Uncertainty and propagation of errors

[mccabec]

I recently used DPlot to manipulate a large amount of data for a report. (280 individual files of 50k+ measurements) With each file I used DPlot to trim data, perform basic calculations, and integrate using the trapeziodal method with the built in tools. My editors are now asking that I include a treatment of uncertainties. I am familiar with estimates of uncertainty and propagation of errors in basic arithmetic operations, but have no idea how to track generated errors through DPlot, nor particularly how to be accountable for uncertainties accrued through use of the Integration tool provided. Any advice? Thanks..
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WEED

[DPlotAdmin]

Statistics is definitely not my strength, so you may get a better answer elsewhere... but here goes:

The only sources of error I can think of for integration are

1. Your input. If you are reading your input from text files rather than some binary format, there will be at least some roundoff error regardless of how many significant digits were used in your files. For example if your Y values in the text file have only 2 decimal places then each Y has an uncertainty of +0.005, and the result of integration at any X may be off by as much as +0.005*X (though that's an extreme and would only be true if the Y values were either all low or all high).
2. The assumption that whatever phenomenon you are measuring varies linearly between data points. In most cases you may as well assume that, since that's the only data you have. And really if that assumption isn't close to true then all hope is lost unless you can fill in the blanks. I don't really see a good way to quantify any uncertainty on this one, though - since doing so would require guesswork about what the input might look like between points if you had sampled at a higher frequency.

The trapezoidal rule is fairly straightforward and (if you make it past the 2 gotchas mentioned above) the uncertainty at any Xi should be no more than the uncertainty at Xi-1 + machine epsilon * (Yi-1 + Yi)/2 * (Xi - Xi-1). For the double-precision numbers used by DPlot on a PC, the machine epsilon is 2^-52, or about 2.22E-16.