# Chi squared test for differences between constructed variable

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.

That is:

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-

1. Is it statistically meaningful to construct a new variable 'overall' that takes on the average value from a, b and c?

That is:

Variable Overall (average from A , B and C)
Treatment:  885 yes / 115 no
Control:       832 yes /  168 no

1. If 1 makes sense, can I test for significant differences for this constructed variable using a chi squared test?