Curvefitting - Error Representation and Curvefitting

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Error Representation and Curvefitting ( ) This article is a follow-up to the article titled "Error analysis and significant figures," which introduces important terms and concepts. The present article covers the rationale behind the reporting of random (experimental) error, how to represent random error in text, tables, and in figures, and considerations for fitting curves to experimental data. WHEN TO REPORT RANDOM ERROR Random error, known also as experimental error, contributes uncertainty to any experiment or observation that involves measurements. One must take such error into account when making critical decisions. When you present data that are based on uncertain quantities, people who see your results should have the opportunity to take random error into account when deciding whether or not to agree with your conclusions. Without an estimate of error, the implication is that the data are perfect. Random error plays such an important role in decision making, it is necessary to represent such error appropriately in text, tables, and in figures. When we study well defined relationships such as those of Newtonian mechanics, we may not require replicate sampling. We simply select enough intervals at which to collect data so that we are confident in the relationship. Connecting the data points is then sufficient, although it may be desirable to use error bars to represent the accuracy of the measurements. When random error is unpredictable enough and/or large enough in magnitude to obscure the relationship, then it may be appropriate to carry out replicate sampling and represent error in the figure. REPRESENTING EXPERIMENTAL ERROR The definitions of mean, standard deviation, and standard deviation of the mean were made in the previous article. You may also encounter the terms standard error or standard error of the mean, both of which usually denote the standard deviation of the mean. The first set of terms are unequivocal, and their use is preferred. However, in the biological sciences one most often encounters the term standard error of the mean (SEM) rather than standard deviation of the mean. Assumptions The methods described here assume that you have an unbiased sample that is subject to random deviations. Furthermore, it is assumed that the deviations yield a valid sample mean with individual data points scattered above and below the mean in a distribution that is symmetrical, at least theoretically. We call such a distribution the normal distribution, but you may know it better as a "bell curve." Most of us assume that we have a normal distribution, and sometimes that assumption is not correct. Some data distributions are skewed (i.e., shifted to the right or left) or multi-modal
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This note was uploaded on 10/19/2011 for the course CHEM 197 taught by Professor Bonk during the Summer '11 term at Duke.

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Curvefitting - Error Representation and Curvefitting

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