Measurement Analysis

This book deals with the statistical treatment of experimental data. It is also meant for those who are entirely new to the field of statistics and probability calculus, and those who wish to obtain rigorous estimates of the uncertainties associated with the experimental results of any discipline, such as meteorology, engineering, physics, chemistry and the life sciences. To understand the text, only a basic understanding of differential calculus is required.

As an innovative teaching approach, simple laboratory class experiments are used as the basis for developing a detailed statistical analysis. This is done by directly using the students' logbooks without re-elaboration. The approach is profitable and can be easily pursued by the layman.

People have, in the past, been confused by the many statistical definitions, formulae and assumptions. This book tries to avoid any arbitrary definition by using the recently introduced ISO directives.

All the concepts, parameters and test variables for the modern treatment of experimental data are included. Among them are the error, uncertainty and its estimate, the distribution functions and the associated parameters. Every concept is associated with a simple experimental situation and the data analysis is performed in numerical detail. For completeness, the correlation of uncertainties with the error matrix is dealt with in greater detail. All the tests of hypotheses are presented. They are introduced from simple arguments and developed up to the analytical details. The applications of the tests to the fitting of experimental curves of the χ², t and F tests, as well as the one most often used in the life sciences, the ANOVA, are shown.

Sample Chapter(s)
Chapter 1: Measurements, errors and estimates (62 KB)

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• Measurements, Errors and Estimates:
  • Error and Uncertainty
  • Uncertainty and Casual Error
• Distribution of Data and Errors:
  • Probability and Distributions
  • Distribution Functions
• Processing of Data and Uncertainties:
  • The Combination of Uncertainties
  • The Number of Significant Digits
  • The Problem of Correlation
  • Interpolation and Combination of Uncertainties
  • Extrapolation and Combination of Uncertainties
  • Mean Standard Deviation and the Weighted Mean
• Accuracy Test:
  • Hypotheses and the Verification of Accuracy
  • Maximum Likelihood
  • The χ² Parameter
  • Minimisation
  • The χ² Accuracy Test
  • The t Accuracy Test
  • The F Accuracy Test
  • The Generalised χ² Accuracy Test
  • Confidence, Trust and Expanded Uncertainty
  • Exclusion of Data