对应分析应用中的量纲问题

对应分析中原始数据矩阵Ｘ作ｚｉｊ＝ｘｉｊ－ｘｉ．ｘ．ｊ／Ｔｘｉ．ｘ．ｊ变换，变换后的数据有量纲，因此Ｒ型分析的特征向量有量纲，Ｑ型分析的特征向量无量纲，两种分析方法并不对称。同一物理量用不同量纲，其数量值有变化，对应分析的结果也有变化，其结论不一，甚至结论对立，因此使用有量纲的数据作对应分析是不恰当的，应该用无量纲的数据作对应分析。

ON THE DIMENSION PROBLEM IN APPLIANCE OF CORRESPONDENCE ANALYSIS

In correspondence analysis,matrix X with raw data should be transformed into another one by z ij =x ij -x i. x .j /Tx i. x .j .We will still obtain matrix with dimensional data. However ,the characteristic vector in R-type analysis is a dimensional one,but the characteristic vector in Q-type analysis is a non -dimensional one,thus we may treat the same problem with two asymmetric methods.If we measure the same physical quantity by different units,it will result in the problem of diverse magnitudes ,furthermore we may acquire different or opposite conclusions due it different outcomes by correspondence analysis.Therefore,we must first standarded the data to ensure the matrix with only non-dimensional elements,and then do correspondence analysis .