Comparing survey results when response rate differ I need to compare the results of a national satisfaction survey across regions.
The best region (a) has 87% satisfaction rate and the second best (b) has an 82% satisfaction rate (chi square test of independence statistically significant at the 99% CL).
However, the response rate are not the same : region a has a 39% response rate while region b has a 45% response rate.
Is it reasonable to conclude that region a has better results than region b ?
Thanks
 A: The  more people that respond, the more precise the estimates are. To determine whether one location is truly more satisfied than the other, you would have to use confidence intervals for the sample proportion. Lower response leads to wider intervals, and if they overlap the other estimates there is no statistically significant difference. However another thing you may be hinting at is nonresponse bias where dissatisfied people respond less often. There is no solution to that scenario. You can impute worst possible case, but that's usually an unreasonable assumption. Simply report the response rates at each site, then calculate the complete case statistics. 
A: Assuming that response rate  has no effect ,  you may compare the results - 87% satisfaction rate for region" a"with 82% satisfaction rate for region "b" -  by conducting t-test of differenence in proportions. Chi-squared test is not suitable for the given situation.  Further, a response rate of 30% or more could be considered adequate in a large scale national sample survey. The two rates do not seem to be statistically much different.
And if you still do feel need for correcting your results (satisfaction rate) , work out for possible effects of difference in response rates and rectify the satisfaction rates before executing t-test.
