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karweillas · 2023年08月12日

题目的意思说是2个类别3个等级，不应该是2行3列吗？

  1. CFA I
  2. Quantitative

NO.PZ2021062201000019

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：

A is correct. 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.

本题考察关于卡方检验的概念，由于检验统计量包含观测值和预期值之间的平方差，因此检验仅涉及一侧，即右侧，所以选A。


那自由度应该是（2-1）*（3-1）=2

为什么解释是（3-1）*（3-1）=4？

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1 个答案

星星_品职助教 · 2023年08月13日

同学你好，

两个类别不是两行。题干中已经说明这两个类别里“each” with three levels or groups，即每个类别都有三个level/group。也就是三行和三列。

讲义上的例子就是两个类别对应三行三列，如下。红框圈出来的即为两个category。蓝框为对应的三行和三列。

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