【统计学】第九章分类数据分析

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分类数据分析与卡方统计量

统计数据的类型有：分类数据、顺序数据和数值型数据，分类数据是对事物进行分类的结果，其特征是，结果虽然是用数值显示，但是不同的数值描述了调查对象的不同特征。
对分类数据进行分析的统计方法主要是利用卡方分布，又称卡方检验。
卡方检验的应用主要表现在：
1.拟合优度检验--一个变量的检验
2.独立向检验(列联表是进行独立性检验的重要工具)--两个变量之间的检验
卡方统计量：χ2主要用于两个分类变量之间的相关度。若用f0表示观察值频数，用f0表示期望频数，则χ2统计量可以写为χ2=∑fe(f0fe)2
统计量有如下特征：
1.χ2≥0,因为它是对平方结果的汇总
2.χ2的分布于自由度有关
3.χ2描述了观察值与期望值的接近程度
χ2检验正是通过对χ2的计算结果与χ2的临界值进行比较，做出是否拒绝原假设的决策。

拟合优度检验

拟合优度检验：拟合优度检验是用χ2统计量进行统计显著性检验的重要程度之一。它是依据总体分布的状况，计算出分类变量中的各类别的期望频数，与分布的观察频数进行比较，判断期望频数是否有显著差异，从而达到对分类变量进行分析的目的。

列联分析：独立性检验

拟合优度检验是对一个变量的检验，当遇到两个分类变量的问题看这两个变量是否存在联系
对于两个分类变量的分析，成为独立性分析

列联表中的相关测度

相关系数：一般用来描述2X2列联表，=nχ2，n为列联表中的总频数，也就是样本量
列联相关系数：当行数或列数大于2的时候，使用列联表关系系数，计算公式c=χ2+nχ2,当c=0时，两个变量相互独立
优点：1.计算简便，2.对总体分布没有要求；缺点：最大值依赖于行数，随着R和C的增大而增大，根据不同行数和列数计算的列联系数不便于比较，除非两个列联表的行数与列数一致
V相关系数：由于系数无上限，c系数小于1，提出V系数，V=nmin[(R1),(C1)]2,两个变量相互独立时，V=0，两个变量完全相关时，V=1，V的取值介入0~1之间
数值分析
前面利用卡方分布对两个分类变量之间的相关性进行了统计检验

列联分析中应注意的问题

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