Partially Replicated Latin Squares
Abstract
Latin squares have been used for over 30 years in agricultural field trials (1). Often the double restriction imposed by the row and column arrangement brought a welcome reduction in the mean square for error. The row and column mean squares were of no interest. Eventually the Latin square arrangement found application where the rows and columns corresponded to clearly defined physical entities. Youden (3) in studies on tobacco mosaic virus observed that the number of lesions produced on leaves depended upon the position of the leaf on the plant and that plants also differed markedly in susceptibility to lesions. Furthermore, for a given lot of plants, the effect of leaf position was closely the same from one plant to another. Very large reductions in the error mean square resulted from the use of a Latin square. The plants were columns and leaf positions were rows. Here there was some interest in the mean squares for rows and columns though the chief concern was with the treatments applied to the leaves. Later Yates (2) introduced confounding into Latin square designs. Probably it was inevitable that the Latin square arrangement would be tried when the rows and columns were used for factors that not only were likely to interact with the treatments (letters) but also with each other. The form or appearance of a Latin square remains but the substance is lost. The fractional replication of a factorial experiment that results from this practice is a particularly unfortunate one…
Integrity signals
Registry
Cites
Statistics
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
A 4 × 5 fractionally replicated Latin Square was used to test the hypotheses, deployed in accordance with principles outlined in the prior literature.
“A 4 × 5 fractionally replicated Latin Square [50] was used to test these hypotheses (Table 1a) and was deployed in accordance with the principles outlined in the prior literature [51].”
From Marketing Tactics for Sustainable Fashion and the Circular Economy: The Impact of Ethical Labels on Fast Fashion Choice (2023) · cites this paper as [50]
Cites
Statistical Methods for Research Workers
Fisher, R. A. (1945) · American Journal of Clinical Pathology · doi:10.1093/ajcp/15.11.552b · Cited by 10,883 · see citing works
Design and Analysis of Factorial Experiments
Yates, F. (1958) · Rothamsted Repository (Rothamsted Repository) · Cited by 472 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Statistical principles in experimental design.
Winer, B. J. (1962) · McGraw-Hill Book Company · doi:10.1037/11774-000 · Cited by 27,137 · see citing works
Statistical Design Applied to Product Design
Hunter, J. S. (1985) · Journal of Quality Technology · doi:10.1080/00224065.1985.11978971 · Cited by 184 · see citing works
Self-citationSecond report on a cooperative investigation of the composition of two silicate rocks
Stevens, R. E., & others, A. (1960) · doi:10.3133/b1113 · Cited by 80 · see citing works
Graphical diagnostics for occupancy models with imperfect detection
Warton, D. I., Stoklosa, J., Guillera‐Arroita, G., MacKenzie, D. I., & Welsh, A. H. (2017) · Methods in Ecology and Evolution · doi:10.1111/2041-210x.12761 · Cited by 62 · see citing works
Hamlin, R. P., McNeill, L. S., & Moore, V. (2015) · Public Health Nutrition · doi:10.1017/s1368980014002997 · Cited by 60 · see citing works
The consumer testing of food package graphic design
Hamlin, R. P. (2016) · British Food Journal · doi:10.1108/bfj-03-2015-0105 · Cited by 28 · see citing works
Design and Analysis of Two-Level Factorial Experiments With Partial Replication
Liao, C., & Chai, F. (2009) · Technometrics · doi:10.1198/tech.2009.0007 · Cited by 22 · see citing works
Retailer branding of consumer sales promotions. A major development in food marketing?
Hamlin, R. P., Lindsay, S., & Insch, A. (2011) · Appetite · doi:10.1016/j.appet.2011.10.008 · Cited by 19 · see citing works
The rise and fall of the Latin Square in marketing: A cautionary tale
Hamlin, R. P. (2005) · European Journal of Marketing · doi:10.1108/03090560510581809 · Cited by 22 · see citing works
A Note on Partially Replicated Orthogonal Main-Effect Plans
Pigeon, J. G., & McAllister, P. R. (1989) · Technometrics · doi:10.2307/1268822 · Cited by 15 · see citing works
Spiegelman, C. H., & Tobin, W. A. (2012) · Law Probability and Risk · doi:10.1093/lpr/mgs028 · Cited by 14 · see citing works
Hamlin, R., & Hamlin, B. (2020) · Nutrients · doi:10.3390/nu12061545 · Cited by 12 · see citing works
Functional or constructive attitudes: Which type drives consumers' evaluation of meat products?
Hamlin, R. P. (2016) · Meat Science · doi:10.1016/j.meatsci.2016.02.038 · Cited by 12 · see citing works
Hamlin, R. P., & McNeill, L. S. (2023) · Sustainability · doi:10.3390/su151310331 · Cited by 10 · see citing works
A Class of Partially Replicated Two Level Fractional Factorial Designs
Lupinacci, P. J., & Pigeon, J. G. (2008) · Journal of Quality Technology · doi:10.1080/00224065.2008.11917724 · Cited by 10 · see citing works
Garrett, R. G. (2013) · Geochemistry Exploration Environment Analysis · doi:10.1144/geochem2011-085 · Cited by 7 · see citing works
Package graphic design development
Hamlin, R. P., Gin, M. J., Nyhof, F., & Bogue, J. (2017) · British Food Journal · doi:10.1108/bfj-09-2016-0428 · Cited by 7 · see citing works
Hamlin, R. (2022) · Nutrients · doi:10.3390/nu14214649 · Cited by 6 · see citing works
Assessing interaction effects in Latin square-type designs
Kohli, R. (1988) · International Journal of Research in Marketing · doi:10.1016/0167-8116(88)90014-6 · Cited by 6 · see citing works
On the Construction of Minimal Partially Replicated Orthogonal Main-Effect Plans
Jacroux, M. (1993) · Technometrics · doi:10.1080/00401706.1993.10484991 · Cited by 6 · see citing works
Partial duplication in two-level fractional factorial designs
Liau, P.-H. (2006) · Statistical Papers · doi:10.1007/s00362-006-0018-3 · Cited by 4 · see citing works
Annual Report 1956 National Bureau of Standards
Standards, N. B. O. (1956) · doi:10.6028/nbs.mp.220 · Cited by 4 · see citing works
Pollution Determined by Using Magnetic Susceptibility Measurements: A Case Study from İzmir-Aliağa
Kamacı, Z., & Uysal, G. (2017) · Acta Physica Polonica A · doi:10.12693/aphyspola.132.487 · Cited by 3 · see citing works
Shorter Communication: A Note on Partially Replicated Orthogonal Main-Effect Plans
Pigeon, J. G., & McAllister, P. R. (1989) · Technometrics · doi:10.1080/00401706.1989.10488518 · Cited by 2 · see citing works
Classification of Latin squares
Lakić, N. (2002) · Journal of Agricultural Sciences Belgrade · doi:10.2298/jas0201105l · Cited by 2 · see citing works
Multiple Factor Experimentation with Reference to Biosynthetic Yield of Aterrimin
Lewis, J. C., & Ijichi, K. (1957) · Applied Microbiology · doi:10.1128/am.5.2.124-130.1957 · Cited by 2 · see citing works
Hamada, M. S. (2022) · Quality Engineering · doi:10.1080/08982112.2022.2036345 · Cited by 1 · see citing works
Bestimmung des Umfanges von Versuchen in lateinischen Quadraten
Rasch, D. (1975) · Biometrische Zeitschrift · doi:10.1002/bimj.19750170706 · Cited by 1 · see citing works
Keedwell, A. D. (2014) · Wiley StatsRef: Statistics Reference Online · doi:10.1002/9781118445112.stat02251
Ku, H. H., & Rosenblatt, J. R. (2001) · Springer eBooks · doi:10.1007/978-1-4613-0179-0_103
A Conversation with J. Stuart (Stu) Hunter
Veaux, R. D. D. (2020) · Statistical Science · doi:10.1214/19-sts766
Keedwell, A. D. (2004) · Encyclopedia of Statistical Sciences · doi:10.1002/0471667196.ess0896
Keedwell, A. D. (2005) · Encyclopedia of Statistical Sciences · doi:10.1002/0471667196.ess0896.pub2
(1984) · Elsevier eBooks · doi:10.1016/b978-0-08-091831-0.50018-7
Keedwell, A. D. (2008) · Encyclopedia of Statistical Sciences · doi:10.1002/0471667196.ess0896.pub3
- Authors
- Youden, W. J., & Hunter, J. S.
- ORCID
- Hunter, J. S.
- Venue
- Biometrics
- Publisher
- JSTOR
- Published
- 1955-12
- Volume
- 11
- Issue
- 4
- Pages
- 399
- ISSN
- 0006-341X (ISSN-L)
- OpenAlex
- W2320093983
- Cited by
- 35
- References
- 2
- Citations by year
- 2023: 1 · 2022: 2 · 2020: 2 · 2017: 3 · 2016: 2 · 2014: 2 · 2013: 1 · 2012: 1
- FWCI
- 1.32
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Biometrics (publishedVersion)
- Topics
- Social Sciences › Decision Sciences › Management Science and Operations Research › Optimal Experimental Design Methods
- Physical Sciences › Mathematics › Discrete Mathematics and Combinatorics › Advanced Combinatorial Mathematics
- Life Sciences › Agricultural and Biological Sciences › Ecology, Evolution, Behavior and Systematics › Agriculture, Soil, Plant Science
- Keywords
- Latin squares, fractional replication, factorial design, confounding, row and column effects, interaction effects, agricultural field trials
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
