Basic Statistical Methods and Models for the Sciences

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Basic Statistical Methods and Models for the Sciences

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  • 製本 Hardcover:ハードカバー版/ページ数 352 p.
  • 言語 ENG,ENG
  • 商品コード 9781584881476
  • DDC分類 507.27

Full Description


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.

Table of Contents

  Introduction                                     1  (18)
Scientific Method 1 (1)
The Aims of Medicine, Science, and 2 (2)
Engineering
The Roles of Models and Data 4 (2)
Deterministic and Statistical Models 6 (2)
Deterministic models 6 (1)
Statistical models 7 (1)
Probability Theory and Computer Simulation 8 (11)
Monte Carlo simulation 9 (10)
Classes of Models and Statistical Inference 19 (28)
Statistical Models --- the Frequency 19 (4)
Interpretation
The frequency interpretation 19 (4)
Some Useful Statistical Models 23 (12)
Normal (Gaussian) distributions 24 (6)
Binomial distributions 30 (1)
Poisson distributions 31 (1)
Uniform distributions 31 (1)
Exponential distributions 32 (1)
Weibull distributions 32 (1)
Gamma distributions 32 (1)
Negative binomial distributions 33 (1)
Hypergeometric distributions 33 (2)
Narrowing Down the Class of Potential Models 35 (12)
Distinguishing characteristics of 37 (10)
statistics
Sampling and Descriptive Statistics 47 (42)
Representative and Random Samples 47 (13)
Representative sample 47 (1)
Random sampling from a finite population 48 (1)
without replacement
Random sampling from a finite population 49 (1)
with replacement
Assertion The importance of random 50 (1)
sampling
Sampling from a theoretical population 50 (1)
Random sampling from a finite population 51 (9)
Descriptive Statistics of Location 60 (6)
Long-run usual (and unusual) behavior of 63 (3)
successive means
Descriptive Statistics of Variability 66 (4)
Population and sample standard deviations 67 (1)
The two-sigma rule-of-thumb 68 (2)
Other Descriptive Statistics 70 (19)
Time series plots 72 (2)
Scatter plots 74 (2)
The Correlation Coefficient 76 (1)
Sample Correlation Coefficient 76 (4)
The empirical cumulative distribution 80 (9)
function (EDF)
Survey of Basic Probability 89 (54)
Introduction 89 (3)
Probability and its Basic Rules 92 (13)
Sample space 94 (1)
Event, occurrence of a given event 94 (1)
Formation of events from other events 95 (2)
Definitions Formation of events from 97 (3)
other events
Probability Measure 100(3)
Bonferroni Inequalities 103(2)
Discrete Uniform Models and Counting 105(8)
Systematic counting methods 106(1)
Counting sequences 107(1)
Corollary to Theorem 4.11, ordered 107(1)
sampling
Symbols for j-factorial and the binomial 108(1)
coefficient
Corollary to Theorems 4.11 and 4.12 108(5)
Conditional Probability 113(7)
Conditional probability of A given B 114(2)
The stratified sampling theorem 116(3)
Relation between random sample and random 119(1)
sampling one at a time without replacement
Probability of intersection and 119(1)
conditional probability
Statistical Independence 120(3)
Statistical independence of events A and B 121(1)
Mutual statistical independence 121(2)
Systematic Approach to Probability Problems 123(2)
Random Variables, Expectation and Variance 125(8)
Random variable 125(1)
Probability function of a discrete RV 126(1)
Probability density of an RV 127(1)
Statistically independent random variables 127(1)
Population mean, mathematical expectation 128(3)
Variance and standard deviation 131(1)
Variance computations 132(1)
The Central Limit Theorem and its 133(10)
applications
Chebychev inequality 133(1)
Expectation and variance of sums 134(1)
Central Limit Theorem 135(6)
Distribution of independent normal sums 141(2)
Introduction to Statistical Estimation 143(38)
Methods of Estimation 143(3)
Maximum likelihood estimators 144(1)
Natural estimators 145(1)
Distribution of Sample Percentiles 146(3)
Order statistics 146(1)
Sample percentiles (quantiles) 147(1)
Distribution of order statistics 147(2)
Adequacy of Estimators 149(3)
Confidence Limits and Confidence Intervals 152(10)
1- a level confidence limits and intervals 152(3)
Elementary confidence interval 155(1)
construction
Standard normal distribution upper 1- 155(1)
point
Summary of normal mean confidence results 156(4)
when standard deviation is known
Confidence limits and intervals for 160(2)
percentiles
Confidence Limits and Interval for Binomial 162(7)
p
Binomial confidence limits and intervals 166(3)
Comparing Estimators 169(4)
The Bootstrap 173(8)
Summary of bootstrap for binomial 174(7)
standard deviation
Testing Hypotheses 181(36)
Introduction 181(6)
Test of hypotheses 182(5)
Some Commonly Used Statistical Tests 187(19)
One-sample Z tests 187(3)
Paired (student) t test 190(2)
Nonparametric alternative to the 192(1)
one-sample t test
Independent two-sample Z tests 193(2)
Independent two-sample student t tests 195(3)
The independent two-sample Wilcoxon test 198(3)
(aka the Mann-Whitney test)
The chi-square tests of homogeneity and 201(3)
independence
Other tests 204(1)
P-values 204(1)
Significance level of a test, p-value of 205(1)
test statistic
Setting up tests of hypotheses 205(1)
Types I and II Errors and (Discriminating) 206(3)
Power
Power function, type I and type II errors 206(3)
The Simulation Approach to Estimating Power 209(4)
Some Final Issues and Comments 213(4)
Basic Regression and Analysis of Variance 217(16)
Introduction 217(1)
Simple Linear Regression 217(4)
Least squares curve fit to data Simple 218(3)
linear regression
Multiple Linear Regression 221(1)
The Anlaysis of Variance 222(11)
The one-way layout 223(4)
The additive two-way layout 227(3)
The general two way-layout 230(3)
Epilogue 233(2)
Bibliography 235(2)
Selected Answers and Solutions 237(36)
Index 273