optimum multifactorial experiments gave constructions for two-level designs with \\( N \\) runs and \\( N - 1 \\) factors, built on R. E. A. C. Paley's 1933 construction of orthogonal matrices.[13](https://doi.org/10.1093/biomet/33.4.305) • [14](https://doi.org/10.1002/sapm1933121311) G. S. Watson's 1961 Technometrics paper studied the group screening method, in which factors are tested in groups.[15](https://doi.org/10.1080/00401706.1961.10489954) Kathleen H. V. Booth and D. R. Cox's 1962 Technometrics paper constructed systematic supersaturated designs using the \\( E(s^{2}) \\) criterion, which makes design-matrix columns as nearly orthogonal as possible.[16](https://doi.org/10.1080/00401706.1962.10490035) Jack P. C. Kleijnen's 1975 Technometrics survey compared incomplete \\( 2^k \\), supersaturated, and group-screening designs and derived new group-screening results.[17](https://doi.org/10.1080/00401706.1975.10489377) Later methodological work includes G. E. P. Box and R. Daniel Meyer's 1993 Bayesian analysis of active factors in fractionated screening experiments,[3](https://williamghunter.net/george-box-articles/finding-the-active-factors-in-fractionated-screening-experiment) M. Hamada and C. F. J. Wu's 1992 treatment of complex aliasing,[18](https://doi.org/10.1080/00224065.1992.11979383) Dennis K. J. Lin and Norman R. Draper's 1992 study of the projection properties of Plackett–Burman designs,[19](https://doi.org/10.2307/1268941) and Ruth K. Meyer and Christopher J. Nachtsheim's 1995 coordinate-exchange algorithm for constructing exact optimal designs.[20](https://doi.org/10.1080/00401706.1995.10485889) Bradley Jones and Christopher J. Nachtsheim's 2011 Journal of Quality Technology paper presented a class of three-level designs for definitive screening in the presence of second-order effects,[4](https://www.jmp.com/content/dam/jmp/documents/en/white-papers/definitive-screening.pdf) building on their 2011 Technometrics work on efficient designs with minimal aliasing;[21](https://doi.org/10.1198/tech.2010.09113) Lili Xiao, Dennis K. J. Lin, and Fengshan Bai gave a conference-matrix construction in 2012,[22](https://doi.org/10.1080/00224065.2012.11917877) and Jones and Nachtsheim extended the family to added two-level categorical factors (2013)[23](https://doi.org/10.1080/00224065.2013.11917921) and to blocking schemes (2015).[24](https://doi.org/10.1080/00401706.2015.1013777) Jones's 2016 Quality Engineering review summarized screening experiments for the 21st century.[25](https://doi.org/10.1080/08982112.2015.1100462)\n\n## Variants\n\n**Fractional factorial designs** (\\( 2^{k-r} \\), runs a power of two) are regular designs with a transparent aliasing structure; a 16-run half fraction of a \\( 2^5 \\) factorial estimates all main effects and two-factor interactions if third-order and higher interactions are negligible.[26](https://pmc.ncbi.nlm.nih.gov/articles/PMC2446451/) **Plackett–Burman designs** are resolution III orthogonal arrays with runs a multiple of four, handling \\( n - 1 \\) factors in \\( n \\) runs.[3](https://williamghunter.net/george-box-articles/finding-the-active-factors-in-fractionated-screening-experiment) **Definitive screening designs** use three levels and \\( 2m + 1 \\) runs: \\( m \\) fold-over pairs plus a center point, with exactly one factor at its middle level in each non-center run, so main effects are unbiased by any second-order effect and all quadratic effects are estimable.[4](https://www.jmp.com/content/dam/jmp/documents/en/white-papers/definitive-screening.pdf) DSDs for six or more factors fit the full quadratic model in any three factors.[11](https://www.jmp.com/en/statistics-knowledge-portal/design-of-experiments/screening-designs/definitive-screening-designs) **Group screening** tests factors in groups, in stages.[15](https://doi.org/10.1080/00401706.1961.10489954) **Supersaturated designs** run fewer experiments than factors, accepting biased main-effect estimators; their use has been controversial.[5](https://ar5iv.labs.arxiv.org/html/1510.05248)\n\n## Applications\n\nScreening designs are used in industrial process development, behavioral intervention research, and experiments on expensive computer simulations. The first DSD conducted in a manufacturing setting took place in 2015 at 3M: six factors (one categorical), three responses, and the minimum \\( 2k + 2 = 14 \\) runs, analyzed with stepwise regression using AICc-based stopping, which simulations suggest finds active effects better than p-value criteria.[12](https://community.jmp.com/kvoqx44227/attachments/kvoqx44227/discovery-2016-content/80/2/Lessons%20from%20Definitive%20Screening%20Designs%20Document.pdf) In behavioral intervention research, fractional factorials are embedded in multiphase strategies where refining-phase follow-up experiments verify aliasing assumptions; the complex aliasing of Plackett–Burman designs makes them hard to recommend for that setting.[26](https://pmc.ncbi.nlm.nih.gov/articles/PMC2446451/)\n\n## Limitations and alternatives\n\nThe central failure mode is aliasing. Resolution III fractional factorials completely confound main effects with one or more two-factor interactions;[4](https://www.jmp.com/content/dam/jmp/documents/en/white-papers/definitive-screening.pdf) a resolution III design for 15 factors in 16 runs aliases each main effect with seven two-factor interactions, while a resolution IV design for eight factors in 16 runs leaves 42 full aliases among two-factor interactions; comparable DSDs have none and additionally estimate quadratic effects.[27](https://www.intechopen.com/chapters/84998) Complex (partial) aliasing can bias effects upward, producing false positives (amalgamation), or downward, causing active factors to be missed (cancellation).[5](https://ar5iv.labs.arxiv.org/html/1510.05248) Adding center points to a resolution III or Plackett–Burman design aliases all quadratic effects together, so curvature can be detected but not attributed to a factor.[28](https://support.minitab.com/en-us/minitab/help-and-how-to/statistical-modeling/doe/supporting-topics/factorial-and-screening-designs/definitive-screening-designs/) Supersaturated designs depend heavily on effect sparsity and can show spurious significance.[29](https://www.sciencedirect.com/science/article/abs/pii/S0167947310000824) Relative to a full factorial, which estimates everything but at \\( 2^k \\) runs, screening trades resolution for economy; relative to response-surface work, screening is a precursor that locates the active subspace, and projections of Plackett–Burman designs into 3, 4, or 5 dimensions support follow-up modeling.[30](https://link.springer.com/article/10.1007/BF01894291) Published sources do not directly compare screening with one-factor-at-a-time experimentation.\n\n## References\n\n1. [5.3.3.4.6. Screening designs (NIST/SEMATECH e-Handbook)](https://www.itl.nist.gov/div898/handbook/pri/section3/pri3346.htm)\n2. [5.5.9. An EDA approach to experimental design (NIST/SEMATECH e-Handbook)](https://www.itl.nist.gov/div898/handbook/pri/section5/pri59.htm)\n3. [Box & Meyer, Finding the Active Factors in Fractionated Screening Experiments (JQT 1993)](https://williamghunter.net/george-box-articles/finding-the-active-factors-in-fractionated-screening-experiment)\n4. [Jones & Nachtsheim, A Class of Three-Level Designs for Definitive Screening in the Presence of Second-Order Effects (JQT 2011, JMP-hosted copy)](https://www.jmp.com/content/dam/jmp/documents/en/white-papers/definitive-screening.pdf)\n5. [Design of Experiments for Screening (arXiv:1510.05248 review)](https://ar5iv.labs.arxiv.org/html/1510.05248)\n6. [Fractional Factorial Designs (JMP Statistics Knowledge Portal)](https://www.jmp.com/en/statistics-knowledge-portal/design-of-experiments/screening-designs/fractional-factorial-designs)\n7. [Using Definitive Screening Designs to Identify Active First- and Second-Order Factor Effects (Errore, Jones, Li, Nachtsheim, JQT 2017)](https://asq.org/quality-resources/articles/using-definitive-screening-designs-to-identify-active-first-and-second-order-factor-effects?id=1ea39098244341969ef1ff7eea6638e5)\n8. [8.1 - More Fractional Fractional Designs (Penn State STAT 503)](https://online.stat.psu.edu/stat503/book/export/html/673)\n9. [Box & Hunter, The 2^k-p Fractional Factorial Designs Part I (Technometrics 1961)](https://www.stat.cmu.edu/technometrics/59-69/VOL-03-03/v0303311.pdf)\n10. [Handout #13: Fractional factorial designs and orthogonal arrays (UC Berkeley)](https://www.stat.berkeley.edu/~cheng/Handout13.pdf)\n11. [Definitive Screening Designs (JMP knowledge portal)](https://www.jmp.com/en/statistics-knowledge-portal/design-of-experiments/screening-designs/definitive-screening-designs)\n12. [Lessons from Definitive Screening Designs (3M, Discovery 2016)](https://community.jmp.com/kvoqx44227/attachments/kvoqx44227/discovery-2016-content/80/2/Lessons%20from%20Definitive%20Screening%20Designs%20Document.pdf)\n13. [R. L. PLACKETT, J. P. BURMAN (1946). THE DESIGN OF OPTIMUM MULTIFACTORIAL EXPERIMENTS. Biometrika.](https://doi.org/10.1093/biomet/33.4.305)\n14. [R. E. A. C. Paley (1933). On Orthogonal Matrices. Studies in Applied Mathematics.](https://doi.org/10.1002/sapm1933121311)\n15. [G. S. Watson (1961). A Study of the Group Screening Method. Technometrics.](https://doi.org/10.1080/00401706.1961.10489954)\n16. [Kathleen H.V. Booth, D. R. Cox (1962). Some Systematic Supersaturated Designs. Technometrics.](https://doi.org/10.1080/00401706.1962.10490035)\n17. [Jack P.C. Kleijnen (1975). Screening Designs for Poly-Factor Experimentation. Technometrics.](https://doi.org/10.1080/00401706.1975.10489377)\n18. [M. Hamada, C. F. J. Wu (1992). Analysis of Designed Experiments with Complex Aliasing. Journal of Quality Technology.](https://doi.org/10.1080/00224065.1992.11979383)\n19. [Dennis K. J. Lin, Norman R. Draper (1992). Projection Properties of Plackett and Burman Designs. Technometrics.](https://doi.org/10.2307/1268941)\n20. [Ruth K. Meyer, Christopher J. Nachtsheim (1995). The Coordinate-Exchange Algorithm for Constructing Exact Optimal Experimental Designs. Technometrics.](https://doi.org/10.1080/00401706.1995.10485889)\n21. [Bradley Jones, Christopher J. Nachtsheim (2011). Efficient Designs With Minimal Aliasing. Technometrics.](https://doi.org/10.1198/tech.2010.09113)\n22. [Lili Xiao, Dennis K. J. Lin, Fengshan Bai (2012). Constructing Definitive Screening Designs Using Conference Matrices. Journal of Quality Technology.](https://doi.org/10.1080/00224065.2012.11917877)\n23. [Bradley Jones, Christopher J. Nachtsheim (2013). Definitive Screening Designs with Added Two-Level Categorical Factors. Journal of Quality Technology.](https://doi.org/10.1080/00224065.2013.11917921)\n24. [Bradley Jones, Christopher J. Nachtsheim (2015). Blocking Schemes for Definitive Screening Designs. Technometrics.](https://doi.org/10.1080/00401706.2015.1013777)\n25. [Bradley Jones (2016). 21st century screening experiments: What, why, and how. Quality Engineering.](https://doi.org/10.1080/08982112.2015.1100462)\n26. [Screening Experiments and the Use of Fractional Factorial Designs in Behavioral Intervention Research](https://pmc.ncbi.nlm.nih.gov/articles/PMC2446451/)\n27. [Designs for Screening Experiments with Quantitative Factors (IntechOpen chapter)](https://www.intechopen.com/chapters/84998)\n28. [Definitive screening designs - Minitab](https://support.minitab.com/en-us/minitab/help-and-how-to/statistical-modeling/doe/supporting-topics/factorial-and-screening-designs/definitive-screening-designs/)\n29. [A comparison of design and model selection methods for supersaturated experiments (Computational Statistics & Data Analysis)](https://www.sciencedirect.com/science/article/abs/pii/S0167947310000824)\n30. [Screening properties of certain two-level designs (Lin & Draper, Metrika, 1995)](https://link.springer.com/article/10.1007/BF01894291)\n31. [5.3.3.2.4. Design resolution: A measure of merit](https://www.itl.nist.gov/div898/handbook/pri/section3/pri3324.htm)\n\n---\n*Topic: Encyclopedia › Physical world and mathematics › Mathematics and statistics › Statistics and probability › Statistical inference, estimation, sampling, and testing*\n\n*Initially written Sep 29, 2026 · Edited: Oct 15, 2026*\n\n*Copyright 2026 EdgeChat AI, a subsidiary of Biostate AI.*\n\nLicense: Edgepedia Community License 1.0, https://www.edgepedia.org/edgepedia/license\n", "same_as": [ "https://www.stat.berkeley.edu/~cheng/Handout13.pdf" ], "url": "https://www.edgepedia.org/screening-design", "markdown_url": "https://www.edgepedia.org/screening-design.md", "license": { "name": "Edgepedia Community License 1.0", "url": "https://www.edgepedia.org/edgepedia/license", "summary": "Free with credit, commercial use included. AI training is open to everyone. For other uses, organizations over USD 100M in revenue or 100M monthly users license separately.", "spdx": "LicenseRef-Edgepedia-Community-1.0" }, "credit": "\"Screening design\", Edgepedia (EdgeChat), https://www.edgepedia.org/screening-design. Edgepedia Community License 1.0.", "credit_md": "\"[Screening design](https://www.edgepedia.org/screening-design)\", Edgepedia (EdgeChat), [https://www.edgepedia.org/screening-design](https://www.edgepedia.org/screening-design). [Edgepedia Community License 1.0](https://www.edgepedia.org/edgepedia/license).", "credit_html": "\"Screening design\", Edgepedia (EdgeChat), https://www.edgepedia.org/screening-design. Edgepedia Community License 1.0.", "speakable": "A screening design is a statistical experimental plan that identifies the few significant factors among many candidates, emphasizing main effects, and typically opens a sequence of experiments." }