# How to test normalized frequencies

I have extracted the frequency of two words (can, may) from two corpora (Corpus1, Corpus2).

I want to test if there is a significant difference between the counts in the two corpora, but since the corpora are of different different sizes I have to normalized these counts (for instance to occurrence per 1000 words).

Any ideas for how I can do this in R? And what statistical test would you recommend?

• "What statistical test..." is an on-topic question here, but "how can I do it in R" is not. Be aware that you may not get answers for the latter. – gung Feb 28 at 12:21

In statistical terms, your question is about a test for the difference in probability for two binomial random variables with different population sizes. I.e. we have that number of occurrences of a word in the corpora are distributed $$X_1 \sim \text{Binomial}(n_1, p_1),$$ and $$X_2\sim\text{Binomial}(n_2, p_2),$$ and we want to test the hypothesis $$H_0: p_1 = p_2.$$ In this setting, I would recommend using the function prop.test(), which computes the test you want if you give it the data in the form a vector of occurrences $$(x_1, x_2)$$ and a vector of corpus lengths $$(n_1, n_2).$$ I.e. If there are 400 words in the first corpus, with 20 occurrences of "can", and 700 words in the second corpus with 60 occurrences of "can", then executing the line
will compute the test (p-values, confidence interval for $$p_1 - p_2$$, etc) for the difference.