When calculating the repeatability, like when you want to know how good the measurement of the length of a ruler is, I often read that it is sufficient to calculate the standard deviation.
I wonder about why not using a confidence interval? Or also not the standard error?
I'm not familiar with measures of repeatability, but what I think you're getting at is measuring uncertainty. I think this is a good opportunity to talk about uncertainty at various levels.
Let's say were are measuring the precision of some instrument, like a ruler, where we make measurements and compare with some ground truth. We can estimate the average error (which is a parameter) of the ruler by using the individual error measurements we make.
There are different kinds of uncertainty in this experiment. There is:
Uncertainty in the data: What is the size of the next error I will observe?, and
Uncertainty in the parameters: Were I to perform my experiment again, what would my estimated average error be?
Confidence intervals, which use the standard error, give a measure of uncertainty for the second kind. They tell you, given the experiment you just performed, what are some of the values of the average error consistent with the data you just observed (I'm being a bit fast and loose with the definition of the confidence interval). What a confidence interval does not tell you is where you are likely to see new observations.
This is easily demonstrated. Consider 1000 data points from a standard normal. A confidence interval for data from this distribution might be $[-2/\sqrt{1000}, 2/\sqrt{1000}]$. However, we know we can (and often will) observe data outside this interval.
On the other hand, the standard deviation gives a measure of uncertainty of the first kind. The standard deviation is the square root of the variance, which is the expectation of the squared distance of observations from the mean (wow, that's a mouthful). If you wanted an interval estimator of uncertainty of the first kind, you could make use of tolerance interval or similar estimators.
So, in conclusion, confidence intervals don't measure uncertainty in the observations. They measure uncertainty in the parameters. If you want uncertainty in the observations, its best to use something on the same scale as the observations, and that would be the standard deviation.
