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Foundations of Statistics: A Simulation-based Approach [Kõva köide]

  • Formaat: Hardback, 178 pages, kõrgus x laius: 235x155 mm, kaal: 465 g, XV, 178 p., 1 Hardback
  • Ilmumisaeg: 03-Dec-2010
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3642163122
  • ISBN-13: 9783642163128
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  • Formaat: Hardback, 178 pages, kõrgus x laius: 235x155 mm, kaal: 465 g, XV, 178 p., 1 Hardback
  • Ilmumisaeg: 03-Dec-2010
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3642163122
  • ISBN-13: 9783642163128
Statistics and hypothesis testing are routinely used in areas (such as linguistics) that are traditionally not mathematically intensive. In such fields, when faced with experimental data, many students and researchers tend to rely on commercial packages to carry out statistical data analysis, often without understanding the logic of the statistical tests they rely on. As a consequence, results are often misinterpreted, and users have difficulty in flexibly applying techniques relevant to their own research they use whatever they happen to have learned. A simple solution is to teach the fundamental ideas of statistical hypothesis testing without using too much mathematics.

This book provides a non-mathematical, simulation-based introduction to basic statistical concepts and encourages readers to try out the simulations themselves using the source code and data provided (the freely available programming language R is used throughout). Since the code presented in the text almost always requires the use of previously introduced programming constructs, diligent students also acquire basic programming abilities in R.



The book is intended for advanced undergraduate and graduate students in any discipline, although the focus is on linguistics, psychology, and cognitive science. It is designed for self-instruction, but it can also be used as a textbook for a first course on statistics. Earlier versions of the book have been used in undergraduate and graduate courses in Europe and the US.

 

Vasishth and Broe have written an attractive introduction to the foundations of statistics. It is concise, surprisingly comprehensive,self-contained and yet quite accessible. Highly recommended.

Harald Baayen, Professor of Linguistics, University of Alberta, Canada

 

By using the text students not only learn to do the specific things outlined in the book, they also gain a skill set that empowers them to explore new areas that lie beyond the books coverage.

Colin Phillips, Professor of Linguistics, University of Maryland, USA

Arvustused

From the reviews:

"Vasishth and Broe have written an attractive introduction to the foundations of statistics. It is concise, surprisingly comprehensive, self-contained and yet quite accessible. Students will find the simulation-based approach using R very helpful for acquiring an intuitive appreciation of the central concepts and ideas of statistical analysis. Highly recommended."

Harald Baayen, Professor of Linguistics, University of Alberta, Canada

 

My students very much appreciated the simulation-based approach of the text, the fact that it was based upon a powerful, cross-platform analysis package (i.e., R), and the fact that it dealt with issues that are very relevant to the analytical problems that they encounter in their own research. By using the text students not only learn to do the specific things outlined in the book, they also gain a skill set that empowers them to explore new areas that lie beyond the books coverage.

Colin Phillips, Professor of Linguistics, University of Maryland, USA

The Foundations of Statistics provides a step-by-step guide to introductory statistics. this is an introductory text for non-mathematicians, specifically those in the field of linguistics. The topics presented make it also relevant for students in other fields of the social sciences. The book provides a very non-theoretical and non-technical introduction to topics in statistics . the book serves its intended purpose very well. I would happily use it in undergraduate courses for social science students. (Ita Cirovic Donev, The Mathematical Association of America, September, 2011)

1 Getting Started
1(8)
1.1 Installation: R, LATEX, and Emacs
1(1)
1.2 How to read this book
2(1)
1.3 Some Simple Commands in R
2(4)
1.4 Graphical Summaries
6(3)
2 Randomness and Probability
9(34)
2.1 Elementary Probability Theory
9(10)
2.1.1 The Sum and Product Rules
9(2)
2.1.2 Stones and Rain: A Variant on the Coin-toss Problem
11(8)
2.2 The Binomial Distribution
19(3)
2.3 Balls in a Box
22(11)
2.4 Standard Deviation and Sample Size
33(6)
2.4.1 Another Insight: Mean Minimizes Variance
36(3)
2.5 The Binomial versus the Normal Distribution
39(2)
Problems
41(2)
3 The Sampling Distribution of the Sample Mean
43(38)
3.1 The Central Limit Theorem
47(2)
3.2 σ and σx
49(1)
3.3 The 95% Confidence Interval for the Sample Mean
50(2)
3.4 Realistic Statistical Inference
52(1)
3.5 s is an Unbiassed Estimator of Σ
52(3)
3.6 The t-distribution
55(1)
3.7 The One-sample t-test
56(1)
3.8 Some Observations on Confidence Intervals
57(4)
3.9 Sample SD, Degrees of Freedom, Unbiased Estimators
61(2)
3.10 Summary of the Sampling Process
63(1)
3.11 Significance Tests
64(1)
3.12 The Null Hypothesis
65(1)
3.13 z-scores
66(1)
3.14 P-values
67(4)
3.15 Hypothesis Testing: A More Realistic Scenario
71(4)
3.16 Comparing Two Samples
75(4)
3.16.1 H0 in Two-sample Problems
76(3)
Problems
79(2)
4 Power
81(16)
4.1 Hypothesis Testing Revisited
81(1)
4.2 Type I and Type II Errors
82(9)
4.3 Equivalence Testing
91(3)
4.3.1 Equivalence Testing Example
91(1)
4.3.2 TOST Approach to the Stegner et al. Example
92(2)
4.3.3 Equivalence Testing Example: CIs Approach
94(1)
4.4 Observed Power and Null Results
94(2)
Problems
96(1)
5 Analysis of Variance (ANOVA)
97(30)
5.1 Comparing Three Populations
97(2)
5.2 ANOVA
99(12)
5.2.1 Statistical Models
100(3)
5.2.2 Variance of Sample Means as a Possible Statistic
103(2)
5.2.3 Analyzing the Variance
105(6)
5.3 Hypothesis Testing
111(10)
5.3.1 MS-within, MS-between as Statistics
112(1)
5.3.2 The F-distribution
113(5)
5.3.3 ANOVA in R
118(1)
5.3.4 MS-within, Three Non-identical Populations
118(2)
5.3.5 The F-distribution with Unequal Variances
120(1)
5.4 ANOVA as a Linear Model
121(4)
Problems
125(2)
6 Bivariate Statistics and Linear Models
127(18)
6.1 Variance and Hypothesis Testing for Regression
137(5)
6.1.1 Sum of Squares and Correlation
142(1)
Problems
142(3)
7 An Introduction to Linear Mixed Models
145(16)
7.1 Introduction
145(1)
7.2 Simple Linear Model
146(9)
7.3 The Levels of the Complex Linear Model
155(4)
7.4 Further Reading
159(2)
A Random Variables
161(10)
A.1 The Probability Distribution in Statistical Inference
162(1)
A.2 Expectation
162(2)
A.3 Properties of Expectation
164(1)
A.4 Variance
165(1)
A.5 Important Properties of Variance
165(1)
A.6 Mean and SD of the Binomial Distribution
166(1)
A.7 Sample versus Population Means and Variances
167(1)
A.8 Summing up
168(1)
Problems
169(2)
B Basic R Commands and Data Structures
171(4)
References 175(2)
Index 177