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Barlow R. Ч Statistics: A Guide and Reference to the Use of Statistical Methods in the Physical Sciences
Barlow R. Ч Statistics: A Guide and Reference to the Use of Statistical Methods in the Physical Sciences



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Ќазвание: Statistics: A Guide and Reference to the Use of Statistical Methods in the Physical Sciences

јвтор: Barlow R.

јннотаци€:

An introduction to the techniques of applied statistics. Provides background information on each method covered, focusing on the theory of measurements and errors and the problem of estimation.


язык: en

–убрика: ‘изика/

—татус предметного указател€: √отов указатель с номерами страниц

ed2k: ed2k stats

√од издани€: 1989

 оличество страниц: 222

ƒобавлена в каталог: 13.04.2008

ќперации: ѕоложить на полку | —копировать ссылку дл€ форума | —копировать ID
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ѕредметный указатель
$\chi^2$      see chi squared
$\gamma$      see skew
$\kappa$      see cumulants
$\rho$      see correlation
$\Sigma$      see standard deviatioi
ACCEPT      141Ч144
Acceptance region      143Ч145
Action level      10
Alternative hypothesis      142Ч145
Analysis of variance (Anova)      164Ч169
Arithmetic mean      6Ч7
Asymptotic limit for ML estimators      85Ч86
Averaging measurements      51Ч55
Axioms of probability      119
Bar charts      4
Bavesian statistics      121Ч125 127 130Ч132
Bayes* theorem      122
Bessel's correction      77Ч78 80
Between-group variance      165Ч166
Bias of ML estimators      84Ч85
Bias, biased      69Ч73
Binned data      4Ч7
Binned data, fitting      105Ч106
Binned data, goodness of fit      152Ч153
Binning, avoidance of      155
Binomial distribution      24Ч30
Binomial distribution, approximated by Gaussian      41
Binomial distribution, approximated by Poisson      32
Binomial tests      147
Binormal distribution      42Ч44
BLOCKS      4
Breit Ч Wigner distribution      46
Cauchy distribution      11 46
Central confidence interval      127
Central limit theorem      49Ч51
Central limit theorem, proof      196Ч198
Central moments      14
Characteristic function      196
Chebyshev polynomials      184
Chi squared      98
Chi squared and contingency tables      169
Chi squared and run test      154
Chi squared distribution      106Ч108
Chi squared distribution, mean and variance      107
Chi squared distribution, proof      108Ч109
Chi squared for binned data      105Ч106
Chi squared in ANOVA      165
Chi squared of straight line fit      100
Chi squared, approximated by Gaussian      152
Chi squared, critical values      151
Chi squared, matrix expression      111
Chi squared, probability      150
Chi squared, test      150Ч153
Classes      4
CLT      see Central Limit Theorem
Collective      120
Combination of errors      55Ч60
Combination of errors, matrix form      60
Combining measurements      53
Composite hypothesis      142
Computing      180Ч186
Concordance      178Ч179
Conditional probability      121Ч122
Confidence belt      128
confidence intervals      125Ч134
Confidence intervals for a constrained quantity      130Ч132
Confidence intervals for a Poisson distribution      133Ч134
Confidence intervals for binomial distribution      132Ч133
Confidence intervals for Gaussian distribution      129Ч130
Confidence intervals, several variables      134
Confidence level      118 125Ч134
Confidence level and hypothesis testing      146
Confidence level, descriptive      125Ч127
Confidence level, estimation      127Ч134
Confidence regions      134
Consistency of ML estimators      84
Consistency, consistent      69Ч70 72
Contingency tables      169Ч170
Continuous data      4
Continuous variables      23 121
Convolution      197
Correlated samples      159Ч161
Correlation and errors      58Ч60
Correlation and the binormal      43 44
Correlation for ranked data      177
Correlation in straight line fit      100Ч102
Correlation matrix      18 59
Correlation of data      15Ч18
Correlation, estimation of coefficient      80
Correlation, Pearson's      177
Correlation, Spearman's      177
Covariance and errors      58Ч60
Covariance in straight line fit      100Ч102
Covariance matrix      18 59
Covariance matrix and chi squared      150
Covariance matrix and systematic errors      65
Covariance of data      15Ч18
Covariance of moments      78
Cramer Ч Rao inequality      75
Critical values, for Student's t      137
Cumulants      198
Curtosis      13
Deciles      13
Degree of belief      123Ч124
Degrees of freedom and chi squared distribution      107Ч108
Degrees of freedom and Student's t      135Ч136
Degrees of freedom in chi squared test      151 -152
Degrees of freedom in contingency tables      170
Degrees of freedom in the F distribution      160Ч164
Descriptive statistics      3
Directional test      142
Discrete data      4
dispersion      8
Distribution free tests      173
Efficiency, efficient      69Ч73
Ensemble      120
Equally-likely cases      121 124
Error      48Ч66
Error matrix      18 59Ч60
Error, estimating      79 107
Error, systematic      61Ч66 80
Error, type I      142
Error, type II      142
Errors on ML estimators      86 87
Estimate, estimation, estimator      68Ч95
Estimation of a half-life      82
Estimation of the correlation coefficient      80
Estimation of the error      79 107
Estimation of the mean      76 83
Estimation of the standard deviation      11 78 83
Estimation of the variance      76
Events      3
expectation value      22Ч24
Expectation value and estimation      70Ч74
Expectation value in the asymptotic limit      85
Extended maximum likelihood      90Ч91
Extrapolation      103
F distribution      160Ч164
Factors (in ANOVA)      167
Failure      24 25
Fisher distribution      160Ч164
Fitting curves      184
Fourier transform      197
Frechet inequality      75
Ftest, and concordance      178
Full width at half maximum, FWHM      13
Gaussian and the CLT      49Ч51
Gaussian approximation to binomial      41
Gaussian approximation to chi squared      107 152
Gaussian approximation to the F distribution      161
Gaussian distribution      34Ч41
Gaussian distribution, and Student's t      134Ч136
Gaussian limit of likelihood function      85
Gaussian, cumulants      198
Gaussian, definite integrals      36Ч37
Gaussian, estimating the mean      73 76 83
Gaussian, estimating the standard deviation      79 83
Gaussian, integrated      37
Gaussian, many dimensional      41 42
Gaussian, one-tailed integral      39
Gaussian, probability content      37
Gaussian, two samples      156Ч161
Gaussian, two-tailed integral      38
Geometric mean      7
Goodness of fit      141 149Ч156
groups      4
Half-life, estimation of      82
Harmonic mean      7
Histograms      4
Histograms, goodness of fit      152Ч153
Hypothesis      141
Hypothesis testing      141Ч171
Hypothesis, alternative      142Ч145
Hypothesis, composite      142
Hypothesis, null      146
Hypothesis, simple      142
Ignorance      125
Inconsistent      see consistent
Independent      23
Inefficient      see efficient
information      75
Interpretation of experiments      141 145Ч147
Interquartile range      12
Invariance of ML estimators      84 87
Kolmogorov test      155Ч156
Kolmogorov test and the two-sample problem      164
Kolmogorov test for ranked data      174
Kolmogorov, probability axioms      119 188
kurtosis      14
Latin square      169
Law of Large Numbers      21Ч23
Least squares estimation      68 97Ч107
Least squares, derived from maximum likelihood      93
Least squares, fitting a parabola      114Ч115
Least squares, fitting a straight line      99Ч105
Least squares, fitting polynomials      114Ч115
Least squares, several variables (linear)      111Ч115
Least squares, several variables (non-linear)      115Ч116
Least squares, using matrices      111Ч116
Likelihood function      71Ч73 81Ч90 111
Linear least squares      111Ч115
Linearity      112
Loss of precision      180Ч184
Lower limit      127Ч129 132Ч134
Lower quartile      12
Mann Ч Whitney test      174
Many-dimensional Gaussian      41 42
Matched pairs, for ranked data      175Ч177
Matched samples      159Ч161
Matrix inversion      183
Maximum Likelihood Estimation      81Ч90
Maximum likelihood estimation, asymptotic limit      85Ч86 89
Maximum likelihood estimation, confidence intervals      134
Maximum likelihood estimation, efficiency      86
Maximum likelihood estimation, errors      86
Maximum likelihood estimation, several variables      88
Mean      6Ч9
Mean absolute deviation      12
Mean deviation      12
Mean for binomial      26
Mean for chi squared distribution      107
Mean for Gaussian      35
Mean for Poisson      30
Mean of a sum of variables      49 50
Mean, estimation of      76 83
Median      7
Median, sign test for      173
Method of moments      92
Minimum variance bound      73Ч75
ML      see maximum likelihood
MODE      7
Moments      14 92
Monte Carlo      185
Multi-dimensional Gaussian      41 42
Multiway analysis of variance      166Ч169
MVB (Minimum Variance Bound)      73Ч75
Neyman Pearson test      144Ч145
Non-directional test      142
Non-linear least squares      115Ч116
Non-numeric data      3
Non-parametric methods      173
Non-uniform bins      4
Normal distribution      see Gaussian distribution
Normal equations      111Ч112
Null hvpothesis      146Ч149
Null hvpothesis in ANOVA      165
Null hvpothesis in Mann Ч Whitney test      174
numeric data      3
Numerical methods      180Ч185
One-tailed probability      40
One-tailed test      142
Parabola fit      114Ч115
Parent distribution      11
Parent population      69
Pearson's correlation      177
Pearson's skew      14
Peirce, C.S.      120
Percentage errors      58
Percentiles      13
Poisson approximated by Gaussian      40
Poisson approximation of binomial      32
Poisson distribution      28Ч33
Poisson tests      148
Polynomials      92 114
Polynomials, Chebyshev      184
Pooled estimate of standard deviation      158 165
Popper, K.      121 188
Power      143Ч144
Precision, loss of      180Ч184
probability      118Ч125
Probability as limit of a frequency      119Ч120 124 128
probability density      23 24
probability distribution      21
Probability, Bayesian      121Ч125
Probability, conditional      121Ч122
Probability, empirical      119Ч120
Probability, mathematical      119
Probability, objective      120Ч121 124
Probability, subjective      121Ч125
Programming      185
Propagation of errors      see combination of errors
Propensity      120Ч121 124
Quadratic equations, and significance errors      183
Quadrature      57
Qualitative data      3Ч4
Quantitative data      3Ч4
Random errors      61 64
Random number distribution, arbitrary function      184
Random number distribution, exponential      184
Random number distribution, Gaussian      51
Random number distribution, weighted rejection      184
Random numbers      184
RANGE      12
Rank      7 172Ч179
Rank sum test      174
Regression      104Ч105
Rejecting a hypothesis      141Ч144
Rejecting measurements      54Ч55
Rejection region      143Ч145
Repeated measurements      51Ч52 76
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