【摘要】 本文以方差分析的观点探讨正交试验设计的实践与理论问题,及试验误差与效率问题。作者运用试验实践数据资料,在相同的试验规模下,分析不同设计方案的误差与效率,并与随机区组类设计比较以评价不同方案的优、劣,并对正交试验上的某些存在向题总结出八点改进意见。更多还原

【Abstract】 The theory of variance components was used to analyse the orthogonal factorial design in this study, and compared with the usual types of randomized designs (including the completely randomized design, randomized block design, and BIB design,etc.)The data of the field experiment (taked from the "Research on Appropriate Rice Seedlings, Growing in A Greenhouse Design, for the Power Transplanters" )were utilized for numerical examples to verify the reasoning that the author set up.In order to obtain the appropriate F-test, the estimate of the expected variance components of the orthogonal factorial design is necessary. Statistical analyses of different types of designs were calculated from the same size of experiments (the same numbers of plots or runs) for comparing the error variance and the relative efficency of these experiments.The statistical analysis shows that the analysis of the error variance of an orthogonal factorial design with replicates by the indirect method of subtracting from the total sum of squares is much more convenient and time-saving than that of calculating directly from an orthogonal main effect, plan.It is not advisable to eliminate the interactions from the model without conclusive evidence that it is appropriate to do so. An example from a wrong conclusion made by a factory experiment is used to emphasize this idea.The analysis of multiple factorial design with orthgonal main effect plan is not considered to be worth recommending because there would be too many interactions in the multiple factorial model, which could’t be separated. A better idea for conducing multiple factorial experiments is to organize the factors and levels by the orthogonal main effect plan, but the treatment combinations would be arranged and analysed by the methods of the types of randomized designs, such, as Completely Randomized Design, Randomized Block Design, BIB, PB1B, or other multiple factorial designs.更多还原