Correlation of bivariate grouped data? Which test should I use, if I want to test the correlation between 2 bivariate grouped variables?
The case is: I have asked several hotel owners about their feelings about the occupational rate of their hotel and the propagation of the region, where the hotel is. Both of the questions had ordinal scales, spreading from "low" to "high". Because of few participants of the survey I had to categorize the answers to both of the questions to two categories: "low" and "high".
My hypothesis is, that there is a correlation between the occupational rate and the propagation of the region, so for example, the owner, who feels like his hotel has a high occupational rate, also feels like the propagation of the region is high. 
My question is, which test could I use to test this hypothesis.
I would appreciate any kind of help! Thank you!
 A: I'm still not certain that you need to group your ordinal responses into two categories, but once you have done so you simply have a 2x2 contingency table with the counts for the number of observations that fall into each of the four possible combinations.  If you want to see if these two variables are associated, you can use the $\chi^2$ test for independence.  
A: There are a number of ways to assess the correlation between two binomial variables.  The most common in my experience is the Phi coefficient.  Notably, this coefficient for a 2x2 table has the same value as a regular correlation coefficient (Pearson's product moment) and bears a direct relationship with the $\chi^2$ test mentioned by gung.
With a 2x2 table of counts, you can do a Fisher's exact test instead of a $\chi^2$ without the requirement that you have all cells with N >= 5.  I haven't vetted it, but a quick Google search shows this calculator available online.
All of this being said... given that you have a cell in your design where N < 5, I'd recommend caution in interpreting your correlation coefficient.
