I have already spoken to a statistician and he did not seem certain about the answer, so perhaps it may be of use to others. The study is not typical, so please bear with me while I try to explain it.
I have about 75,000 sentences of English conversations for a sample. I'm interested in whether sentences with a certain grammatical structure (specifically, missing verb phrases) tend to clump together. First, I calculated the relative frequency (empirical probability) of these sentences and got 910 hits/75,000 total sentences ≈ 0.012. To get confidence intervals for this statistic, I used bootstrapping with 10,000 resamples of the entire data set with replacement, and found that the 99% confidence interval is about 0.0109 - 0.0134.
To see whether and to what extent these sentences tend to be near each other in the data, I made a new sub-sample. For each sentence with a missing verb phrase, I counted how many sentences also had missing verb phrases in the five previous sentences. So, I have five "slots", each with a relative frequency of how often sentences in that slot lack verb phrases (i.e., the immediately preceding sentence is a slot, then the next preceding sentence, and so on). This gives me results like this:
Slot 1: 56 hits/910 total sentences = 0.061
Slot 2: 32 hits/902 total sentences = 0.035
etc...
My question is this. Can I compare these relative frequencies for each slot to the confidence interval I calculated from the whole data set? In other words, if slot 1 has a relative frequency of .061, that is beyond the 99% confidence interval from my bootstrap of the whole data set, so is it therefore valid to claim that this is higher than could be expected in that slot?
And if it isn't, is there a relatively straightforward way to make it work?
