Let's assume I have a control and a treatment group with 1000 participants each and I ask each of them three questions regarding their risk perception. Each of the three questions is concerned with another domain: a, b, c
Furthermore I am also interested in the overall risk perception and I assume that this can be inferred from the answers to a, b, and c.
Unfortunately I missed to ask a fourth question concerning the overall risk perception ( That's why I want to know if this alternative way might work or not)
In a first step I check for significant differences between treatment and control group for each variable using a chi squared test.
Variable A: Treatment: 900 yes / 100 no Control: 847 yes / 153 no Variable B: Treatment: 948 yes / 152 no Control: 888 yes / 112 no Variable C: Treatment: 808 yes / 193 no Control: 760 yes / 240 no
I find that the differences are significant for A and B but not for C.
Now I am wondering if it is possible to construct one general variable based on A,B C-
- Is it statistically meaningful to construct a new variable 'overall' that takes on the average value from a, b and c?
Variable Overall (average from A , B and C) Treatment: 885 yes / 115 no Control: 832 yes / 168 no
- If 1 makes sense, can I test for significant differences for this constructed variable using a chi squared test?