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The purpose of this introductory article is to discuss the experimental uncertainty analysis of a ''derived'' quantity, based on the uncertainties in the experimentally ''measured'' quantities that are used in some form of mathematical relationship ("model") to calculate that derived quantity. The model used to convert the measurements into the derived quantity is usually based on fundamental principles of a science or engineering discipline. The uncertainty has two components, namely, bias (related to ''accuracy'') and the unavoidable random variation that occurs when making repeated measurements (related to ''precision''). The measured quantities may have biases, and they certainly have random variation, so that what needs to be addressed is how these are "propagated" into the uncertainty of the derived quantity. Uncertainty analysis is often called the "propagation of error." It will be seen that this is a difficult and in fact sometimes intractable problem when handled in detail. Fortunately, approximate solutions are available that provide very useful results, and these approximations will be discussed in the context of a practical experimental example. ==Introduction== Rather than providing a dry collection of equations, this article will focus on the experimental uncertainty analysis of an undergraduate physics lab experiment in which a pendulum is used to estimate the value of the local gravitational acceleration constant ''g''. The relevant equation〔The exact period requires an elliptic integral; see, e.g., This approximation also appears in many calculus-based undergraduate physics textbooks.〕 for an idealized simple pendulum is, approximately, : This is the equation, or model, to be used for estimating ''g'' from observed data. There will be some slight bias introduced into the estimation of ''g'' by the fact that the term in brackets is only the first two terms of a series expansion, but in practical experiments this bias can be, and will be, ignored. The procedure is to measure the pendulum length ''L'' and then make repeated measurements of the period ''T, ''each time starting the pendulum motion from the same initial displacement angle ''θ. ''The replicated measurements of ''T'' are averaged and then used in Eq(2) to obtain an estimate of ''g''. Equation (2) is the means to get from the ''measured'' quantities ''L'', ''T'', and ''θ'' to the ''derived'' quantity ''g''. Note that an alternative approach would be to convert all the individual ''T'' measurements to estimates of ''g'', using Eq(2), and then to average those ''g'' values to obtain the final result. This would not be practical without some form of mechanized computing capability (i.e., computer or calculator), since the amount of numerical calculation in evaluating Eq(2) for many ''T'' measurements would be tedious and prone to mistakes. Which of these approaches is to be preferred, in a statistical sense, will be addressed below. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Experimental uncertainty analysis」の詳細全文を読む スポンサード リンク
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