Can you make conclusions about statistical significance from aggregate data? I have aggregate data on complaints filed by two groups - group A and group B. I say 'aggregate' because I don't know how many complaints a particular individual filed. I just know that:
There are 100 people in group A. There were 30 complaints from group A.
There are 100 people in group B. There were 33 complaints from group B.
So, group B complained more (by 3 complaints). But can I make a conclusion about statistical significance of the difference in number of complaints? What test would I use?
 A: Comment: Strictly speaking, in order to make a valid comparison using prop.test in R, you need to compare the number of people making complaints, not the number of complaints.
(One person making two or more complaints does not lead to multiple independent complaints.)
However, even if you had true binomial data, there would
still be no significant difference (5% level, 10% level, etc.) between 30 and and 33 people out of 100 making complaints:
prop.test(c(30,33), c(100,100))

        2-sample test for equality of proportions 
        with continuity correction

data:  c(30, 33) out of c(100, 100)
X-squared = 0.092689, df = 1, p-value = 0.7608
alternative hypothesis: two.sided
95 percent confidence interval:
 -0.1686877  0.1086877
sample estimates:
prop 1 prop 2 
  0.30   0.33 

The P-value is not below $0.05 = 5\%$ and the 95% confidence
interval contains $0.$
However, if you had similar proportions with 20 times
the sample sizes with true binomial data, you would (just barely) have a significant
result at the 5% level.
prop.test(c(600,660), c(2000,2000))$p.val
[1] 0.04461493

