How to summarize measurement variability for repeated measures? I have a data set where different measures are taken repeatedly (3) times for multiple samples, like so:
   A B C
 X  ...
 Y  ...

So, for people X, Y, etc I have measures A, B, C and so on. Each of A, B, C are measured 3 times for each sample. That is, for each person, I have 3 measures of A (A1, A2, A3), 3 measures of B (B1, B2, B3), for each of the columns.
What I'd like to know is, how can I summarize the variability or the reliability of each column? So, over the entire data set, how reliable is the measurement for A?
Thanks for the help!
 A: the sample variance of the measurements A1, A2, A3, for a person X is:
\begin{equation}
\sigma_X(A) = \frac{1}{2} \sum_{i=1}^{3} (A_{i,X} - \bar{A}_X)^2
\end{equation}
where $\bar{A}_X$ is the arithmetic mean of the measurement A for person X. Now you can look at the $\sigma_X(A)$ values across all samples (people) in your study, and for example consider mean value $\bar{\sigma}(A)$ to quantify the reliability of measurements A. 
\begin{equation}
\bar{\sigma}(A) = \frac{1}{N} \sum_X \sigma_X(A)
\end{equation}
Another way of looking at it is if you consider each $A_i$, for $i=1,2,3$, across all samples. Define $\bar{A}_i$ as the mean value of the $A_i$ measurements across samples. This allows us to characterize the standard deviation $\sigma_i(A)$ of a particular measurement $A_i$ across samples.
\begin{equation}
\sigma_i(A) = \frac{1}{2} \sum_{X} (A_{i,X} - \bar{A}_i)^2
\end{equation}
The average $\sigma_i(A)$ for all $i=1,2,3$ indicates the average variability of the measurement A. 
Hope it was helpful! 
