Solving the incomplete data problem in Greco-Latin square experimental design by exact-scheme analysis of variance without data imputation
This study introduced a novel exact-scheme analysis of variance to tackle the challenge of incomplete data within the Greco-Latin square experimental design (GLSED), specifically for scenarios with a single missing observation across any treatment and block level, thus eliminating the need for conve...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-11-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20241601 |
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| author | Kittiwat Sirikasemsuk Sirilak Wongsriya Kanogkan Leerojanaprapa |
| author_facet | Kittiwat Sirikasemsuk Sirilak Wongsriya Kanogkan Leerojanaprapa |
| author_sort | Kittiwat Sirikasemsuk |
| collection | DOAJ |
| description | This study introduced a novel exact-scheme analysis of variance to tackle the challenge of incomplete data within the Greco-Latin square experimental design (GLSED), specifically for scenarios with a single missing observation across any treatment and block level, thus eliminating the need for conventional data imputation methods. This approach innovatively addresses and mitigates the bias in the treatment sum of squares, a significant drawback of traditional missing plot techniques, by providing a precise, exact-scheme-based formula for calculating the treatment sum of squares in fixed-effect GLSED contexts with unrecorded values. Moreover, it offers a method for correcting biased treatment sum of squares values, presenting an adjustment mechanism for instances where the least squares method was previously employed to estimate missing values. This comprehensive strategy not only enhances the methodological accuracy and integrity of GLSED studies but also contributes significantly to the field by offering a solution to navigate the complexities of incomplete datasets without resorting to data imputation, thus improving the rigor and validity of experimental designs in the face of missing data challenges. |
| format | Article |
| id | doaj-art-ab276aeff789426f8c645580eea8dd2b |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-ab276aeff789426f8c645580eea8dd2b2025-01-23T07:53:24ZengAIMS PressAIMS Mathematics2473-69882024-11-01912335513357110.3934/math.20241601Solving the incomplete data problem in Greco-Latin square experimental design by exact-scheme analysis of variance without data imputationKittiwat Sirikasemsuk0Sirilak Wongsriya1Kanogkan Leerojanaprapa2Department of Industrial Engineering, School of Engineering, King Mongkut's Institute of Technology Ladkrabang, Bangkok, ThailandDepartment of Industrial Engineering, School of Engineering, King Mongkut's Institute of Technology Ladkrabang, Bangkok, ThailandStatistics Department, Faculty of Science, King Mongkut's Institute of Technology Ladkrabang, Bangkok, ThailandThis study introduced a novel exact-scheme analysis of variance to tackle the challenge of incomplete data within the Greco-Latin square experimental design (GLSED), specifically for scenarios with a single missing observation across any treatment and block level, thus eliminating the need for conventional data imputation methods. This approach innovatively addresses and mitigates the bias in the treatment sum of squares, a significant drawback of traditional missing plot techniques, by providing a precise, exact-scheme-based formula for calculating the treatment sum of squares in fixed-effect GLSED contexts with unrecorded values. Moreover, it offers a method for correcting biased treatment sum of squares values, presenting an adjustment mechanism for instances where the least squares method was previously employed to estimate missing values. This comprehensive strategy not only enhances the methodological accuracy and integrity of GLSED studies but also contributes significantly to the field by offering a solution to navigate the complexities of incomplete datasets without resorting to data imputation, thus improving the rigor and validity of experimental designs in the face of missing data challenges.https://www.aimspress.com/article/doi/10.3934/math.20241601design of experimentanovalinear algebra equationsgreco-latin square designunrecorded observationmissing value |
| spellingShingle | Kittiwat Sirikasemsuk Sirilak Wongsriya Kanogkan Leerojanaprapa Solving the incomplete data problem in Greco-Latin square experimental design by exact-scheme analysis of variance without data imputation AIMS Mathematics design of experiment anova linear algebra equations greco-latin square design unrecorded observation missing value |
| title | Solving the incomplete data problem in Greco-Latin square experimental design by exact-scheme analysis of variance without data imputation |
| title_full | Solving the incomplete data problem in Greco-Latin square experimental design by exact-scheme analysis of variance without data imputation |
| title_fullStr | Solving the incomplete data problem in Greco-Latin square experimental design by exact-scheme analysis of variance without data imputation |
| title_full_unstemmed | Solving the incomplete data problem in Greco-Latin square experimental design by exact-scheme analysis of variance without data imputation |
| title_short | Solving the incomplete data problem in Greco-Latin square experimental design by exact-scheme analysis of variance without data imputation |
| title_sort | solving the incomplete data problem in greco latin square experimental design by exact scheme analysis of variance without data imputation |
| topic | design of experiment anova linear algebra equations greco-latin square design unrecorded observation missing value |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241601 |
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