A method is described for the minimization of a function of n variables, which depends on the comparison of function values at the (n 4-1) vertices of a general simplex, followed by the replacement of the vertex with the highest value by another point. The simplex adapts itself to the local landscape, and contracts on to the final minimum. The method is shown to be effective and computationally compact. A procedure is given for the estimation of the Hessian matrix in the neighbourhood of the minimum, needed in statistical estimation problems.

SUMMARYCriteria for evaluating different intercropping situations are suggested, and the Land Equivalent Ratio (LER) concept is considered for situations where intercropping must be compared with growing each crop sole. The need to use different standardizing sole crop yields in forming LERs is discussed, and a method of calculating an ‘effective LER’ is proposed to evaluate situations where the yield proportions achieved in intercropping are different from those that might be required by a farmer. The possible importance of effective LERs in indicating the proportions of crops likely to give biggest yield advantages is discussed.

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This book is about the statistical principles behind the design of effective experiments and focuses on the practical needs of applied statisticians and experimenters engaged in design, implementation and analysis. Emphasising the logical principles of statistical design, rather than mathematical calculation, the authors demonstrate how all available information can be used to extract the clearest answers to many questions. The principles are illustrated with a wide range of examples drawn from real experiments in medicine, industry, agriculture and many experimental disciplines. Numerous exercises are given to help the reader practise techniques and to appreciate the difference that good design can make to an experimental research project. Based on Roger Mead's excellent Design of Experiments, this new edition is thoroughly revised and updated to include modern methods relevant to applications in industry, engineering and modern biology. It also contains seven new chapters on contemporary topics, including restricted randomisation and fractional replication.