Suppose I have a survey where respondents rate different questions as positive (1), negative (-1), or neutral (0), and their responses are given a different weight based on which job they have and which city they live in. Let's say we have questions A, B, C and D, where A and B are grouped and C and D are also group. Suppose we have respondents r1 through r6 rate them (but also suppose we could have different respondents rate each of the questions)
A B C D Weight r1 1 1 1 0 72 r2 0 1 0 0 72 r3 1 -1 0 0 23 r4 0 1 1 1 45 r5 1 0 -1 0 23 r6 -1 1 -1 1 45
Responses for each question are weighted based on the respondent and then added up for a difference between positive and negative ratings (Pos * Weight - Neg * Weight). This result is then divided by the total weights for all respondents (Proportion of pos weights - Prop of neg weights). For example, for question A we would have:
A Weight WeightedA r1 1 72 72 r2 0 72 0 r3 1 23 23 r4 0 45 0 r5 1 23 23 r6 -1 45 -45
The final score for question A would be $\sum(WeightedA)/Sum(Weight) = 26%$.
In this case, this would mean that question A is more positively viewed by respondents when taking their weights into account. The same is done for other questions so we end up with:
A Score: 26% B Score: 44% C Score: -20% D Score: 1%
A final score for question group AB is the average 35% and for CD it is -10%.
How can I test the difference between 35% and -10% to understand whether the difference in respondent satisfaction is statistically significant? I was thinking some sort of t-test but not sure what is appropriate in this instance.