Second Edition. — Society for Industrial and Applied Mathematics, Philadelphia, PA- 2005. — 478 p.Basic Concepts fills the need for an introduction to the fundamental ideas of modem statistics that was mathematically rigorous but did not require calculus. This was achieved by restricting attention to discrete situations. The book was translated into Italian, Hebrew, Danish, and, more recently, Farsi. The book in many ways is modem in outlook. This is particularly true for its emphasis on models and model-building but also by its coverage of such topics as survey sampling (both simple and stratified), experimental design (with a proof of the superiority of factorial design over varying one factor at a time), its presentation of nonparametric tests such as the Wilcoxon, and its discussion of power (including the Neyman—Pearson lemma). The book is very much in the spirit of texts on discrete mathematics and could well be used to supplement high school and college courses on this subject.
Although the book contains a large number of examples from a great variety of fields of application, it does not base these on real data. When used as a textbook, this drawback could be remedied by adding a laboratory in which actual situations are discussed.Probability models.
Random experiments
Empirical basis of probability
Simple events and their probabilities
Definition of a probability model
Uniform probability models
The algebra of events
Some laws of probability
Sampling.
A model for sampling
The number of samples
Ordered sampling
Some formulas for sampling
Product models.
Product models for two-part experiments
Realism of product models
Binomial trials
The use of random numbers to draw samples
Conditional probability.
The concept of conditional probability
Independence
Two-stage experiments
Properties of two-stage models; Bayes' law
Applications of probability to genetics
Marriage of relatives
Personal probability
Random variables.
Definitions
Distribution of a random variable
Expectation
Properties of expectation
Laws of expectation
Variance
Laws of variance
Special distributions.
The binomial distribution
The hypergeometric distribution
Standard units
The normal curve and the central limit theorem
The normal approximation
The Poisson approximation for np = 1
The Poisson approximation: general case
The uniform and matching distributions
The law of large numbers
Sequential stopping
Multivariate distributions.
Joint distributions
Covariance and correlation
The multinomial distribution
Estimation.
Unbiased estimation
The accuracy of an unbiased estimate
Sample size
Estimation in measurement and sampling models.
A model for sampling
A model for measurements
Comparing two quantities or populations
Estimating the effect of a treatment
Estimation of variance
Optimum methods of estimation.
Choice of an estimate
Experimental design
Stratified sampling
An inequality and its applications
Tests of significance.
First concepts of testing
Methods for computing significance
The chi-square test for goodness of fit
Tests for comparative experiments.
Comparative experiments
The Fisher-Irwin test for two-by-two tables
The Wilcoxon two-sample test
The Wilcoxon distribution
The sign test for paired comparisons
Wilcoxon‘s test for paired comparisons
The problem of ties
The concept of power.
The two kinds of error
Determination of sample size. Power of a test
The power curve
One- and two-sided tests
Choice of test statistic
The X, t and Wilcoxon one-sample tests
Tables.
Number of combinations
Binomial distributions
Square roots
Normal approximation
Poisson approximation
Chi-square approximation
Wilcoxon two-sample distribution
Wilcoxon paired-comparison distribution.
