Dealing with Data
The Commonwealth and International Library: Physics Division
Published on 22. October 2013
410 pages
978-1-4831-5573-9 (ISBN)
Description
Dealing with Data is an introductory course to problems and techniques dealing with data analysis, with emphasis on the physical and engineering sciences. The book starts with the basics of data analysis through non-statistical and non-mathematical assessments of error and uncertainty conditions. Experimental and maximum errors and the use of simple graphical methods are briefly described. Applying quick methods on data analysis such as frequency distributions, determination of standard errors, and applications of significance tests are explained. Special attention is given to the statistical quick methods where the range is preferred to traditional methods of calculation. The author notes that the quick methods have more practical applications in physics and engineering. The use of the quick methods of calculation is more precise in error estimation, confidence limits, and tests for outliers that the error is very negligible when applied to actual conditions. Dealing with errors of computation arising from rounding of values, and those arising from the use of slide rules and of the logarithm tables, is explained. The use of numerical methods (integration, differentiation, and interpolation) and graphical methods (like curve fitting) is briefly explained, with the author's emphasis on choosing the simpler methods. Sixth formers, engineering undergraduates, statisticians, and students of mathematics will find the information in this book useful.
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Content
PrefaceChapter 1 Experimental Errors 1 Error and Uncertainty in Measurements 2 Reading and Setting Errors 2.1 Resolution of a Measurement 3 Assessment of Error Limits by Bracketing 3.1 Null Measurements 3.2 Calibration of Standards 4 Random and Systematic Errors 4.1 Systematic Errors 4.2 Random Errors 4.3 Error and Uncertainty 4.4 Distribution of Random Errors 4.5 Erratic Errors 4.6 Assessment of Random Error 4.7 Accuracy and Precision : Discovery of Systematic Errors 4.8 Combination of Random and Systematic Errors 5 Random Fluctuations 5.1 Estimation of Standard Deviation 6 Random Sampling 7 Personal Error 8 Instrumental Errors 8.1 Replication Error 9 Errors of Approximation 10 Ill-Defined Magnitudes 11 Classification of Types and Sources of ErrorChapter 2 Maximum Errors 12 Propagation of Errors 12.1 Errors in u, Where u = Kxn 12.2 Absolute and Relative Errors 13 Combination of Maximum Errors 13.1 The Generalized Product 13.2 Errors in a Sum or Difference 13.3 A General Formula 14 Errors of Computation 14.1 Significant Figures 14.2 Rounding off 14.3 Rounding off a Final Result 14.4 Rounding off in a Sum of Terms 14.5 Rounding off in Products, Quotients, etc. 14.6 Use of the Slide Rule Exercises on Chapter 2Chapter 3 Frequency Distributions 15 The Frequency Function 15.1 Histograms and Frequency Polygons 16 Probability Distributions 17 Characteristics of a Frequency Distribution 17.1 Location Indices 17.2 Indices of Dispersion 18 Properties of Some Common Distributions 18.1 The Normal or Gaussian Distribution 18.2 The Rectangular, Binomial and Poisson Distributions 19 Percentage Points 19.1 The Distribution of Range 20 Comparison of Observed and Predicted Frequencies Exercises on Chapter 3Chapter 4 Standard Errors 21 Estimation of the Mean 21.1 The Meaning of "True Value" 21.2 Use of a Working Mean 22 The Range Estimator of Standard Deviation 22.1 Further Notes on the Range Estimator 23 The Standard Error 23.1 Standard Error of the Sample Mean 23.2 Standard Error and Standard Deviation 23.3 Other Indices of Error 24 The Standard Error of Measurements 24.1 Standard Error and Replication Error 24.2 Limitations of Standard Error Estimates 25 Increase in Resolution by Averaging: Chapman's Detection of an Atmospheric Lunar Tide 26 The Standard Error of an Estimate of Standard Error 26.1 The Efficiency of Estimators 26.2 Some Possible objections to the Use of the Range Estimator 27 Combination of Standard Errors 28 Considerations of Precision in the Design of Experiments Exercises on Chapter 4Chapter 5 Significance Tests 29 Statistical Interpretation of the Standard Error 29.1 Confidence Limits 29.2 Fiducial Probability 29.3 Allowing for Statistical Uncertainty in Sm 30 Standard Errors and Maximum Errors 31 Significance of Discrepancies 31.1 Discrepancy between Measured and Alleged True Value 31.2 Choice of Significance Level 31.3 Effective Values of N in Table A.4 31.4 Discrepancy between Two Measured Values 31.5 Accuracy Required in Significance Calculations 31.6 Discrepancy between Estimates of Standard Deviation 31.7 Discrepancies in Range 32 Problems of Error Analysis 32.1 Weighting of Observations 32.2 Range Estimator of a with Unequal Groups 32.3 Consistency of Several Observations 32.4 The ¿2-Test 32.
