Contents
Preface
1 Statistics,
Experiments,
and Data
1.1 Experiments
and Observations
1.2 Displaying
Data
1.3 Summarising
Data Numerically
1.3.1 Measures
of location
1.3.2 Measures
of spread
1.3.3 More
than one variable
1.4 Large
Samples
1.5 Experimental
Errors
Problems 1
2. Probability
2.1 Axioms of
Probability
2.2 Calculus
of Probabilities
2.3 The
Meaning of Probability
2.3.1 Frequency
interpretation
2.3.2 Subjective
interpretation
Problems 2
3. Probability
Distributions I: Basic Concepts
3.1 Random
Variables
3.2 Single
Variates
3.2.1 Probability
distributions
3.2.2 Expectation
values
3.2.3 Moment-generating,
and characteristic functions
3.3 Several
Variates
3.3.1 Joint
probability distributions
3.3.2 Marginal
and conditional distributions
3.3.3 Moments
and expectation values
3.4 Functions
of a Random Variable
Problems 3
4
Probability Distributions II: Examples
4.1 Uniform
4.2 Univariate
Normal (Gaussian)
4.3 Multivariate
Normal
4.3.1 Bivariate
normal
4.4 Exponential
4.5 Cauchy
4.6
Binomial
4.7
Multinomial
4.8
Poisson
Problems 4
5
Sampling and Estimation
5.1 Random
Samples and Estimators
5.1.1 Samplng
distributions
5.1.2 Properties
of point estimators
5.2 Estimators
for the Mean, Variance, and Covariance
5.3 Laws
of Large Numbers and the Central Limit Theorem
5.4 Experimental
Errors
5.4.1 Propagation
of errors
Problems 5
6
Sampling Distributions Associated with the Normal
Distribution
6.1 Chi-Squared
Distribution
6.2 StudentŐs
t Distribution
6.3 F
Distribution
6.4 Relations
Between 
, t and F Distributions
Problems 6
7
Point Estimation I: Maximum Likelihood and Minimum
Variance
7.1 Estimation
of a Single Parameter
7.2 Variance
of an Estimator
7.2.1 Approximate
methods
7.3 Simultaneous
Estimation of Several Parameters
7.4 Minimum
Variance
7.4.1 Parameter
estimation
7.4.2 Minimum
variance bound
Problems 7
8
Point Estimation II: Least-Squares and Other Methods
8.1 Unconstrained
Linear Least-Squares
8.1.1 General
solution for the parameters
8.1.2 Errors
on the parameter estimates
8.1.3 Quality
of the fit
8.1.4 Orthogonal
polynomials
8.1.5 Fitting
a straight line
8.1.6 Combining
experiments
8.2 Linear
Least-Squares with Constraints
8.3 Non-Linear
Least-Squares
8.4 Other
Methods
8.4.1 Minimum
chi-squared
8.4.2 Method
of moments
8.4.3 BayesŐ
estimators
Problems 8
9
Interval Estimation
9.1 Confidence
Intervals: Basic Ideas
9.2 Confidence
Intervals: General Method
9.3 Normal
Distribution
9.3.1 Confidence
intervals for the mean
9.3.2 Confidence
intervals for the variance
9.3.3 Confidence
regions for the mean and variance
9.4 Poisson
Distribution
9.5 Large
Samples
9.6 Confidence
Intervals Near Boundaries
9.7 Bayesian
confidence
intervals
Problems 9
10 Hypothesis
Testing I: Parameters
10.1 Statistical
Hypotheses
10.2 General
Hypotheses: Likelihood Ratios
10.2.1 Simple
hypothesis: one simple alternative
10.2.2 Composite
hypotheses
10.3 Normal
Distribution
10.3.1 Basic
ideas
10.3.2 Specific
tests
10.4 Other
Distributions
10.5 Analysis
of Variance
Problems 10
11 Hypothesis
Testing II: Other Tests
11.1 Goodness-Of-Fit
Tests
11.1.1 Discrete
distributions
11.1.2 Continuous
distributions
11.1.3 Linear
hypotheses
11.2 Tests for
Independence
11.3 Nonparametric
Tests
11.3.1 Sign
test
11.3.2 Signed-rank
test
11.3.3 Rank-sum
test
11.3.4 Run
test
11.3.5 Rank
correlation coefficient
Problems 11
Appendices
A Miscellaneous
Mathematics
A.1 Matrix
Algebra
A.2 Classical
Theory of Minima
B
Optimisation of Nonlinear Functions
B.1 General
Principles
B.2 Unconstrained
Minimisation of Functions of One variable
B.3 Unconstrained
Minimisation of Multivariable Functions
B.3.1 Direct
search methods
B.3.2 Gradient
methods
B.4 Constrained
Optimisation
C Statistical Tables
C.1 Normal
Distribution
C.2 Binomial
Distribution
C.3 Poisson
Distribution
C.4 Chi-squared
Distribution
C.5 StudentŐs
t Distribution
C.6 F distribution
C.7 Signed-Rank
Test
C.8 Rank-Sum
Test
C.9 Run
Test
C.10 Rank
Correlation Coefficient
D Solutions to
Odd-Numbered Problems
Bibliography
Index