statistics - Assumptions of the Chi-square test of independence

Question

I want to use the Chi-square test of independence to test the following two variables: Student knowledge v.s. course attendance

The null hypothesis is: student knowledge and course attendance (X and Y) are independent

Members in each student knowledge group: Low (12), average(29), high(9)

The results show that there are two degrees of freedom, the chi-square statistic is 0.20, and the p-value is 0.90, and we cannot accept the null hypothesis. I added an image of my test.

click to see the image of the test

I have little doubts regarding the following two issues: the student knowledge groups have an unequal number of participants, the number of participated students in each course is fewer than 10.

My question is: does this test fit for my data?

In case, this test cannot be used for my data, what statistical test I should use instead?

标签： statisticschi-squaredhypothesis-test

Answer 1

欢迎来到堆栈交换。使用卡方检验独立性可能是小细胞大小的问题（即 G3，课程 Y，细胞计数为 2）。这与使用卡方分布作为近似值有关。

我会推荐费舍尔精确检验。它通常被指定为小样本的工具，但对于大样本仍然有效。