How to analyse a study where measures are taken repeatedly from right and left legs in five walking conditions? There are 13 subjects in this study, each subject was "repeatedly measured" right and left legs on five walking conditions. The variables of this data set is: ID, Y, Leg, Conditions.
The research questions are to find the difference between legs and conditions.
At beginning, I plan to use RM-ANOVA: $Y = \text{Leg} + \text{Conditions} + \text{Leg}\times\text{Conditions}$. But the RM-ANOVA might not be appropriate because right and left legs are also correlated (from same subject). 
Does anyone have an idea how to analyze this type of data?
 A: Your instinct about the R and L legs' results being correlated seems right, but even so, I think repeated measures anova is appropriate.  You have no between subject factors, just 2 within-subject factors.  These are R vs. L Leg (2 levels) and what you've been hitherto calling "conditions" but which I would rename (5 levels).  These make 2*5=10 within-subject conditions.
A: As you stated, observations from the same individual will be correlated, as will observations from the same leg. You can estimate and compare the strength of these correlations using a mixed effects model.
Walking condition is a fixed effect. Leg is a random effect nested within subjects, unless for some reason you believe there is a left-right leg difference, in which case you could model it as a crossed effect within subjects. The nested model can be written:
$$ y_{ijk} = \mu + c_j + s_i + e_{ik} + \epsilon_{ijk} $$
where $i = 1,2,\ldots,15$ indexes subjects, $j = 1,2,\ldots, 5$ indexes the walking condition, and $k = 1,2$ indexes left and right legs. $c_j$ is fixed, $s_i \sim N(0, \sigma_s^2)$, $e_{ik} \sim N(0, \sigma_e^2)$, and $\epsilon_{ijk} \sim N(0, \sigma^2)$. Since the total variance is $\sigma_s^2 + \sigma_e^2 + \sigma^2$, the correlation between measurements on the same subject is $\sigma_s^2 / (\sigma_s^2 + \sigma_e^2 + \sigma^2)$ and on the same leg is $\sigma_e^2 / (\sigma_s^2 + \sigma_e^2 + \sigma^2)$. You can compare these two numbers in your analysis to discuss the relative magnitude of the two correlations. Another way to think about this approach is that you are comparing the amount of variation across subjects to the amount of variation across left and right legs. 
Finally, a likelihood ratio test will tell you whether condition is a significant predictor of $y$, given the nested structure of your data. If you expect variance terms to depend on the walking condition, the model will become more complicated.
