Computational Linguistics 3, Exercise 2: observed versus expected

Code (run with py -X utf8, after the chapter's script):

for pair in [("the", "sea"), ("the", "lighthouse"), ("strong", "winds")]:
    obs = pairs[pair]
    exp = c[pair[0]] * c[pair[1]] / n
    print(pair, obs, round(exp, 2))

Output from the run:

('the', 'sea') 2 0.42
('the', 'lighthouse') 1 0.42
('strong', 'winds') 1 0.05

Largest ratio: "strong winds" (1 observed, 0.05 expected: about 20 times chance).

Why to hesitate: it occurred once. One occurrence in a 66-word paragraph is
no evidence of a pattern; the ratio is large only because the expected value
is tiny. "the sea" (2 against 0.42) is a smaller ratio but twice observed.
The Collocation article defines collocation as co-occurring more often than
would be expected by chance and says the association scores are used to test
whether co-occurrence is due to chance; with counts this small, no such test
could support a claim. The expected calculation is my simplification, not one
of the measures the article names (mutual information, t-scores,
log-likelihood).