Basic Statistics

Power analysis is an essential tool for determining whether a statistically significant result can be expected in a scientific experiment prior to the experiment being performed. Many funding agencies and institutional review boards now require power analyses to be carried out before they will approve experiments, particularly where they involve the use of human subjects. This comprehensive, yet accessible, book provides practising researchers with step-by-step instructions for conducting power/sample size analyses, assuming only basic prior knowledge of summary statistics and the normal distribution. It contains a unified approach to statistical power analysis, with numerous easy-to-use tables to guide the reader without the need for further calculations or statistical expertise. This will be an indispensable text for researchers and graduates in the medical and biological sciences needing to apply power analysis in the design of their experiments.

This work documents the history of techniques that statisticians have used to manipulate economic, meteorological, biological and physical data taken from observations recorded over time. The manipulation tools include per cent change, index numbers, moving averages and 'first differences', i.e., subtracting one observation from the previous value. Professor Klein argues that nineteenth-century business journals, such as The Economist, were as important to the development of time series analysis as Latin treatises on probability theory. While examining the roots of mathematical statistics in commercial practice, she traces changes in analytical forms from table to graph to equation. Klein cautions that we risk measurement without history in unduly mechanistic blending of stationary probability theory with the practical dynamics of commercial traders. This history is accessible to students with a basic knowledge of statistics as well as financial analysts, statisticians and historians o

This 2002 book presents the reader with mathematical tools taken from matrix calculus and zero-one matrices and demonstrates how these tools greatly facilitate the application of classical statistical procedures to econometric models. The matrix calculus results are derived from a few basic rules that are generalizations of the rules of ordinary calculus. These results are summarized in a useful table. Well-known zero-one matrices, together with some newer ones, are defined, their mathematical roles explained, and their useful properties presented. The basic building blocks of classical statistics, namely the score vector, the information matrix, and the Cramer-Rao lower bound, are obtained for a sequence of linear econometric models of increasing statistical complexity. From these are obtained interactive interpretations of maximum likelihood estimators, linking them with efficient econometric estimators. Classical test statistics are also derived and compared for hypotheses of intere

Includes practical elements of matrix theory, continuous multivariate distributions and basic multivariate statistics in the normal distribution; regression and the analysis of variance; factor analys

SPSS Explained provides the student with all that they need to undertake statistical analysis using SPSS, guiding the student from the basic rationale behind the statistics, through detailed explanati

This book was first published in 2004. Many observed phenomena, from the changing health of a patient to values on the stock market, are characterised by quantities that vary over time: stochastic processes are designed to study them. This book introduces practical methods of applying stochastic processes to an audience knowledgeable only in basic statistics. It covers almost all aspects of the subject and presents the theory in an easily accessible form that is highlighted by application to many examples. These examples arise from dozens of areas, from sociology through medicine to engineering. Complementing these are exercise sets making the book suited for introductory courses in stochastic processes. Software (available from www.cambridge.org) is provided for the freely available R system for the reader to apply to all the models presented.

This is a lively textbook providing a solid introduction to financial option valuation for undergraduate students armed with a working knowledge of a first year calculus. Written in a series of short chapters, its self-contained treatment gives equal weight to applied mathematics, stochastics and computational algorithms. No prior background in probability, statistics or numerical analysis is required. Detailed derivations of both the basic asset price model and the Black–Scholes equation are provided along with a presentation of appropriate computational techniques including binomial, finite differences and in particular, variance reduction techniques for the Monte Carlo method. Each chapter comes complete with accompanying stand-alone MATLAB code listing to illustrate a key idea. Furthermore, the author has made heavy use of figures and examples, and has included computations based on real stock market data.

Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.

This concise, entry level text provides an introduction to the importance of genetic studies in conservation and presents the essentials of the discipline in an easy-to-follow format, with main points and terms clearly highlighted. The authors assume only a basic knowledge of Mendelian genetics and simple statistics, making the book accessible to those with a limited background in these areas. Connections between conservation genetics and the wider field of conservation biology are interwoven throughout the book. Worked examples are provided throughout to help illustrate key equations and glossary and suggestions for further reading provide additional support for the reader. Many beautiful pen and ink portraits of endangered species are included to enhance the text. Written for short, introductory level courses in genetics, conservation genetics and conservation biology, this book will also be suitable for practising conservation biologists, zoo biologists and wildlife managers.

Association schemes are of interest to both mathematicians and statisticians and this book was written with both audiences in mind. For statisticians, it shows how to construct designs for experiments in blocks, how to compare such designs, and how to analyse data from them. The reader is only assumed to know very basic abstract algebra. For pure mathematicians, it tells why association schemes are important and develops the theory to the level of advanced research. This book arose from a course successfully taught by the author and as such the material is thoroughly class-tested. There are a great number of examples and exercises that will increase the book's appeal to both graduate students and their instructors. It is ideal for those coming either from pure mathematics or statistics backgrounds who wish to develop their understanding of association schemes.

An accessible, clearly organized survey of the basic topics of measure theory for students and researchers in mathematics, statistics, and physicsIn order to fully understand and appreciate advanced p

Asymmetric information (the fact that borrowers have better information than their lenders) and its theoretical and practical evidence now forms part of the basic tool kit of every financial economist. It is a phenomenon that has major implications for a number of economic and financial issues ranging from both micro and macroeconomic level - corporate debt, investment and dividend policies, the depth and duration of business cycles, the rate of long term economic growth - to the origin of financial and international crises. Asymmetric Information in Financial Markets aims to explain this concept in an accessible way, without jargon and by reducing mathematical complexity. Using elementary algebra and statistics, graphs, and convincing real-world evidence, the author explores the foundations of the problems posed by asymmetries of information in a refreshingly accessible and intuitive way.

Asymmetric information (the fact that borrowers have better information than their lenders) and its theoretical and practical evidence now forms part of the basic tool kit of every financial economist. It is a phenomenon that has major implications for a number of economic and financial issues ranging from both micro and macroeconomic level - corporate debt, investment and dividend policies, the depth and duration of business cycles, the rate of long term economic growth - to the origin of financial and international crises. Asymmetric Information in Financial Markets aims to explain this concept in an accessible way, without jargon and by reducing mathematical complexity. Using elementary algebra and statistics, graphs, and convincing real-world evidence, the author explores the foundations of the problems posed by asymmetries of information in a refreshingly accessible and intuitive way.

This book provides a multi-level introduction to Bayesian reasoning (as opposed to “conventional statistics”) and its applications to data analysis. The basic ideas of this “new” approach to the quant

This book provides a multi-level introduction to Bayesian reasoning (as opposed to “conventional statistics”) and its applications to data analysis. The basic ideas of this “new” approach to the quant

Thompson (statistics, Rice U.), Williams (business, Rice U.), and Findlay present a new, antiefficient markets approach to investment theory and management. Coverage includes the basic institutional

Power analysis is an essential tool for determining whether a statistically significant result can be expected in a scientific experiment prior to the experiment being performed. Many funding agencies and institutional review boards now require power analyses to be carried out before they will approve experiments, particularly where they involve the use of human subjects. This comprehensive, yet accessible, book provides practising researchers with step-by-step instructions for conducting power/sample size analyses, assuming only basic prior knowledge of summary statistics and the normal distribution. It contains a unified approach to statistical power analysis, with numerous easy-to-use tables to guide the reader without the need for further calculations or statistical expertise. This will be an indispensable text for researchers and graduates in the medical and biological sciences needing to apply power analysis in the design of their experiments.

Stressing the concrete applications of economic forecasting, Practical Business Forecasting is accessible to a wide-range of readers, requiring only a familiarity with basic statistics. The text focus

Stressing the concrete applications of economic forecasting, Practical Business Forecasting is accessible to a wide-range of readers, requiring only a familiarity with basic statistics. The text focus

Climatology is, to a large degree, the study of the statistics of our climate. The powerful tools of mathematical statistics therefore find wide application in climatological research. The purpose of this book is to help the climatologist understand the basic precepts of the statistician's art and to provide some of the background needed to apply statistical methodology correctly and usefully. The book is self contained: introductory material, standard advanced techniques, and the specialised techniques used specifically by climatologists are all contained within this one source. There are a wealth of real-world examples drawn from the climate literature to demonstrate the need, power and pitfalls of statistical analysis in climate research. Suitable for graduate courses on statistics for climatic, atmospheric and oceanic science, this book will also be valuable as a reference source for researchers in climatology, meteorology, atmospheric science, and oceanography.

Rigorous probabilistic arguments, built on the foundation of measure theory introduced eighty years ago by Kolmogorov, have invaded many fields. Students of statistics, biostatistics, econometrics, finance, and other changing disciplines now find themselves needing to absorb theory beyond what they might have learned in the typical undergraduate, calculus-based probability course. This 2002 book grew from a one-semester course offered for many years to a mixed audience of graduate and undergraduate students who have not had the luxury of taking a course in measure theory. The core of the book covers the basic topics of independence, conditioning, martingales, convergence in distribution, and Fourier transforms. In addition there are numerous sections treating topics traditionally thought of as more advanced, such as coupling and the KMT strong approximation, option pricing via the equivalent martingale measure, and the isoperimetric inequality for Gaussian processes. The book is not ju

Rigorous probabilistic arguments, built on the foundation of measure theory introduced eighty years ago by Kolmogorov, have invaded many fields. Students of statistics, biostatistics, econometrics, finance, and other changing disciplines now find themselves needing to absorb theory beyond what they might have learned in the typical undergraduate, calculus-based probability course. This 2002 book grew from a one-semester course offered for many years to a mixed audience of graduate and undergraduate students who have not had the luxury of taking a course in measure theory. The core of the book covers the basic topics of independence, conditioning, martingales, convergence in distribution, and Fourier transforms. In addition there are numerous sections treating topics traditionally thought of as more advanced, such as coupling and the KMT strong approximation, option pricing via the equivalent martingale measure, and the isoperimetric inequality for Gaussian processes. The book is not ju

This 2002 book presents the reader with mathematical tools taken from matrix calculus and zero-one matrices and demonstrates how these tools greatly facilitate the application of classical statistical procedures to econometric models. The matrix calculus results are derived from a few basic rules that are generalizations of the rules of ordinary calculus. These results are summarized in a useful table. Well-known zero-one matrices, together with some newer ones, are defined, their mathematical roles explained, and their useful properties presented. The basic building blocks of classical statistics, namely the score vector, the information matrix, and the Cramer-Rao lower bound, are obtained for a sequence of linear econometric models of increasing statistical complexity. From these are obtained interactive interpretations of maximum likelihood estimators, linking them with efficient econometric estimators. Classical test statistics are also derived and compared for hypotheses of intere

The massive research effort known as the Human Genome Project is an attempt to record the sequence of the three trillion nucleotides that make up the human genome and to identify individual genes within this sequence. While the basic effort is of course a biological one, the description and classification of sequences also lend themselves naturally to mathematical and statistical modeling. This short textbook on the mathematics of genome analysis presents a brief description of several ways in which mathematics and statistics are being used in genome analysis and sequencing. It will be of interest not only to students but also to professional mathematicians curious about the subject.

This general introduction to the ideas and techniques required for the mathematical modelling of diseases begins with an outline of some disease statistics dating from Daniel Bernoulli's 1760 smallpox data. The authors then describe simple deterministic and stochastic models in continuous and discrete time for epidemics taking place in either homogeneous or stratified (non-homogeneous) populations. Several techniques for constructing and analysing models are provided, mostly in the context of viral and bacterial diseases of human populations. These models are contrasted with models for rumours and vector-borne diseases like malaria. Questions of fitting data to models, and their use in understanding methods for controlling the spread of infection, are discussed. Exercises and complementary results at the end of each chapter extend the scope of the text, which will be useful for students taking courses in mathematical biology who have some basic knowledge of probability and statistics.

This textbook introduces students progressively to various aspects of qualitative models and assumes a knowledge of basic principles of statistics and econometrics. Inferring qualitative characteristics of data on socioeconomic class, education, employment status, and the like - given their discrete nature - requires an entirely different set of tools from those applied to purely quantitative data. Written in accessible language and offering cogent examples, students are given valuable means to gauge real-world economic phenomena. After the introduction, early chapters present models with endogenous qualitative variables, examining dichotomous models, model specification, estimation methods, descriptive usage, and qualitative panel data. Professor Gourieroux also looks at Tobit models, in which the exogenous variable is sometimes qualitative and sometimes quantitative, and changing-regime models, in which the dependent variable is qualitative but expressed in quantitative terms. The fi

This textbook introduces students progressively to various aspects of qualitative models and assumes a knowledge of basic principles of statistics and econometrics. Inferring qualitative characteristics of data on socioeconomic class, education, employment status, and the like - given their discrete nature - requires an entirely different set of tools from those applied to purely quantitative data. Written in accessible language and offering cogent examples, students are given valuable means to gauge real-world economic phenomena. After the introduction, early chapters present models with endogenous qualitative variables, examining dichotomous models, model specification, estimation methods, descriptive usage, and qualitative panel data. Professor Gourieroux also looks at Tobit models, in which the exogenous variable is sometimes qualitative and sometimes quantitative, and changing-regime models, in which the dependent variable is qualitative but expressed in quantitative terms. The fi

In The Math Behind Wall Street, Nick Teebagy speaks intelligently to investors at all levels of experience. A mathematician, Teebagy begins by exploring key terms ranging from statistics and probabil

The fundamental concepts of fractal geometry and chaotic dynamics, along with the related concepts of multifractals, self-similar time series, wavelets, and self-organised criticality, are introduced in this book, for a broad range of readers interested in complex natural phenomena. Now in a greatly expanded second edition, this book relates fractals and chaos to a variety of geological and geophysical applications. These include drainage networks and erosion, floods, earthquakes, mineral and petroleum resources, fragmentation, mantle convection and magnetic field generation. Many advances have been made in the field since the first edition was published. In this edition coverage of self-organised criticality is expanded and statistics and time series are included to provide a broad background for the reader. All concepts are introduced at the lowest possible level of mathematics consistent with their understanding, so that the reader requires only a background in basic physics and mat

This volume is an introduction to stochastic processes and their statistics. Basic stochastic processes are developed from real world situations to the need for generating mathematical models, while a

This book is about some of the basic ideas in mathematics that people are likely to encounter in the normal course of their lives. It is about money-statistics, relations, probabilit graphs, decision

Making a substantiated choice of the most efficient statistical test is one of the basic problems of statistics. Asymptotic efficiency is an indispensable technique for comparing and ordering statistical tests in large samples. It is especially useful in nonparametric statistics where it is usually necessary to rely on heuristic tests. This monograph presents a unified treatment of the analysis and calculation of the asymptotic efficiencies of nonparametric tests. Powerful new methods are developed to evaluate explicitly different kinds of efficiencies. Of particular interest is the description of domains of the Bahadur local optimality and related characterisation problems based on recent research by the author. Other Russian results are also published here for the first time in English. Researchers, professionals and students in statistics will find this book invaluable.

Generations of biologists have relied upon this useful book, which presents the basic concepts of statistics so lucidly and convincingly. It recognises that students must be aware of when to use standard techniques and how to apply the results they obtain. Since many biologists do not have a strong mathematical background, the arguments are gauged in terms which can be easily understood by those with only an elementary knowledge of algebra. Mathematical derivations are avoided and formulae are only used as a convenient shorthand. Although the subject is presented with great simplicity, the coverage is wide and will satisfy the needs of those working in many disciplines. New material for this third edition includes consideration of pocket electronic calculators, and a special chapter is devoted to a discussion of the problems associated with numerical calculation, electronic calculators and computers.

By using familiar concepts from classical measurement methods and basic statistics, this book introduces the basics of item response theory (IRT) and explains the application of IRT methods to problem

This unique book develops the classical subjects of geometric probability and integral geometry, and the more modern one of stochastic geometry, in rather a novel way to provide a unifying framework in which they can be studied. The author focuses on factorisation properties of measures and probabilities implied by the assumption of their invariance with respect to a group, in order to investigate non-trivial factors. The study of these properties is the central theme of the book. Basic facts about integral geometry and random point process theory are developed in a simple geometric way, so that the whole approach is suitable for a non-specialist audience. Even in the later chapters, where the factorisation principles are applied to geometrical processes, the prerequisites are only standard courses on probability and analysis. The main ideas presented here have application to such areas as stereology and tomography, geometrical statistics, pattern and texture analysis. This book will b

This was the first paperback edition of a classic work of recent English historiography, first published in 1981. In analysing the population of a country over several centuries, the authors qualify, confirm or overturn traditional assumptions and marshal a mass of statistical material into a series of clear, lucid arguments about past patterns of demographic behaviour and their relationship to economic trends. The Population History of England presents basic demographic statistics - monthly totals of births, deaths and marriages - and uses them in conjunction with new methods of analysis to determine population size, gross production rates, expectation of life at birth, age structure and net migration totals. The results make it possible to construct a new model of the interplay of economic and demographic variables in England before and during the industrial picture of English population trends between 1541 and 1871 is a remarkable achievement and in a short preface, the authors cons

The advent of electronic computing permits the empirical analysis of economic models of far greater subtlety and rigour than before, when many interesting ideas were not followed up because the calculations involved made this impracticable. The estimation and testing of these more intricate models is usually based on the method of Maximum Likelihood, which is a well-established branch of mathematical statistics. Its use in econometrics has led to the development of a number of special techniques; the specific conditions of econometric research moreover demand certain changes in the interpretation of the basic argument. This book is a self-contained introduction to this field. It consists of three parts. The first deals with general features of Maximum Likelihood methods; the second with linear and nonlinear regression; and the third with discrete choice and related micro-economic models. Readers should already be familiar with elementary statistical theory, with applied econometric res

This textbook, covering the basic mathematics taught to first-year students of science and engineering, reflects the growing awareness that ancillary mathematics should not be taught in isolation from its applications. Topics covered include calculus, ordinary and partial differential equations and statistics. Each chapter starts with two or three examples setting the new techniques to be studied in the context of the scientific world; the mathematics is then presented, along with worked examples. Numerical methods are integrated with analytical techniques where appropriate. The resulting textbook provides the teacher with a rich and varied source of applications for classroom use and students with a textbook for self-learning, giving insight into the significance and role of mathematics in science and engineering.

With a large index, concise commentary, and dozen of charts of statistics, this book can serve as a basic reference and a unique perspective on a turbulent era of military history.

This is a straightforward and practical introduction to statistics for students without any advanced knowledge of mathematics who need to use statistical techniques. The author provides a wide selection of effective tools of the trade so that the reader can tackle a whole variety of concrete situations. No attempt is made to give a comprehensive account of the subject. Enough technique is explained so that the reader can appreciate when there is a need to turn to more advanced material elsewhere. The basic mathematics required is at the level of senior secondary school education, although even less is necessary for the earlier chapters of the book.