Taylor J.R. — An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements :: Электронная библиотека попечительского совета мехмата МГУ

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Taylor J.R. — An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements

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Название: An Introduction to Error Analysis: The Study of Uncertainties in Physical Measurements

Автор: Taylor J.R.

Аннотация:

This best-selling text by John Taylor, now released in its second edition, introduces the study of uncertainties to lower division science students. Assuming no prior knowledge, the author introduces error analysis through the use of familiar examples ranging from carpentry to well-known historic experiments. Pertinent worked examples, simple exercises throughout the text, and numerous chapter-ending problems combine to make the book ideal for use in physics, chemistry, and engineering lab courses. The first edition of this book has been translated into six languages.

Язык:

Рубрика: Физика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2-nd edition

Год издания: 1996

Количество страниц: 349

Добавлена в каталог: 24.11.2013

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Предметный указатель

$B_{n, p}(v)$ , binomial distribution      230 (see also Binomial distribution)
, measurement with pendulum      68—69 88
$G_{X, \sigma}(x)$ , Gauss function      133 (see also Normal distribution)
$P_{\mu}(v)$ , Poisson distribution      246 (see also Poisson distribution)
, correlation coefficient      216—217 (see also Correlation coefficient)
$x_{best}$ estimate for       14
$x_{wav}$ , weighted average      175
$\delta x$ , uncertainty in       14 (see also Uncertainty and Error
$\sigma$ , width of Gauss distribution      131 (see also Normal distribution)
$\sigma_{x}$ , covariance of and       212 (see also Covariance)
$\sigma_{x}$ , standard deviation      99—101 (see also Standard deviation)
$\sigma_{\bar{x}}$ , standard deviation of mean      102 (see also Standard deviation of mean)
Absolute uncertainty      29
Absolute zero of temperature      190
Absorption coefficient and photon energy      84
Acceleration of cart on slope      71—73 89
Accepted value      18
Accepted value, compared with measured value      18—20
Addition in quadrature      58
Addition in quadrature, can give smaller answer      62
Addition in quadrature, for independent random errors      57—62
Addition in quadrature, justification of      141—146
Adjusted chi squared      283 (see also Chi squared)
Archimedes’ problem      5—6
Area of a rectangle      104—105 115
Average      see Mean and Weighted average
Average deviation      99
Background events, subtraction of      254—255
Bar histogram      124
Bell-shaped curve      129—130 (see also Normal distribution)
Bending of light by sun      7
Best estimate, $x_{best}$       14
bin      124
Bin histogram      125
Bin, choice of      125—126 262 266—268 272
Binomial coefficient      229
Binomial distribution      228—235
Binomial distribution, compared with Gaussian      232—235
Binomial distribution, definition      230
Binomial distribution, mean for      231 242
Binomial distribution, standard deviation of      232
Binomial distribution, symmetry when $p =\frac{1}{2}$       232
Binomial expansion      230
Binomial series      52 80
Bubble chamber      223
Cart on slope      71—73 89
Chauvenet’s criterion      166—169
Chauvenet’s criterion, to reject several data      169
Chi squared, $\chi^{2}$       266 268
Chi squared, adjusted      283
Chi squared, as indicator of agreement      264
Chi squared, per degree of freedom      271
Chi squared, probabilities for      271—273
Chi squared, reduced, $\tilde{\chi}^{2}$       271
Chi squared, table of probabilities for      292—293
Chi-squared test      261—278
Chi-squared test, for dice experiment      267—268 275
Chi-squared test, for Gauss distribution      261—265 274—275
Chi-squared test, for Poisson distribution      276—277
Coefficient of correlation      see Correlation coefficient
Coefficient of determination      217 (see also Correlation coefficient)
Coefficient of expansion      59
Comparison, of measured and accepted values      18—20 149—151
Comparison, of two measured numbers      20—23 149—151
Compensating errors      74
Confidence level for uncertainty      149 (see also Significance level)
Consistent measurements      173
Constraints      269—270
Correlation coefficient      216—217
Correlation coefficient, probabilities for      219—220
Correlation coefficient, table of probabilities for      290—291
correlation, negative      218
Correlation, of I.Q.      225
Correlation, significant      220
Cosmic rays      253
Counting experiments, uncertainty in      48—49 249
Covariance      212
Covariance, and correlation coefficient      216—217
Covariance, in error propagation      211—215
Critical angle      63
Decay, radioactive      245
Definition, problems of      4 46
Degrees of freedom      188 269—271
Density of gold      5
Determination, coefficient of      217 (see also Correlation coefficient
Deviation      98
Deviation, average      99
Deviation, mean of is zero      111 (see also Standard deviation
Dice experiments      228
Dice experiments, and chi-squared test      267—268 275
Difference of measured numbers      22—24 41—42 49—50 60
Digital displays      47
Discrepancy      16—18
Discrepancy, significant and insignificant      17—18 150—151
Discrete distributions      232
distribution      123
Distribution, binomial      see Binomial distribution
Distribution, discrete      232
Distribution, exponential      155 158
Distribution, Gauss      see Normal distribution
Distribution, limiting      see Limiting distribution
Distribution, Lorentzian      266
Distribution, normal      see Normal distribution
Distribution, parent      126
Distribution, Poisson      see Poisson distribution
Distribution, universe      126 (see also Limiting distribution)
Dividing measured numbers      51—53 61
Door, measurement of      3—4
Erf()      see Normal error integral
Error      3 14
Error bar      5 25—27
Error function      see Normal error integral
Error of the mean      102 (see also Standard deviation of mean)
Error propagation      45—91 209—215
Error propagation, covariance in      211—215
Error propagation, for function of one variable      63—65
Error propagation, for function of several variables      74—77
Error propagation, for independent errors      57—62
Error propagation, for powers      55—56 66
Error propagation, for products and quotients      51—54 61
Error propagation, for sums and differences      49—50 60
Error propagation, general formula      73—77
Error propagation, proof of general formula      146
Error propagation, step-by-step      66—68
Error propagation, upper bound for      214—215
Error propagation, with graphs      63 84
Error, compensating      74
Error, in target practice      95—96
Error, probable      137
error, random      94—97
Error, systematic      11 94—97 106—109
Error, true      18 (see also Uncertainty)
Exponential distribution      155 158
Extrapolation      192
Factorial function,       229
Fractional uncertainty      28—31
Fractional uncertainty, and significant figures      30—31
Fractional uncertainty, in products      31—34 (see also Uncertainty)
Full width at half maximum      156
Function of one variable, uncertainty in      65
Function of several variables, uncertainty in      75
FWHM      156
Gauss distribution      see Normal distribution
Gauss function      133 (see also Normal distribution)
Gaussian approximation, to binomial distribution      232—235
Gaussian approximation, to Poisson distribution      250—251
General relativity, test of      7
Gold, density of      5
graphs      24—28
Graphs, and error propagation      63 84

Graphs, error bars on      25—27 39
Graphs, slope of      25 40
Graphs, straight-line      24—27 181—182
Half width at half maximum      156
Highly significant test (1%)      237 272
histogram      124
Histogram, bar      124
Histogram, bin      125
HWHM      156
Hypotheses      237 238
Hypotheses, null      237
Hypothesis testing      236—240
Inconsistent measurements      173
Independent errors, propagation of      57—62
Interpolation      9
Least squares      174 (see also Least-squares fit to a line and Least-squares fit to curves)
Least-squares fit to a line      182—192
Least-squares fit to a line, estimates for and       184
Least-squares fit to a line, line through origin      200 204
Least-squares fit to a line, uncertainty $\sigma_{y}$       186—188
Least-squares fit to a line, uncertainty in and       188
Least-squares fit to a line, weighted      201 204
Least-squares fit to a line, when both and are uncertain      188—190
Least-squares fit to curves      193—196
Least-squares fit to curves, exponential      194—196
Least-squares fit to curves, polynomial      193—194
Light, bending by sun      7
Limiting distribution      126—129 227
Limiting distribution, as probability      128
Limiting distribution, mean of      129
Limiting distribution, normalization of      128
Limiting distribution, standard deviation of      129 (see also Distribution)
Line of regression      184
Linear correlation      see Correlation coefficient
Linear graphs      24—27 181—182
Linear graphs, slope of      25 40
Linear regression      182 (see also Least-squares fit to a line)
Linearization      194
Lorenzian distribution      266
Margin of error      14 (see also Uncertainty)
Maximum likelihood      see Principle of maximum likelihood
Mean, as best estimate      97—98 137—139
Mean, of binomial distribution      231 242
Mean, of limiting distribution      129
Mean, of normal distribution      134
Mean, of Poisson distribution      247
Mean, standard deviation of      see Standard deviation of mean
Method of least squares      174 (see also Least-squares fit to a line and Least — Squares fit to curves)
Millikan’s measurement of e      109 116
Multiple regression      196—197
Multiplying measured numbers      31—34 53 61
negative correlation      218
Nonparametric tests      238
Normal density function      131
Normal distribution      129—135
Normal distribution, as limit of binomial      232—236
Normal distribution, as limit of Poisson distribution      250—251
Normal distribution, chi-squared test for      261—265 274—275
Normal distribution, compared with binomial      232—235
Normal distribution, compared with Poisson      250
Normal distribution, definition      133
Normal distribution, mean of      134
Normal distribution, normalization of      132
Normal distribution, points of inflection of      157
Normal distribution, proof of for random errors      235—236
Normal distribution, standard deviation of      134
Normal distribution, width parameter of      131
Normal equations      184 194 197
Normal error function      131
Normal error integral      136—137
Normal error integral, tables of      286—289
Normalization condition      124 128
Normalization condition, for normal distribution      132
Normalization condition, for Poisson distribution      257
Normally distributed measurements      133
Null hypothesis      237
One-tailed probability      239
Opinion poll      238—239
Parallax      97
Parent population      126 (see also Limiting distribution)
Partial differentiation      74 90
Partial uncertainty      76
Pendulum      68—69 88
Percent uncertainty      29 (see also Fractional uncertainty)
photoelectric effect      225
Points of inflection of Gauss function      157
Poisson distribution      245—260
Poisson distribution, approximate symmetry for $\mu$ large      250
Poisson distribution, as limit of binomial      246
Poisson distribution, chi-squared test for      276—277
Poisson distribution, compared with Gaussian      250—251
Poisson distribution, definition      246
Poisson distribution, for cosmic rays      253
Poisson distribution, mean of      247
Poisson distribution, normalization of      257
Poisson distribution, standard deviation of      249
Polynomial regression      194
Population standard deviation      100
PRECISION      28 (see also Fractional uncertainty)
Principle of maximum likelihood      139
Principle of maximum likelihood, applied to Poisson distribution      257 258
Principle of maximum likelihood, in least-squares fits      182 202
Principle of maximum likelihood, in weighted averaging      174
probability distribution      227 (see also Limiting distribution)
Probability, one- and two-tailed      239
Probable error      137
Problems of definition      4 46
Product of measured numbers      31—34 42—43 53 61
Propagation of errors      see Error propagation
Quadratic sum      58 (see also Addition in quadrature)
Quotient of measured numbers      51—53 61
Radioactive decay      245
Random component of error      106
Random errors      94—97
Random errors, can become systematic      117
Reduced chi squared, $\tilde{\chi}^{2}$       271 (see also Chi squared)
Refractive index, from critical angle      63
Refractive index, using Snell’s law      69—70 89
Regression, line of      184
Regression, linear      182
Regression, multiple      196—197
Regression, polynomial      194 (see also Least-squares fit to a line and Least-squares fit to curves)
Rejection of data      165—169
Relative uncertainty      28 (see also Fractional uncertainty)
Relativity, test of      7
Residual      98 (see also Deviation)
RMS deviation      99
Sample standard deviation      100
Sample standard deviation as best estimate for width $\sigma$       296
Scatter plot      216
Schwarz inequality      214 224
SD      see Standard deviation
SDOM      (see also Standard deviation of mean)
Sigma notation, $\Sigma$       98
Significance level      238 272
Significant correlation      220
Significant discrepancy      151
Significant figures      14—16 30
Significant figures, and fractional uncertainty      30—31
Significant figures, in products      42—43
Significant figures, need to keep extra      16
Significant test (5%)      237 272
simple pendulum      68—69 88
Ski wax, tests of      236—238
Snell’s law      69—70 89
spreadsheets      112 179 202
Spring constant,       101—103 105—106 200
Square root, uncertainty in      66
Square-root rule      48 249
Standard deviation      98—101

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