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Exploratory data analysis.

Cox, M G; Harris, P M; Kenward, P D; Smith, I M (2004) Exploratory data analysis. NPL Report. CMSC 47/04

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Abstract

Least-squares data approximation or regression is a technique widely used in metrology (and other scientific disciplines) for modelling experimental data. Often, and certainly when there is no information to the contrary, the regression is undertaken under the assumption that the measurement deviations (‘errors’) associated with the data are independent and identically distributed. Model validation is used to establish confidence in the reliability of a least-squares fitted model and hence predictions made on the basis of the model. The application of standard statistical tests, such as the X2 (x squared)goodness-of-fit, Kolmogorov-Smirnov and Shapiro-Wilks’ tests, is considered with the aim of validating assumptions made about the statistical model for the experimental data, viz., the distribution for the measurement deviations. In cases where these tests indicate there is doubt that the assumed statistical model applies, an approach is presented to improve knowledge of the statistical model. The approach involves applying a local analysis of the data to evaluate the standard uncertainties associated with the measurements. Applications to simulated data and to real data arising in the application of thermal analysis techniques are given.

Item Type: Report/Guide (NPL Report)
NPL Report No.: CMSC 47/04
Subjects: Mathematics and Scientific Computing
Mathematics and Scientific Computing > Numerical Computation
Last Modified: 02 Feb 2018 13:16
URI: http://eprintspublications.npl.co.uk/id/eprint/2920

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