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E-raamat: Basic Statistical Methods and Models for the Sciences

  • Formaat: 296 pages
  • Ilmumisaeg: 12-Jul-2017
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-13: 9781482285659
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  • Formaat: 296 pages
  • Ilmumisaeg: 12-Jul-2017
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-13: 9781482285659

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A textbook explaining the principles behind the statistical analysis software used in scientific research. Using the package MINITAB because it is simple to learn and use and widely available, Rosenblatt (biomathematics, U. of Texas-Galveston) focuses on understanding the assumptions under which the analysis is operating, the characteristics of data emerging from different kinds of systems, and what to expect when statistical procedures are applied to data with special characteristics. She does not specify prerequisites. Annotation c. Book News, Inc., Portland, OR (booknews.com)

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.
Introduction
1(18)
Scientific Method
1(1)
The Aims of Medicine, Science, and Engineering
2(2)
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 Interpretation
19(4)
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 statistics
37(10)
Sampling and Descriptive Statistics
47(42)
Representative and Random Samples
47(13)
Representative sample
47(1)
Random sampling from a finite population without replacement
48(1)
Random sampling from a finite population with replacement
49(1)
Assertion The importance of random sampling
50(1)
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 successive means
63(3)
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 function (EDF)
80(9)
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 other events
97(3)
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 sampling
107(1)
Symbols for j-factorial and the binomial coefficient
108(1)
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 sampling one at a time without replacement
119(1)
Probability of intersection and conditional probability
119(1)
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 applications
133(10)
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 construction
155(1)
Standard normal distribution upper 1- point
155(1)
Summary of normal mean confidence results when standard deviation is known
156(4)
Confidence limits and intervals for percentiles
160(2)
Confidence Limits and Interval for Binomial p
162(7)
Binomial confidence limits and intervals
166(3)
Comparing Estimators
169(4)
The Bootstrap
173(8)
Summary of bootstrap for binomial standard deviation
174(7)
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 one-sample t test
192(1)
Independent two-sample Z tests
193(2)
Independent two-sample student t tests
195(3)
The independent two-sample Wilcoxon test (aka the Mann-Whitney test)
198(3)
The chi-square tests of homogeneity and independence
201(3)
Other tests
204(1)
P-values
204(1)
Significance level of a test, p-value of test statistic
205(1)
Setting up tests of hypotheses
205(1)
Types I and II Errors and (Discriminating) Power
206(3)
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 linear regression
218(3)
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
Rosenblatt, Judah