Measurement analysis : an introduction to the statistical analysis of laboratory data in physics, chemistry and the life sciences

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 X[superscript 2], T And F Tests, As Well As The One Most Often Used In The Life Sciences, The Anova, Are Shown. 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. Content: Measurements, errors and estimates -- Error and Uncertainty -- Resolution and reading error -- The illegitimate error -- Uncertainty and systematic error -- Uncertainty and casual error -- The expression of expanded uncertainty -- Distribution of data and errors -- Probability and distributions -- Distribution functions -- The Binomial distribution function -- The Poisson distribution function -- The Guass distribution function -- Relations between distribution functions -- The constant distribution function and the reading error -- Processing of data and uncertainties -- The combination of uncertainties -- Rigorous calculation for the estimate of the combined uncertainty -- The number of significant digits -- The problem of correlation -- The error matrix or matrix of uncertainties -- Interpolation and combination of uncertainties -- Extrapolation and combination of uncertainties -- Mean standard deviation and the weighted mean -- Accuracy tests -- Hypotheses and the verification of accuracy -- Maximum likelihood -- The x[superscript 2] parameter -- Minimisation -- The x[superscript 2] accuracy test -- The number of degrees of freedom -- The parameter x[superscript 2 subscript r] -- The x[superscript 2] probability function -- The t accuracy test -- The F accuracy test -- The F test for the analysis of one variance or ANOVA -- The generalised x[superscript 2] accuracy test -- Confidence, trust and expanded uncertainty -- Probability intervals -- The confidence or trust level -- The t parameter and the confidence level. This text deals with the statistical treatment of experimental data. It can be used by those who are entirely new to the field of statistics and probability calculus. All the concepts, parameters and test variables for the modern treatment of experimental data are included. In general we can say that we all agree more or less on the meaning of the word error.