[R] Statistical question: one-sample binomial test for clustered data

Matthias Gondan matthias-gondan at gmx.de
Tue Nov 25 15:52:43 CET 2008

Dear list,

I hope the topic is of sufficient interest, because it is not
R-related. I have N=100 yes/no-responses from a psychophysics
paradigm (say Y Yes and 100-Y No-Responses). I want to see
whether these yes-no-responses are in line with a model
predicting a certain amount p of yes-responses. Standard
procedure would be a one-sample binomial test for the observed

chi²(1 df) = (Y-Np)²/(Np) + [(100-Y)-N(1-p)]²/[N(1-p)]

Actually, this is the approximate chi²-test, but the sample
size seems to be reasonably high for an asymptotic test.

The problem is that the experiment took quite a while, and
the 100 responses are grouped into 20 blocks of 5 responses
each. The responses within the blocks are clustered, ICC is
about 0.13 or so.

Can anyone point me to some literature explaining a one-sample
binomial test / or chi² test for correlated data? Most of the
literature I found starts with more advanced stuff, e.g.
2x2 cross-tabulated data.

Best wishes,


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