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| 題 名 | Efficient Semi-Latin Squares |
|---|---|
| 作 者 | Bailey,R. A.; | 書刊名 | Statistica Sinica |
| 卷 期 | 2:2 1992.07[民81.07] |
| 頁 次 | 頁413-437 |
| 分類號 | 319.5 |
| 關鍵詞 | 拉丁方; 不完全區組設計; 最優設計; Efficiency factor; Incomplete block design; Latin square; Optimal design; Semi-Latin square; Trojan square; |
| 語 文 | 英文(English) |
| 英文摘要 | Consider an n × n square array in which each small square is divided into k plots. A semi-Latin square is an allocation of nk treatments to the plots of such an array so that each treatment occurs once in each row and once in each column. Several different practical situations are discussed which all lead to this same abstract structure. There are two reasonable models for data from semi-Latin squares. Under the first, all semi-Latin squares are equally efficient, while under the second there is a wider range of efficiencies. Attention is focused on the problem of finding efficient semi-Latin squares for the second model. There is a family of semi-Latin squares called Trojan squares, which are know to be optimal, as are certain squares derived from the Trojan squares. Unfortunately, these do not exist for all Paris of values of n and k. Recent agricultural experiments have required efficient semi-Latin squares for some of these other values of n and k. New designs for these values are presented and their deficiencies and possible optimality discussed. |
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