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| Ïîèñê ïî óêàçàòåëÿì |
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| Barlow R. — Statistics: A Guide and Reference to the Use of Statistical Methods in the Physical Sciences |
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| Ïðåäìåòíûé óêàçàòåëü |
 see chi squared
 see skew
 see cumulants
 see correlation
 see standard deviatioi
ACCEPT 141—144
Acceptance region 143—145
Action level 10
Alternative hypothesis 142—145
Analysis of variance (Anova) 164—169
Arithmetic mean 6—7
Asymptotic limit for ML estimators 85—86
Averaging measurements 51—55
Axioms of probability 119
Bar charts 4
Bavesian statistics 121—125 127 130—132
Bayes* theorem 122
Bessel's correction 77—78 80
Between-group variance 165—166
Bias of ML estimators 84—85
Bias, biased 69—73
Binned data 4—7
Binned data, fitting 105—106
Binned data, goodness of fit 152—153
Binning, avoidance of 155
Binomial distribution 24—30
Binomial distribution, approximated by Gaussian 41
Binomial distribution, approximated by Poisson 32
Binomial tests 147
Binormal distribution 42—44
BLOCKS 4
Breit — Wigner distribution 46
Cauchy distribution 11 46
Central confidence interval 127
Central limit theorem 49—51
Central limit theorem, proof 196—198
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 106—108
Chi squared distribution, mean and variance 107
Chi squared distribution, proof 108—109
Chi squared for binned data 105—106
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 150—153
Classes 4
CLT see Central Limit Theorem
Collective 120
Combination of errors 55—60
Combination of errors, matrix form 60
Combining measurements 53
Composite hypothesis 142
Computing 180—186
Concordance 178—179
Conditional probability 121—122
Confidence belt 128
confidence intervals 125—134
Confidence intervals for a constrained quantity 130—132
Confidence intervals for a Poisson distribution 133—134
Confidence intervals for binomial distribution 132—133
Confidence intervals for Gaussian distribution 129—130
Confidence intervals, several variables 134
Confidence level 118 125—134
Confidence level and hypothesis testing 146
Confidence level, descriptive 125—127
Confidence level, estimation 127—134
Confidence regions 134
Consistency of ML estimators 84
Consistency, consistent 69—70 72
Contingency tables 169—170
Continuous data 4
Continuous variables 23 121
Convolution 197
Correlated samples 159—161
Correlation and errors 58—60
Correlation and the binormal 43 44
Correlation for ranked data 177
Correlation in straight line fit 100—102
Correlation matrix 18 59
Correlation of data 15—18
Correlation, estimation of coefficient 80
Correlation, Pearson's 177
Correlation, Spearman's 177
Covariance and errors 58—60
Covariance in straight line fit 100—102
Covariance matrix 18 59
Covariance matrix and chi squared 150
Covariance matrix and systematic errors 65
Covariance of data 15—18
Covariance of moments 78
Cramer — Rao inequality 75
Critical values, for Student's t 137
Cumulants 198
Curtosis 13
Deciles 13
Degree of belief 123—124
Degrees of freedom and chi squared distribution 107—108
Degrees of freedom and Student's t 135—136
Degrees of freedom in chi squared test 151 -152
Degrees of freedom in contingency tables 170
Degrees of freedom in the F distribution 160—164
Descriptive statistics 3
Directional test 142
Discrete data 4
dispersion 8
Distribution free tests 173
Efficiency, efficient 69—73
Ensemble 120
Equally-likely cases 121 124
Error 48—66
Error matrix 18 59—60
Error, estimating 79 107
Error, systematic 61—66 80
Error, type I 142
Error, type II 142
Errors on ML estimators 86 87
Estimate, estimation, estimator 68—95
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 22—24
Expectation value and estimation 70—74
Expectation value in the asymptotic limit 85
Extended maximum likelihood 90—91
Extrapolation 103
F distribution 160—164
Factors (in ANOVA) 167
Failure 24 25
Fisher distribution 160—164
Fitting curves 184
Fourier transform 197
Frechet inequality 75
Ftest, and concordance 178
Full width at half maximum, FWHM 13
Gaussian and the CLT 49—51
Gaussian approximation to binomial 41
Gaussian approximation to chi squared 107 152
Gaussian approximation to the F distribution 161
| Gaussian distribution 34—41
Gaussian distribution, and Student's t 134—136
Gaussian limit of likelihood function 85
Gaussian, cumulants 198
Gaussian, definite integrals 36—37
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 156—161
Gaussian, two-tailed integral 38
Geometric mean 7
Goodness of fit 141 149—156
groups 4
Half-life, estimation of 82
Harmonic mean 7
Histograms 4
Histograms, goodness of fit 152—153
Hypothesis 141
Hypothesis testing 141—171
Hypothesis, alternative 142—145
Hypothesis, composite 142
Hypothesis, null 146
Hypothesis, simple 142
Ignorance 125
Inconsistent see consistent
Independent 23
Inefficient see efficient
information 75
Interpretation of experiments 141 145—147
Interquartile range 12
Invariance of ML estimators 84 87
Kolmogorov test 155—156
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 21—23
Least squares estimation 68 97—107
Least squares, derived from maximum likelihood 93
Least squares, fitting a parabola 114—115
Least squares, fitting a straight line 99—105
Least squares, fitting polynomials 114—115
Least squares, several variables (linear) 111—115
Least squares, several variables (non-linear) 115—116
Least squares, using matrices 111—116
Likelihood function 71—73 81—90 111
Linear least squares 111—115
Linearity 112
Loss of precision 180—184
Lower limit 127—129 132—134
Lower quartile 12
Mann — Whitney test 174
Many-dimensional Gaussian 41 42
Matched pairs, for ranked data 175—177
Matched samples 159—161
Matrix inversion 183
Maximum Likelihood Estimation 81—90
Maximum likelihood estimation, asymptotic limit 85—86 89
Maximum likelihood estimation, confidence intervals 134
Maximum likelihood estimation, efficiency 86
Maximum likelihood estimation, errors 86
Maximum likelihood estimation, several variables 88
Mean 6—9
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 73—75
ML see maximum likelihood
MODE 7
Moments 14 92
Monte Carlo 185
Multi-dimensional Gaussian 41 42
Multiway analysis of variance 166—169
MVB (Minimum Variance Bound) 73—75
Neyman Pearson test 144—145
Non-directional test 142
Non-linear least squares 115—116
Non-numeric data 3
Non-parametric methods 173
Non-uniform bins 4
Normal distribution see Gaussian distribution
Normal equations 111—112
Null hvpothesis 146—149
Null hvpothesis in ANOVA 165
Null hvpothesis in Mann — Whitney test 174
numeric data 3
Numerical methods 180—185
One-tailed probability 40
One-tailed test 142
Parabola fit 114—115
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 28—33
Poisson tests 148
Polynomials 92 114
Polynomials, Chebyshev 184
Pooled estimate of standard deviation 158 165
Popper, K. 121 188
Power 143—144
Precision, loss of 180—184
probability 118—125
Probability as limit of a frequency 119—120 124 128
probability density 23 24
probability distribution 21
Probability, Bayesian 121—125
Probability, conditional 121—122
Probability, empirical 119—120
Probability, mathematical 119
Probability, objective 120—121 124
Probability, subjective 121—125
Programming 185
Propagation of errors see combination of errors
Propensity 120—121 124
Quadratic equations, and significance errors 183
Quadrature 57
Qualitative data 3—4
Quantitative data 3—4
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 7 172—179
Rank sum test 174
Regression 104—105
Rejecting a hypothesis 141—144
Rejecting measurements 54—55
Rejection region 143—145
Repeated measurements 51—52 76
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