分类数据分析

Posted 2022-08-20 pandaboy1123

Evernote Export

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

%23%23%23%23%20%E5%88%86%E7%B1%BB%E6%95%B0%E6%8D%AE%E5%88%86%E6%9E%90%E4%B8%8E%E5%8D%A1%E6%96%B9%E7%BB%9F%E8%AE%A1%E9%87%8F%0A%3E%E7%BB%9F%E8%AE%A1%E6%95%B0%E6%8D%AE%E7%9A%84%E7%B1%BB%E5%9E%8B%E6%9C%89%EF%BC%9A%E5%88%86%E7%B1%BB%E6%95%B0%E6%8D%AE%E3%80%81%E9%A1%BA%E5%BA%8F%E6%95%B0%E6%8D%AE%E5%92%8C%E6%95%B0%E5%80%BC%E5%9E%8B%E6%95%B0%E6%8D%AE%EF%BC%8C%E5%88%86%E7%B1%BB%E6%95%B0%E6%8D%AE%E6%98%AF%E5%AF%B9%E4%BA%8B%E7%89%A9%E8%BF%9B%E8%A1%8C%E5%88%86%E7%B1%BB%E7%9A%84%E7%BB%93%E6%9E%9C%EF%BC%8C%E5%85%B6%E7%89%B9%E5%BE%81%E6%98%AF%EF%BC%8C%E7%BB%93%E6%9E%9C%E8%99%BD%E7%84%B6%E6%98%AF%E7%94%A8%E6%95%B0%E5%80%BC%E6%98%BE%E7%A4%BA%EF%BC%8C%E4%BD%86%E6%98%AF%E4%B8%8D%E5%90%8C%E7%9A%84%E6%95%B0%E5%80%BC%E6%8F%8F%E8%BF%B0%E4%BA%86%E8%B0%83%E6%9F%A5%E5%AF%B9%E8%B1%A1%E7%9A%84%E4%B8%8D%E5%90%8C%E7%89%B9%E5%BE%81%E3%80%82%0A%3E%E5%AF%B9%E5%88%86%E7%B1%BB%E6%95%B0%E6%8D%AE%E8%BF%9B%E8%A1%8C%E5%88%86%E6%9E%90%E7%9A%84%E7%BB%9F%E8%AE%A1%E6%96%B9%E6%B3%95%E4%B8%BB%E8%A6%81%E6%98%AF%E5%88%A9%E7%94%A8%E5%8D%A1%E6%96%B9%E5%88%86%E5%B8%83%EF%BC%8C%E5%8F%88%E7%A7%B0%E5%8D%A1%E6%96%B9%E6%A3%80%E9%AA%8C%E3%80%82%0A%3E%E5%8D%A1%E6%96%B9%E6%A3%80%E9%AA%8C%E7%9A%84%E5%BA%94%E7%94%A8%E4%B8%BB%E8%A6%81%E8%A1%A8%E7%8E%B0%E5%9C%A8%EF%BC%9A%0A%3E1.%E6%8B%9F%E5%90%88%E4%BC%98%E5%BA%A6%E6%A3%80%E9%AA%8C--%E4%B8%80%E4%B8%AA%E5%8F%98%E9%87%8F%E7%9A%84%E6%A3%80%E9%AA%8C%0A%3E2.%E7%8B%AC%E7%AB%8B%E5%90%91%E6%A3%80%E9%AA%8C(%E5%88%97%E8%81%94%E8%A1%A8%E6%98%AF%E8%BF%9B%E8%A1%8C%E7%8B%AC%E7%AB%8B%E6%80%A7%E6%A3%80%E9%AA%8C%E7%9A%84%E9%87%8D%E8%A6%81%E5%B7%A5%E5%85%B7)--%E4%B8%A4%E4%B8%AA%E5%8F%98%E9%87%8F%E4%B9%8B%E9%97%B4%E7%9A%84%E6%A3%80%E9%AA%8C%0A%3E**%E5%8D%A1%E6%96%B9%E7%BB%9F%E8%AE%A1%E9%87%8F**%EF%BC%9A%24%5Cchi%5E2%24%E4%B8%BB%E8%A6%81%E7%94%A8%E4%BA%8E%E4%B8%A4%E4%B8%AA%E5%88%86%E7%B1%BB%E5%8F%98%E9%87%8F%E4%B9%8B%E9%97%B4%E7%9A%84%E7%9B%B8%E5%85%B3%E5%BA%A6%E3%80%82%E8%8B%A5%E7%94%A8%24f_0%24%E8%A1%A8%E7%A4%BA%E8%A7%82%E5%AF%9F%E5%80%BC%E9%A2%91%E6%95%B0%EF%BC%8C%E7%94%A8%24f_0%24%E8%A1%A8%E7%A4%BA%E6%9C%9F%E6%9C%9B%E9%A2%91%E6%95%B0%EF%BC%8C%E5%88%99%24%5Cchi%5E2%24%E7%BB%9F%E8%AE%A1%E9%87%8F%E5%8F%AF%E4%BB%A5%E5%86%99%E4%B8%BA%24%5Cchi%5E2%3D%5Csum%7B%5Cfrac%7B(f_0-f_e)%5E2%7D%7Bf_e%7D%7D%24%0A%3E**%E7%BB%9F%E8%AE%A1%E9%87%8F%E6%9C%89%E5%A6%82%E4%B8%8B%E7%89%B9%E5%BE%81**%EF%BC%9A%0A%3E1.%24%5Cchi%5E2%20%5Cgeq%200%24%2C%E5%9B%A0%E4%B8%BA%E5%AE%83%E6%98%AF%E5%AF%B9%E5%B9%B3%E6%96%B9%E7%BB%93%E6%9E%9C%E7%9A%84%E6%B1%87%E6%80%BB%0A%3E2.%24%5Cchi%5E2%24%E7%9A%84%E5%88%86%E5%B8%83%E4%BA%8E%E8%87%AA%E7%94%B1%E5%BA%A6%E6%9C%89%E5%85%B3%0A%3E3.%24%5Cchi%5E2%24%E6%8F%8F%E8%BF%B0%E4%BA%86%E8%A7%82%E5%AF%9F%E5%80%BC%E4%B8%8E%E6%9C%9F%E6%9C%9B%E5%80%BC%E7%9A%84%E6%8E%A5%E8%BF%91%E7%A8%8B%E5%BA%A6%0A%3E%24%5Cchi%5E2%24%E6%A3%80%E9%AA%8C%E6%AD%A3%E6%98%AF%E9%80%9A%E8%BF%87%E5%AF%B9%24%5Cchi%5E2%24%E7%9A%84%E8%AE%A1%E7%AE%97%E7%BB%93%E6%9E%9C%E4%B8%8E%24%5Cchi%5E2%24%E7%9A%84%E4%B8%B4%E7%95%8C%E5%80%BC%E8%BF%9B%E8%A1%8C%E6%AF%94%E8%BE%83%EF%BC%8C%E5%81%9A%E5%87%BA%E6%98%AF%E5%90%A6%E6%8B%92%E7%BB%9D%E5%8E%9F%E5%81%87%E8%AE%BE%E7%9A%84%E5%86%B3%E7%AD%96%E3%80%82%0A%0A%0A%23%23%23%23%20%E6%8B%9F%E5%90%88%E4%BC%98%E5%BA%A6%E6%A3%80%E9%AA%8C%0A%3E**%E6%8B%9F%E5%90%88%E4%BC%98%E5%BA%A6%E6%A3%80%E9%AA%8C**%EF%BC%9A%E6%8B%9F%E5%90%88%E4%BC%98%E5%BA%A6%E6%A3%80%E9%AA%8C%E6%98%AF%E7%94%A8%24%5Cchi%5E2%24%E7%BB%9F%E8%AE%A1%E9%87%8F%E8%BF%9B%E8%A1%8C%E7%BB%9F%E8%AE%A1%E6%98%BE%E8%91%97%E6%80%A7%E6%A3%80%E9%AA%8C%E7%9A%84%E9%87%8D%E8%A6%81%E7%A8%8B%E5%BA%A6%E4%B9%8B%E4%B8%80%E3%80%82%E5%AE%83%E6%98%AF%E4%BE%9D%E6%8D%AE%E6%80%BB%E4%BD%93%E5%88%86%E5%B8%83%E7%9A%84%E7%8A%B6%E5%86%B5%EF%BC%8C%E8%AE%A1%E7%AE%97%E5%87%BA%E5%88%86%E7%B1%BB%E5%8F%98%E9%87%8F%E4%B8%AD%E7%9A%84%E5%90%84%E7%B1%BB%E5%88%AB%E7%9A%84%E6%9C%9F%E6%9C%9B%E9%A2%91%E6%95%B0%EF%BC%8C%E4%B8%8E%E5%88%86%E5%B8%83%E7%9A%84%E8%A7%82%E5%AF%9F%E9%A2%91%E6%95%B0%E8%BF%9B%E8%A1%8C%E6%AF%94%E8%BE%83%EF%BC%8C%E5%88%A4%E6%96%AD%E6%9C%9F%E6%9C%9B%E9%A2%91%E6%95%B0%E6%98%AF%E5%90%A6%E6%9C%89%E6%98%BE%E8%91%97%E5%B7%AE%E5%BC%82%EF%BC%8C%E4%BB%8E%E8%80%8C%E8%BE%BE%E5%88%B0%E5%AF%B9%E5%88%86%E7%B1%BB%E5%8F%98%E9%87%8F%E8%BF%9B%E8%A1%8C%E5%88%86%E6%9E%90%E7%9A%84%E7%9B%AE%E7%9A%84%E3%80%82%0A%0A%23%23%23%23%20%E5%88%97%E8%81%94%E5%88%86%E6%9E%90%EF%BC%9A%E7%8B%AC%E7%AB%8B%E6%80%A7%E6%A3%80%E9%AA%8C%0A%3E%E6%8B%9F%E5%90%88%E4%BC%98%E5%BA%A6%E6%A3%80%E9%AA%8C%E6%98%AF%E5%AF%B9%E4%B8%80%E4%B8%AA%E5%8F%98%E9%87%8F%E7%9A%84%E6%A3%80%E9%AA%8C%EF%BC%8C%E5%BD%93%E9%81%87%E5%88%B0%E4%B8%A4%E4%B8%AA%E5%88%86%E7%B1%BB%E5%8F%98%E9%87%8F%E7%9A%84%E9%97%AE%E9%A2%98%E7%9C%8B%E8%BF%99%E4%B8%A4%E4%B8%AA%E5%8F%98%E9%87%8F%E6%98%AF%E5%90%A6%E5%AD%98%E5%9C%A8%E8%81%94%E7%B3%BB%0A%3E%E5%AF%B9%E4%BA%8E%E4%B8%A4%E4%B8%AA%E5%88%86%E7%B1%BB%E5%8F%98%E9%87%8F%E7%9A%84%E5%88%86%E6%9E%90%EF%BC%8C%E6%88%90%E4%B8%BA%E7%8B%AC%E7%AB%8B%E6%80%A7%E5%88%86%E6%9E%90%0A%0A%23%23%23%23%20%E5%88%97%E8%81%94%E8%A1%A8%E4%B8%AD%E7%9A%84%E7%9B%B8%E5%85%B3%E6%B5%8B%E5%BA%A6%0A%3E%24%5Cphi%24%E7%9B%B8%E5%85%B3%E7%B3%BB%E6%95%B0%EF%BC%9A%E4%B8%80%E8%88%AC%E7%94%A8%E6%9D%A5%E6%8F%8F%E8%BF%B02X2%E5%88%97%E8%81%94%E8%A1%A8%EF%BC%8C%24%5Cphi%3D%5Csqrt%7B%5Cfrac%7B%5Cchi%5E2%7D%7Bn%7D%7D%24%EF%BC%8Cn%E4%B8%BA%E5%88%97%E8%81%94%E8%A1%A8%E4%B8%AD%E7%9A%84%E6%80%BB%E9%A2%91%E6%95%B0%EF%BC%8C%E4%B9%9F%E5%B0%B1%E6%98%AF%E6%A0%B7%E6%9C%AC%E9%87%8F%0A%3E%E5%88%97%E8%81%94%E7%9B%B8%E5%85%B3%E7%B3%BB%E6%95%B0%EF%BC%9A%E5%BD%93%E8%A1%8C%E6%95%B0%E6%88%96%E5%88%97%E6%95%B0%E5%A4%A7%E4%BA%8E2%E7%9A%84%E6%97%B6%E5%80%99%EF%BC%8C%E4%BD%BF%E7%94%A8%E5%88%97%E8%81%94%E8%A1%A8%E5%85%B3%E7%B3%BB%E7%B3%BB%E6%95%B0%EF%BC%8C%E8%AE%A1%E7%AE%97%E5%85%AC%E5%BC%8F%24c%3D%5Csqrt%7B%5Cfrac%7B%5Cchi%5E2%7D%7B%5Cchi%5E2%2Bn%7D%7D%24%2C%E5%BD%93c%3D0%E6%97%B6%EF%BC%8C%E4%B8%A4%E4%B8%AA%E5%8F%98%E9%87%8F%E7%9B%B8%E4%BA%92%E7%8B%AC%E7%AB%8B%0A%3E**%E4%BC%98%E7%82%B9**%EF%BC%9A1.%E8%AE%A1%E7%AE%97%E7%AE%80%E4%BE%BF%EF%BC%8C2.%E5%AF%B9%E6%80%BB%E4%BD%93%E5%88%86%E5%B8%83%E6%B2%A1%E6%9C%89%E8%A6%81%E6%B1%82%EF%BC%9B**%E7%BC%BA%E7%82%B9**%EF%BC%9A%E6%9C%80%E5%A4%A7%E5%80%BC%E4%BE%9D%E8%B5%96%E4%BA%8E%E8%A1%8C%E6%95%B0%EF%BC%8C%E9%9A%8F%E7%9D%80R%E5%92%8CC%E7%9A%84%E5%A2%9E%E5%A4%A7%E8%80%8C%E5%A2%9E%E5%A4%A7%EF%BC%8C%E6%A0%B9%E6%8D%AE%E4%B8%8D%E5%90%8C%E8%A1%8C%E6%95%B0%E5%92%8C%E5%88%97%E6%95%B0%E8%AE%A1%E7%AE%97%E7%9A%84%E5%88%97%E8%81%94%E7%B3%BB%E6%95%B0%E4%B8%8D%E4%BE%BF%E4%BA%8E%E6%AF%94%E8%BE%83%EF%BC%8C%E9%99%A4%E9%9D%9E%E4%B8%A4%E4%B8%AA%E5%88%97%E8%81%94%E8%A1%A8%E7%9A%84%E8%A1%8C%E6%95%B0%E4%B8%8E%E5%88%97%E6%95%B0%E4%B8%80%E8%87%B4%0A%3EV%E7%9B%B8%E5%85%B3%E7%B3%BB%E6%95%B0%EF%BC%9A%E7%94%B1%E4%BA%8E%24%5Cphi%24%E7%B3%BB%E6%95%B0%E6%97%A0%E4%B8%8A%E9%99%90%EF%BC%8Cc%E7%B3%BB%E6%95%B0%E5%B0%8F%E4%BA%8E1%EF%BC%8C%E6%8F%90%E5%87%BAV%E7%B3%BB%E6%95%B0%EF%BC%8C%24V%3D%5Csqrt%7B%5Cfrac%7B%5Cphi%5E2%7D%7Bn*min%5B(R-1)%2C(C-1)%5D%7D%7D%24%2C%E4%B8%A4%E4%B8%AA%E5%8F%98%E9%87%8F%E7%9B%B8%E4%BA%92%E7%8B%AC%E7%AB%8B%E6%97%B6%EF%BC%8CV%3D0%EF%BC%8C%E4%B8%A4%E4%B8%AA%E5%8F%98%E9%87%8F%E5%AE%8C%E5%85%A8%E7%9B%B8%E5%85%B3%E6%97%B6%EF%BC%8CV%3D1%EF%BC%8CV%E7%9A%84%E5%8F%96%E5%80%BC%E4%BB%8B%E5%85%A50~1%E4%B9%8B%E9%97%B4%0A%0A%3E%E6%95%B0%E5%80%BC%E5%88%86%E6%9E%90%0A%0A%3E%E5%89%8D%E9%9D%A2%E5%88%A9%E7%94%A8%E5%8D%A1%E6%96%B9%E5%88%86%E5%B8%83%E5%AF%B9%E4%B8%A4%E4%B8%AA%E5%88%86%E7%B1%BB%E5%8F%98%E9%87%8F%E4%B9%8B%E9%97%B4%E7%9A%84%E7%9B%B8%E5%85%B3%E6%80%A7%E8%BF%9B%E8%A1%8C%E4%BA%86%E7%BB%9F%E8%AE%A1%E6%A3%80%E9%AA%8C%0A%0A%0A%23%23%23%23%20%E5%88%97%E8%81%94%E5%88%86%E6%9E%90%E4%B8%AD%E5%BA%94%E6%B3%A8%E6%84%8F%E7%9A%84%E9%97%AE%E9%A2%98%0A%3E%E6%9D%A1%E4%BB%B6%E7%99%BE%E5%88%86%E6%AF%94%E7%9A%84%E6%96%B9%E5%90%91%0A%3E%E5%8D%A1%E6%96%B9%E5%88%86%E5%B8%83%E7%9A%84%E6%9C%9F%E6%9C%9B%E5%80%BC%E5%87%86%E5%88%99%0A%3E%E5%88%A9%E7%94%A8%E5%8D%A1%E6%96%B9%E5%88%86%E5%B8%83%E8%BF%9B%E8%A1%8C%E6%A3%80%E9%AA%8C%E7%9A%84%E6%97%B6%E5%80%99%EF%BC%8C%E6%9C%9F%E6%9C%9B%E5%80%BC%E5%BA%94%E8%AF%A5%E8%B6%B3%E5%A4%9F%E5%A4%A7%0A%3E%E5%A6%82%E6%9E%9C%E5%8F%AA%E6%9C%892%E4%B8%AA%E5%8D%95%E5%85%83%EF%BC%8C%E6%AF%8F%E4%B8%AA%E5%8D%95%E5%85%83%E5%BF%85%E9%A1%BB%E6%98%AF5%E6%88%96%E8%80%855%E4%BB%A5%E4%B8%8A%0A%3E%E5%A6%82%E6%9E%9C%E4%B8%A4%E4%B8%AA%E4%BB%A5%E4%B8%8A%E7%9A%84%E5%8D%95%E5%85%83%EF%BC%8C%E5%A6%82%E6%9E%9C20%25%E7%9A%84%E5%8D%95%E5%85%83%E6%9C%9F%E6%9C%9B%E9%A2%91%E6%95%B0%E6%98%AF%E5%B0%8F%E4%BA%8E5%E7%9A%84%EF%BC%8C%E5%88%99%E4%B8%8D%E8%83%BD%E7%94%A8%E5%8D%A1%E6%96%B9%E5%88%86%E5%B8%83%E8%BF%9B%E8%A1%8C%E6%A3%80%E9%AA%8C%0A