Hypothesis testing for equality of proportions Suppose there are $n$ students in a class. Each of them is given an outline map of Europe and asked to mark Great Britain and France. Based on the observed data is it possible to test if the proportion of students who could locate Great Britain same as that of France?
The problem I am facing is due to the dependent structure of the observations. Almost any testing procedure I can think of is falling flat.
Any help?

One idea, the paired design, which introduces dependency, can be handled by a random effects logistic regression. Define the logistic function by $\ell(x) =\frac{e^x}{1+e^x}$, then the logistic regression model is given by
$$
   P(Y_{ij}=1) = \ell(\mu+\eta_i +\Delta I(j=2))
$$
 where $i=1, \dots, n$ indices the $n$ students, $j=1,2$ indices question about (france, britain) so $\eta_i$ is the random effect, which you can model as a mean-zero normal distribution, and $\Delta=0$ represent the null hypothesis of no difference in proportion.  Such a model can be fitted in R with the package lme4.
