How to show that the condition of one hand predicts the condition of the other hand I have this kind of data:
subject    hand    condition
s01        left    1
s01        right   0
s02        left    2
s02        right   2
..         ..      ..

The condition is a variable that gets values between $0$ and $5$ and indicates severity of a certain medical diagnosis.
I would like to show that if there is a problem with the left hand then there is likely a problem with the right hand, too. In other words, I want to show that there is some kind of dependence between the conditions of the different hands.
What kind of statistical test can I use here? I guess it is some kind of paired test I am looking for?
 A: I would simply reorganize your data so that each subject is in their own row (so-called 'wide-form') with the first column indicating the severity rating for their left hand and the second column indicating their right hand.  For example:  
           left    right   
s01        1       0
s02        2       2
..         ..      ..

Then you can simply correlate the two columns / variables.  Since your data are ordinal ratings, you could use the Spearman rank correlation.  (There are several other rank correlations you could use, but that is probably the simplest and most conventional.)  Your observed Spearman's rho can be tested against $\rho=0$ (no association).  In fact, standard statistical software should output the test automatically.  
A: A way to measure this may be the intraclass correlation, which is the proportion of the total variance of the outcome that is explained by the common identifier (here, subject). In your problem, things are complicated by the condition being a categorical rather than a continuous variable. So what I would do is to fit a multilevel/mixed model with an ordinal probit link, say, and compute ICC as variance of the random effects / (variance of the random effects + variance of the residuals) where the latter variance is one for the probit link.
More discussion can probably be found in this post.
