One missing value problem in Latin square design of any order: Exact analysis of variance
This research proposes a simplified exact approach based on the general linear model for solving the K × K Latin square design (LSD) with one replicate and one missing value, given the lack of ready-made mathematical formulas for the sub-variance. Under the proposed scheme, the effects of the potent...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2017-01-01
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| Series: | Cogent Engineering |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1080/23311916.2017.1411222 |
| _version_ | 1797705031961542656 |
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| author | Kittiwat Sirikasemsuk Kanogkan Leerojanaprapa |
| author_facet | Kittiwat Sirikasemsuk Kanogkan Leerojanaprapa |
| author_sort | Kittiwat Sirikasemsuk |
| collection | DOAJ |
| description | This research proposes a simplified exact approach based on the general linear model for solving the K × K Latin square design (LSD) with one replicate and one missing value, given the lack of ready-made mathematical formulas for the sub-variance. Under the proposed scheme, the effects of the potential variable were determined by means of the regression sums of squares under the full and reduced treatment models. The mathematical expressions could be applied to the LSD with one missing value of any order. Moreover, the treatment, row and column sums of squares are unbiased. |
| first_indexed | 2024-03-12T05:30:24Z |
| format | Article |
| id | doaj.art-01430f4c6bf84b1c9d4151e47afba03c |
| institution | Directory Open Access Journal |
| issn | 2331-1916 |
| language | English |
| last_indexed | 2024-03-12T05:30:24Z |
| publishDate | 2017-01-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Cogent Engineering |
| spelling | doaj.art-01430f4c6bf84b1c9d4151e47afba03c2023-09-03T06:54:24ZengTaylor & Francis GroupCogent Engineering2331-19162017-01-014110.1080/23311916.2017.14112221411222One missing value problem in Latin square design of any order: Exact analysis of varianceKittiwat Sirikasemsuk0Kanogkan Leerojanaprapa1King Mongkut’s Institute of Technology LadkrabangKing Mongkut’s Institute of Technology LadkrabangThis research proposes a simplified exact approach based on the general linear model for solving the K × K Latin square design (LSD) with one replicate and one missing value, given the lack of ready-made mathematical formulas for the sub-variance. Under the proposed scheme, the effects of the potential variable were determined by means of the regression sums of squares under the full and reduced treatment models. The mathematical expressions could be applied to the LSD with one missing value of any order. Moreover, the treatment, row and column sums of squares are unbiased.http://dx.doi.org/10.1080/23311916.2017.1411222experimental designincomplete latin squareanovageneral linear model |
| spellingShingle | Kittiwat Sirikasemsuk Kanogkan Leerojanaprapa One missing value problem in Latin square design of any order: Exact analysis of variance Cogent Engineering experimental design incomplete latin square anova general linear model |
| title | One missing value problem in Latin square design of any order: Exact analysis of variance |
| title_full | One missing value problem in Latin square design of any order: Exact analysis of variance |
| title_fullStr | One missing value problem in Latin square design of any order: Exact analysis of variance |
| title_full_unstemmed | One missing value problem in Latin square design of any order: Exact analysis of variance |
| title_short | One missing value problem in Latin square design of any order: Exact analysis of variance |
| title_sort | one missing value problem in latin square design of any order exact analysis of variance |
| topic | experimental design incomplete latin square anova general linear model |
| url | http://dx.doi.org/10.1080/23311916.2017.1411222 |
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