I wanted to test for the effect of question type on students' use of strategies. A four-item (there are four question types) written test was given to students.
The results are recorded in a contingency table like the following, where $x$ is the frequency count. For example, $x_{11}$ means there are $x_{11}$ students use "Strategy1" to solve "Type1" question
+-----------+-------+-------+-------+-------+ | | Type1 | Type2 | Type3 | Type4 | +-----------+-------+-------+-------+-------+ | Strategy1 | x_11 | x_21 | x_31 | x_41 | | Strategy2 | x_12 | x_22 | x_32 | x_42 | | Strategy3 | x_13 | x_23 | x_33 | x_43 | | Strategy4 | x_14 | x_24 | x_34 | x_44 | +-----------+-------+-------+-------+-------+
Question 1: Is it valid for me to use Chi-square test for independence? Since each student (sample) contribute to 4 counts in the table, which is different from usual contingency table.
Question 2: Is there any statistical test for me to test whether a certain strategy is associated with a certain question type?