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Basic Statistical Methods and Models for the Sciences - Judah I. Rosenblatt

Basic Statistical Methods and Models for the Sciences


Published: 1st March 2002
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The use of statistics in biology, medicine, engineering, and the sciences has grown dramatically in recent years and having a basic background in the subject has become a near necessity for students and researchers in these fields. Although many introductory statistics books already exist, too often their focus leans towards theory and few help readers gain effective experience in using a standard statistical software package.

Designed to be used in a first course for graduate or upper-level undergraduate students, Basic Statistical Methods and Models builds a practical foundation in the use of statistical tools and imparts a clear understanding of their underlying assumptions and limitations. Without getting bogged down in proofs and derivations, thorough discussions help readers understand why the stated methods and results are reasonable. The use of the statistical software Minitab is integrated throughout the book, giving readers valuable experience with computer simulation and problem-solving techniques. The author focuses on applications and the models appropriate to each problem while emphasizing Monte Carlo methods, the Central Limit Theorem, confidence intervals, and power functions.

The text assumes that readers have some degree of maturity in mathematics, but it does not require the use of calculus. This, along with its very clear explanations, generous number of exercises, and demonstrations of the extensive uses of statistics in diverse areas applications make Basic Statistical Methods and Models highly accessible to students in a wide range of disciplines.

"Rosenblatt writes for introductory (non-calculus-based) courses in statistics that offer a clear understanding of statistical procedures together with underlying assumptions and limitations. The author brings a fresh approach to the understanding of statistical concepts by integrating throughout Minitab software, providing valuable insight into computer simulation and problem-solving techniquesRosenblatt clearly treats the subject matter by carefully wording the explanations and by having readers work with computer-generated data with properties specified by readers. Numerous solved examples; exercises; epilogue with extensions of topics covered. An interesting and useful book. Recommended. - CHOICE "This text attempts to address the needs of those who use statistics but are not statisticians. Writing such a text poses two challenges. The first challenge is to present mathematically complex ideas in such a way as to engender an intuitive understanding of the concepts without relying on mathematical detail or rigor. The second is to ground these concepts in application, to show how and why they are important from a practical standpointthe book is successful on both points" - TECHNOMETRICS

Introductionp. 1
Scientific Methodp. 1
The Aims of Medicine, Science, and Engineeringp. 2
The Roles of Models and Datap. 4
Deterministic and Statistical Modelsp. 6
Definition: Deterministic modelsp. 6
Definition: Statistical modelsp. 7
Probability Theory and Computer Simulationp. 8
Definition: Monte Carlo simulationp. 9
Classes of Models and Statistical Inferencep. 19
Statistical Models--the Frequency Interpretationp. 19
Definition: The frequency interpretationp. 19
Some Useful Statistical Modelsp. 23
Topic: Normal (Gaussian) distributionsp. 24
Topic: Binomial distributionsp. 30
Topic: Poisson distributionsp. 31
Topic: Uniform distributionsp. 31
Topic: Exponential distributionsp. 32
Topic: Weibull distributionsp. 32
Topic: Gamma distributionsp. 32
Topic: Negative binomial distributionsp. 33
Topic: Hypergeometric distributionsp. 33
Narrowing Down the Class of Potential Modelsp. 35
Topic: Distinguishing characteristics of statisticsp. 37
Sampling and Descriptive Statisticsp. 47
Representative and Random Samplesp. 47
Definition: Representative samplep. 47
Definition: Random sampling from a finite population without replacementp. 48
Definition: Random sampling from a finite population with replacementp. 49
Assertion: The importance of random samplingp. 50
Topic: Sampling from a theoretical populationp. 50
Topic: Random sampling from a finite populationp. 51
Descriptive Statistics of Locationp. 60
Topic: Long-run usual (and unusual) behavior of successive meansp. 63
Descriptive Statistics of Variabilityp. 66
Definition: Population and sample standard deviationsp. 67
Topic: The two-sigma rule-of-thumbp. 68
Other Descriptive Statisticsp. 70
Topic: Time series plotsp. 72
Topic: Scatter plotsp. 74
Topic: The Correlation Coefficientp. 76
Definition: Sample Correlation Coefficientp. 76
Topic: The empirical cumulative distribution function (EDF)p. 80
Survey of Basic Probabilityp. 89
Introductionp. 89
Probability and its Basic Rulesp. 92
Definition: Sample spacep. 94
Definition: Event, occurrence of a given eventp. 94
Topic: Formation of events from other eventsp. 95
Definitions: Formation of events from other eventsp. 97
Definition: Probability Measurep. 100
Theorem: Bonferroni Inequalitiesp. 103
Discrete Uniform Models and Countingp. 105
Topic: Systematic counting methodsp. 106
Theorem: Counting sequencesp. 107
Theorem: Corollary to Theorem 4.11, ordered samplingp. 107
Definition: Symbols for j-factorial and the binomial coefficientp. 108
Theorem: Corollary to Theorems 4.11 and 4.12p. 108
Conditional Probabilityp. 113
Definition: Conditional probability of A given Bp. 114
Theorem: The stratified sampling theoremp. 116
Topic: Relation between random sample and random sampling one at a time without replacementp. 119
Theorem: Probability of intersection and conditional probabilityp. 119
Statistical Independencep. 120
Definition: Statistical independence of events A and Bp. 121
Definition: Mutual statistical independencep. 121
Systematic Approach to Probability Problemsp. 123
Random Variables, Expectation and Variancep. 125
Definition: Random variablep. 125
Definition: Probability function of a discrete RVp. 126
Definition: Probability density of an RVp. 127
Definition: Statistically independent random variablesp. 127
Definition: Population mean, mathematical expectationp. 128
Definition: Variance and standard deviationp. 131
Theorem: Variance computationsp. 132
The Central Limit Theorem and its applicationsp. 133
Theorem: Chebychev inequalityp. 133
Theorem: Expectation and variance of sumsp. 134
Theorem: Central Limit Theoremp. 135
Theorem: Distribution of independent normal sumsp. 141
Introduction to Statistical Estimationp. 143
Methods of Estimationp. 143
Topic: Maximum likelihood estimatorsp. 144
Topic: Natural estimatorsp. 145
Distribution of Sample Percentilesp. 146
Definition: Order statisticsp. 146
Definition: Sample percentiles (quantiles)p. 147
Theorem: Distribution of order statisticsp. 147
Adequacy of Estimatorsp. 149
Confidence Limits and Confidence Intervalsp. 152
Definition: 1- a level confidence limits and intervalsp. 152
Topic: Elementary confidence interval constructionp. 155
Definition: Standard normal distribution upper 1- pointp. 155
Topic: Summary of normal mean confidence results when standard deviation is knownp. 156
Theorem: Confidence limits and intervals for percentilesp. 160
Confidence Limits and Interval for Binomial pp. 162
Theorem: Binomial confidence limits and intervalsp. 166
Comparing Estimatorsp. 169
The Bootstrapp. 173
Topic: Summary of bootstrap for binomial standard deviationp. 174
Testing Hypothesesp. 181
Introductionp. 181
Definition: Test of hypothesesp. 182
Some Commonly Used Statistical Testsp. 187
Topic: One-sample Z testsp. 187
Topic: Paired (student) t testp. 190
Topic: Nonparametric alternative to the one-sample t testp. 192
Topic: Independent two-sample Z testsp. 193
Topic: Independent two-sample student t testsp. 195
Topic: The independent two-sample Wilcoxon test (aka the Mann-Whitney test)p. 198
Topic: The chi-square tests of homogeneity and independencep. 201
Topic: Other testsp. 204
Topic: P-valuesp. 204
Definition: Significance level of a test, p-value of test statisticp. 205
Topic: Setting up tests of hypothesesp. 205
Types I and II Errors and (Discriminating) Powerp. 206
Definition: Power function, type I and type II errorsp. 206
The Simulation Approach to Estimating Powerp. 209
Some Final Issues and Commentsp. 213
Basic Regression and Analysis of Variancep. 217
Introductionp. 217
Simple Linear Regressionp. 217
Definition: Least squares curve fit to data Simple linear regressionp. 218
Multiple Linear Regressionp. 221
The Analysis of Variancep. 222
Topic: The one-way layoutp. 223
Topic: The additive two-way layoutp. 227
Topic: The general two way-layoutp. 230
Epiloguep. 233
Bibliographyp. 235
Selected Answers and Solutionsp. 237
Indexp. 273
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9781584881476
ISBN-10: 158488147X
Audience: Tertiary; University or College
Format: Hardcover
Language: English
Number Of Pages: 296
Published: 1st March 2002
Publisher: Taylor & Francis Inc
Country of Publication: US
Dimensions (cm): 23.5 x 16.51  x 1.91
Weight (kg): 0.59
Edition Number: 1