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番薯shushu · 2025年04月14日

C选项计算自由度没有看懂

NO.PZ2022123001000128

问题如下:

Which of the following statements is correct regarding the chi-square test of independence?

选项:

A.The test has a one-sided rejection region

B.The null hypothesis is that the two groups are dependent

C.If there are two categories, each with three levels or groups, there are six degrees of freedom.

解释:

The test statistic comprises squared differences between the observed and expected values, so the test involves only one side, the right side. B is incorrect because the null hypothesis is that the groups are independent, and C is incorrect because with three levels of groups for the two categorical variables, there are four degrees of freedom.

每个分类各有三个子分类对应三行(r=3)和三列(c=3)正确的自由度应为(r-1)*(c-1)=(3-1)*(3-1)=4。


C的英文表述是什么意思?C选项说2个categories,有3个level,为什么自由度不是1*2?这个英文描述能不能请老师举个例子帮忙理解一下为什么是3行3列。谢谢

1 个答案

袁园_品职助教 · 2025年04月15日

嗨,从没放弃的小努力你好:


C 选项的英文表述意思是:“如果有两个类别,每个类别有三个水平或组,那么自由度是六。”

在卡方独立性检验中,自由度的计算公式是df=(r - 1)*(c - 1),其中r是行数(一个类别变量的水平数),c是列数(另一个类别变量的水平数)。这个表应该是这样哦,所以才是三行三列,自由度=2*2=4。

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