基于Frank Wilcoxon秩和检验的多元统计分析在酿酒葡萄分级中的应用

Application of Multivariate Statistical Analysis Based on Rank Sum Test in Wine Grape Classification

利用2012全国数学建模竞赛A题所提供的某一年份一些葡萄酒的评价结果及该年份这些葡萄酒和酿酒葡萄的成分数据,首先采用Frank Wilcoxon秩和检验对两组评酒员的评价结果有无显著性差异进行了判别,随后对两组葡萄酒样品评价结果的变异系数进行了比较,得出第二组结果的可信度更高;其次对酿酒葡萄的理化指标进行了主成分分析,并将葡萄酒的质量作为一级指标,采用聚类分析法,利用SPSS软件对酿酒葡萄进行了分级,数值结果说明了方法的有效性.

In terms of some wine evaluation results and wine grape composition data of A from the 2012 National Mathematical Modeling Contest, the existence of the significant difference on the liquor judge evaluation results is first distinguished by rank sum test, then coefficient of variation of evaluation results of two groups is compared. It follows that the evaluation results of the second group is of higher reliability. Secondly, the principle component analysis of wine grape physicochemical index is established, and the wine grape is classified with the quality of wine as a level indicator by cluster analysis and software. Finally, the numerical results show the effectiveness of the proposed method.