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A Practical Guide to the Propagation and Analysis of Experimental Error

Anthony Muscat
Organization: University of Arizona
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This hyperlinked Mathematica 4 document presents a practical guide to error analysis or more properly statistical inference. The intent is to present the equations needed to compute common statistical parameters with enough of the underlying theory to skillfully apply statistical inference to data obtained in a typical university laboratory course. The examples given to illustrate use of the equations are taken from an undergraduate semiconductor processing laboratory to obtain the etching rate of silicon dioxide films in aqueous fluoride-bearing solutions. Section 1 examines confidence intervals and describes how to compute them to assess the uncertainty in the thickness of a silicon dioxide film before etching. Section 2 builds on the confidence interval presentation to test the significance of statements made about the film thickness data. Section 3 shows how to combine uncertainty when subtracting film thickness measurements to compute the amount etched and when dividing the amount etched by the time to compute an overall etching rate. Section 4 discusses fitting a linear model to data and shows how to quantify the uncertainty in the slope and intercept of the best fit line to obtain the etching rate and confidence limits from a set of etching measurements as a function of time.

*Mathematics > Probability and Statistics

error analysis, statistical inference, uncertainty, confidence intervals, linear model fitting
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ErrorPropGuide.nb (822.2 KB) - Mathematica Notebook