• 作者： 葉樹藩
• 作者服務機構： 國立臺灣大學農學院
• 中文摘要： 1.本研究之目的在尋求3x3x3部份混同設計多次試驗資料在各種情形下之合理高效合併分析
  法，藉以探求正確之試驗因子效應，因子間之交感及試驗中各種平均數或總數間真正差異，以供實
  際應用。
  2.瓊麻、亞麻、小米及甘藷等肥料三要素試驗及大豆行株距試驗等多次試驗各項性態調查測定
  記錄為本研究主要實際資料，該等試驗皆用3×3×3部份混同設計。今視各資料之性質，研究其適
  當合併分析法。
  3.茲按變方分析之基本原理導得 部份混同設計裂區合併分析法，複因子合併分析法及多次
  試驗重複聯合作為一個試驗重複合併分析法三種。第一法適合於多年生作物，各試項試區固定，多
  次收獲物測定值之合併分析；第二法適合於多地區多年份試驗養料之合併分析；第三法適用於僅欲
  明瞭主試因子效應及因子間交感之多次試驗資料之合併分析。一般情形之下第一及第二法之相對效
  率比第三法為高，獲得有關資料之實情亦多，惟亦隨研究作物之性態不同而異。例如瓊麻乾纖維，
  亞麻種子及小米子實則以第三法之相對效率為高。
  4. 混同設計多次試驗資料試項收量總數，仍可應用 Yates 氏矯正式，並由本研究證明試項
  矯正總數期望值中除含試項效應及機差外，同時含所有區集之平均效應，如兩試項矯正總數對減，
  區集效應自然抵銷。
  5.茲根據試項分次矯正與綜合矯正收量總數公式，機差變方之定義，及期望值定理等導得不同
  混同?在各種場合下之試項矯正收量總數差異變方公式。該等公式分列於各項試驗資料分析研究項
  下。並用各資料分析所得機差均方代入，以求試項矯正總數差異均方，差異標準機差及最小顯著差
  等，藉供測驗矯正總數差異之顯著性。
  6.本研究各項實際試驗資料分析所得各項實用結果，例如欲使瓊麻乾纖維增產每公頃用 N200
  公斤，P50公斤，K50公斤，於後期施用者效果最隹；欲小米子實增產每公頃用N80公斤，P80公
  斤，K40公斤效果最大；欲生產含油量多之大豆，宜推行春作夏作及寬行疏植。以上等等結果，皆
  可供推廣應用。
  7.其他詳情請參閱本文。e
• 英文摘要： 1. The purpose of this study is to find out the effective methods for the com-bined analysis of a grouped data from the partial confounding of effects in factorial experiments in order to increase the precision of the estimates of maineffects of the experimental factors and their important interactions, and to obtainthe real differences of comparisons between various treatment means (or totals)for the practical use. 2. Five kinds of the grouped data obtained from the 3x3×3 NPK tests on sisal,flax, millet, and sweet potatoes, and the variety-spacing test on soybeans wereused in this study. In the whole study, the properties of the data, were examinedfirst, and then the combined analysis methods were tested for the fittness. 3. Three combined analysis methods are deduced from the basic principles ofthe analysis of variance, namely, the method of analysis as the split plot confoundingwhich is good for the yields of perennial crops produced from same plot indifferent seasons, the method of analysis as a multiple factorial experiment whichis good for the data of the experiments conducted at several places in differentyears, and the method of analysis of grouped data as a single factorial confoundingexperiment which is good for knowing the main effects of the experimental factors,and their important interactions. Speaking generally, the first and the secondmethods are more efficient than the third method. However, the efficiency of themethod used are varied with the characters studied sometimes. For example, thethird method is more efficient than the first and the second method when thesemethods are used for the analyses for the yield of the dried sisal fiber, the seedyield of flax, and the yield of millet: 4. By this study, it is verified that Yates' formula for adjusting treatment totalis still valid for applying to the grouped data of confounding in facterial experi-ments. The block effects can be cancelled when two adjusted treatment totals arein comparison. 5. The formulas for the variance of various adjusted treatment total differencesare deduced from the estimators of the true treatment total differences, the definitionof error variance, and the theories of expectation. These formulas are presented inthe sections of various crop experiments studied in this paper. In these formulas,the substitution of the error mean squares of the corresponding experiments for will give the mean squares of the adjusted treatment total differences and thus thestandard error and theleast significant differences are calculated. Consequently, thesignificance of adjusted treatment total differences can be tested. 6. Results from this study appeared that there would be some benefit for thepractical use. The yields of the dried sisal fiber would be increased if the fertilizerwas applied at the levels of N-200 (kg./ha.), P-50 (kg/ha.) and K-50 (kg/ha.). Theyield of millet would also be increased if the fertilizer was applied at the levels ofN-80 (kg/ha.), P-80 (kg/ha.) and K-40 (kg/ha.). Soybeans planted with wider spacingwould have higher oil content in either spring or summer cropping. 7. As to the other results, the readers are requested to refer to the text ofthis study report.
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