Dealing with Data - 1st Edition - ISBN: 9780080063980, 9781483155739

Dealing with Data

1st Edition

The Commonwealth and International Library: Physics Division

Authors: Arthur J. Lyon
Editors: W. Ashhurst
eBook ISBN: 9781483155739
Imprint: Pergamon
Published Date: 1st January 1970
Page Count: 410
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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.

Table of Contents


Chapter 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 Error

Chapter 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 2

Chapter 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 3

Chapter 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 4

Chapter 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 χ2-Test

32.5 The Separation of Factors of Error

33 Rejection of Outliers

Exercises on Chapter 5

Chapter 6 Fitting a Straight Line

34 Graphs

34.1 Graphs and Experimental Laws

34.2 Transformation to Linear Form

34.3 The Problem of "Fitting"

34.4 The Aims of a Graph

34.5 Choosing the Scales of a Graph

35 Fitting a Straight Line Graphically

35.1 Graphical Representation of Errors

35.2 Consistency of Errors with a Fitted Line

35.3 Visual Estimation of the Best Line

35.4 Rejection of an Outlying Point

36 Fitting a Straight Line Numerically

36.1 Criteria for the Best-Fitting Line

36.2 The Least-Squares Formula

36.3 The Three-Group Method

36.4 The Five-Group Method

36.5 Assessment of The Grouping Methods

36.6 Non-Uniform Spacing: A Spacing Criterion

36.7 Fitting a Straight Line through the Origin

37 Errors of a Fitted Straight Line

37.1 Error of the Slope

37.2 Errors of Intercepts and Fitted Values

37.3 Both Variables Subject to Error

37.4 Significance and Elimination of a Systematic Trend

37.5 Correlation and Regression Lines

Exercises on Chapter 6

Chapter 7 Computational Errors

38 Rounding off Errors

Basic Requirements

Standard Deviation of Rounding Errors

38.1 Rounding off a Final Result

38.2 Rounding off an Error Estimate

38.3 Rounding off before and during Calculations

38.4 Rounding off in a Generalized Sum

38.5 Rounding off in a Generalized Product

39 The Slide Rule and Its Errors

39.1 Reading Accuracy of the Slide Rule and Other Scales

39.2 An Experimental Check on Slide-Rule Errors

39.3 Conditions for Adequacy of Slide-Rule Computation

40 Other Computing Aids

40.1 Logarithm Tables

40.2 Calculating Machines

Chapter 8 Numerical Methods

41 Numerical Integration

41.1 The Trapezoidal Method

41.2 Errors in the Trapezoidal Method

41.3 The Mid-Ordinate Method and Simpson's Rule

41.4 Dufton's Method

42 Numerical Differentiation

43 Finite Differences

(a) Central Difference Notation

(b) Backward Difference Notation

44 Interpolation Formula

44.1 Inverse Interpolation

45 Errors in Differences and in Interpolation Formula

46 Differentiation Using Differences

47 Integration Using Differences

Exercises on Chapter 8

Chapter 9 Curve Fitting

48 Fitting a Polynomial

48.1 Least-Squares Method: Orthogonal Polynomials

48.2 Standard Errors of Polynomial Coefficients, etc.

48.3 Significance of Polynomial Coefficients

48.4 Standard Errors of Fitted Values

49 Step-Function Methods in Polynomial Fitting

50 Locating a Maximum or Minimum

Exercises on Chapter 9

Appendix A Tables

Appendix B Summaries

Appendix C Notes on the Tables Using Range

Appendix D Selected Bibliography with Notes



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© Pergamon 1970
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About the Author

Arthur J. Lyon

About the Editor

W. Ashhurst