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Dealing with Data
The Commonwealth and International Library: Physics Division
- 1st Edition - January 1, 1970
- Author: Arthur J. Lyon
- Editor: W. Ashhurst
- Language: English
- eBook ISBN:9 7 8 - 1 - 4 8 3 1 - 5 5 7 3 - 9
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… Read more
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Request a sales quoteDealing 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.
Preface
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
Index
- No. of pages: 410
- Language: English
- Edition: 1
- Published: January 1, 1970
- Imprint: Pergamon
- eBook ISBN: 9781483155739
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