I have a questionnaire (5 point Likert) and I want to compare student responses to 4 items. The 4 items (main variables) ask about 1) student preferences for interaction with the teacher 2) student preferences for interaction with other students, 3) student prefs for well organized materials and 4) student prefs for self-directed learning. I want to see which prefs are stronger/weaker in this group.
If I average responses to get a mean of the likert scores for each item I can do an anova to find if there is a significant difference somewhere among the 4 items. This I would follow with a post hoc - i.e scheff, ect. to test individual differences. So far so good? Yep.
Also, I believe I could do a chi square test for independence (I am imagining a 4 down X 5 across grid) to see if there was a difference somewhere. What post hoc would I then do to compare responses on indiviual items to test for significance? Do chi-squared tests on the post-hoc comparisons that you are focusing on.
Question 2 -
In fact - I have 4 items for each of the 4 variables - so there are 4 items that I use to operationalize: 1) prefs for Student-teacher interaction, prefs for Student-student interaction, etc.
So if I want to group the 4 related items and compare these variable groups. Using mean scores could I average means for the 4 related items and do an anova with averaged means? Yes.
Question 3 -
With chi square- what would I do? One idea is to add the raw scores for each likert choice for each of the 4 related items that comprise a variable. For example if there are 4 items that ask about student prefs for Student-teacher interaction, and if the number of likert 5s is...4,5,6,3, I could aggregate them and say that the total number of 5s for this variable is 18. In other words I would collapse a 4X5 matrix into a 1X5 matrix. I could then do this to each of the 4 variables and do chi square as in the example above. Would this the best way to go? You could do it that way or try other ways of collapsing, i.e., three categories: 1-2, 3, 4-5