What is the best way to estimate the variability of a measurement? I am trying to capture the variability of a specific measurement. I have 9 measurements from each patient – 3 measurements at 1-hour intervals over 3 consecutive days. So it kinda looks like this:
Person |  Day1Trial1 Day1Trial2 Day1Trial3 Day2Trial1 ... Day3Trial3
   1             
   2
   ...

I'm not sure how to proceed from here given very little background in statistics. Do I just calculate the overall variance of all the observations? How do I take into account the error of the device I used, or the variability of a patient's measurements? Can someone please refer me to any literature that I can read that's relevant to this? Are there any specific methods or techniques that seem appropriate in this situation?
 A: A great way to measure the variability in this instance would be to partition the total variance between within days and between days. For within groups variance, the first step is to find the "Sum of Squares Within:"


*

*Find the mean of the day 1 measurements,

*Subtract this mean from each measurement, 

*Square each of these subtractions

*Add of all of these squares

*Repeat this procedure for each day

*Add up all of these sums


In other words:
$SS_w=\sum\limits_{j=1}^g$
$\sum\limits_{i=1}^{n_j}$
$(y_{ij}-\overline{y})^2$
Then, find the "Sum of Squares Between." You need the "grand mean" for this, which is the average of all observations. Next follow a similar procedure as for $SS_w$, but use the grand mean in place of the mean and the group means in place of the measurements:


*

*Find the grand mean,

*Find the mean of each group

*Subtract the grand mean from the mean of each group,

*Square each of these subtractions,

*Sum up all of these squares.


In other words:
$SS_b=\sum\limits_{j=1}^k$
$(\overline{x_j}-\overline{\overline{x}})^2$
Because you have equal groups (3 measurements per day), you do not have to adjust $SS_b$. If the groups are unequal, you need to adjust $SS_b$.
Finally, partition the variance. For the proportion of within groups variance, also known as error variance:
$e=SS_w/SS_w+SS_b$
The more interesting is between days variance, also called effect size or $\eta^2$ ("eta-squared"):
$\eta^2=SS_b/SS_w+SS_b$.
If $\eta^2>0.15$, then you have data suited for a true longitudinal analysis. Given that you've said you don't have much statistics experience, longitudinal analysis using multi level modelling or ARIMA models might require more work than you want.
A: If your device has some error, it just stays there either increasing/decreasing the estimated value of the parameter or, if it is 'noisy' and can be mistaken both ways, increasing the variance.
You may perform a two-way repeated measures analysis of variance (ANOVA) with measurement as one factor and day as the other and subject as a random factor. Read thoroughly how to rearrange your data for ANOVA. This way you may assess whether day or time influence the measurements.
If the measurement is something that is not expected to change systematically, for example, blood pressure in people who receive no treatment, you may just calculate the means and standard deviations for each subject. Standard deviation is just a square root of variance, but it is preferable, because it has the same units as the measurement itself.
NB: using ANOVA you should make sure your data is normally distributed. If it is not, or it is discrete Friedman test is your choice.
A: Since you mentioned "limited statistics", I assume you just need a number to label your measurements variability (very high, high, medium, low, very low...something like that).
If that's the case, I would say just keep it simple.
Suppose there are n patients, each having 9 measurements, your variability is just the standard error:
σ = sqrt[Σ (x-mean(x))^2  / n ]

    where n = 9
    x = individual measurements
    mean(x) = Σ x / n

