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I want to determine the standard deviation for a set of measurements of a cable profile. However, the cable follows the terrain, and thus using a mean value for the entire cable length does not make any sense.

My current thought is to compute the mean and standard deviation at every point based on the point itself and the two previous and the two next points. Then I can construct a confidence interval for the standard deviation, via the chi-squared distribution, at each of these points.

How can I get a single meaningful overall standard deviation and a confidence interval for it for the entire cable?

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    $\begingroup$ It is hard to understand what is being asked here. Could you perhaps provide an excerpt of the data and some description of what these measurements are of? What is the purpose of computing the standard deviation? $\endgroup$ – whuber Nov 8 '12 at 14:56
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What you are trying to do is essentially (1) fitting a model such as a non-parametric smoother for the data mean and then (2) estimating the standard deviation of the data about the mean with that model. Your current model is a nearest-neighbors approach. You might be interested in other more sophisticated approaches to the same problem, such as smoothing splines, kernel regression, or loess (local regression). Once you fit the nonparametric smoother then you can estimate the standard deviation of your measurement error by looking at residuals. All of these methods are available in R, and at least one is probably available in a software package of your choice.

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As far as I understood, you could calculate the standard error for each section of your cable and combine them using some weighted method of error propagation, something like:

Overall_SE = SQRT ( Weight_1^2*Cable_SE_1^2 + Weight_2^2*Cable_SE_2^2 + ... + Weight_n^2*Cable_SE_n^2 )

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