Compare two proportions from same sample (mutually non exclusive) I want to know what test to use to compare 2 percentages from the same sample.
My study is as follows: I conducted a survey on 50 people regarding consent for 2 tests (X and Y). 48 people consented to test X, 40 people consented to test Y. So the consent rate for test X would be 48/50 (96%) and the consent rate for test Y would be 40/50 (80%). 
How to compare these two percentages? Can I say the consent rate for test X is better than the consent rate for test Y? How to know if this is statistically significant? I tried Fisher's exact test and I tried to generate a contingency table, but I don’t know whether I can apply Fisher's exact test for non mutually exclusive data.
 A: I guess you would be having the data on how many subjects consented to both tests. Draw a simple Venn diagram with the information you have. Find out how many are there who consented only for test X and only for test Y and those who consented to both. Now, that makes the categories mutually exclusive. Consider those who provide consent to both the tests as a separate category "agrees to both tests X and Y". This creates three categories and depending on the size of the cells, you can use Chi-square test or Fisher's exact. 
Try this. May help.
A: You can try the McNemar chi squared test and Z test for paired samples. 
Quoted from the book, the type of situation typically involves measurements made on a variable before and after some sort of intervention. 
A: If each person answers about both questions, McNemar's test is best.
Imagine a 2x2 table where the rows are the people who answer Yes/No to X and the columns are the people who answer Yes/No to Y.  The table is then...
$$ \begin{bmatrix} e & f \\ g & h \end{bmatrix}$$ 
Here, $e$ people answer yes to both, $h$ people answer no to both, $g$ answer No to X but Yes to Y, and $f$ answer Yes to X but no to Y.
McNemar's test is 
$$\dfrac{(f-g)^2}{f+g}$$
and is chi-square distributed on one degree of freedom. 
