Study Guide for Practical Statistics for Educators

 Ruth Ravid e Elizabeth Oyer

Rowman & Littlefield Publishers | 2011 - 4ª edição | páginas | rar -pdf | 680 kb

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The fourth edition of the Study Guide for Practical Statistics for Educators serves as a user-friendly and accessible way for students to better understand, review, and apply the concepts introduced in its companion textbook, Practical Statistics for Educators (Ravid, 2011). Since the first edition of this study guide came out in 1994, thousands of students in educational statistics courses and their professors have found it to be an excellent guide with clear and easy-to-follow instructions and examples. The study guide allows students to reinforce and test their knowledge of the concepts addressed in each chapter of the textbook. At the end of each chapter, the best answer for each exercise is given, along with an explanation for why the correct answer is better than the other choices. New in this edition are accompanying Excel exercises, so students may perform data analysis with this commonly-used software, using data available on the web-based portal that accompanies the guide.

Contents
Preface vii
1 An Overview of Educational Research 1
2 Basic Concepts in Statistics 9
3 Organizing and Graphing Data 15
4 Measure of Central Tendency 27
5 Measures of Variability 33
6 The Normal Curve and Standard Scores 39
7 Interpreting Test Scores 45
8 Correlations 49
9 Prediction and Regression 57
10 t Test 65
11 Analysis of Variance 75
12 Chi Square 81
13 Reliability 87
14 Validity 91
15 Planning and Conducting Research Studies 95
About the Authors 101

Practical Statistics for Educators

Ruth Ravid

Rowman & Littlefield Publishers | 2010 - 4ª edição | 273 páginas | pdf | 1 Mb

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Practical Statistics for Educators, 4th edition focuses on the application of research and statistics as applied specifically to education. Since the first edition came out in 1994, thousands of students in educational statistics courses and their professors have found it to be an excellent textbook. Educational practitioners have also appreciated keeping this book on their reference shelf. Now in its fourth edition, this well-regarded text is a clear and easy-to-follow manual for use in introductory statistics or action research courses. Ruth Ravid concentrates on the essential concepts in educational statistics including when to use various statistical tests and how to interpret the results. Testing and test score interpretation, reliability, and validity are included to help students understand these topics which are essential for practitioners in education. 
Real-life examples, used generously throughout, are taken from the field of education and presented to illustrate the various concepts and terms. Chapter previews and summaries, as well as a glossary of the main terms and concepts, help readers navigate the book, focus on the most important points, and build upon the knowledge gained from each chapter.
New in this edition are updated and improved graphics, revised and enhanced text, and examples. Lengthy appendixes-tables are deleted and their relevant sections are integrated into the chapters. Detailed and complicated computational steps have also been eliminated.

Contents
Part I. Introduction 
Chapter 1: An Overview of Educational Research Basic (Pure), Applied, and Action Research Quantitative vs. Qualitative Research Experimental vs. Nonexperimental Research Summary 
Chapter 2: Basic Concepts in Statistics  Variables and Measurement Scales Populations and Samples Parameters and Statistics Methods of Sampling Sample Bias Size of Sample Parametric and Nonparametric Statistics Descriptive and Inferential Statistics Using Hypotheses in Research Probability and Level of Significance Errors in Decision Making Degrees of Freedom Effect Size Using Samples to Estimate Population Values Steps in the Process of Hypothesis Testing And Finally... Summary 
Part II. Descriptive Statistics 
Chapter 3: Organizing and Graphing Data Organizing Data Graphing Data Drawing Accurate Graphs Summary 
Chapter 4: Measures of Central Tendency Mode Median Mean Comparing the Mode, Median, and Mean Summary 
Chapter 5: Measures of Variability The Range Standard Deviation and Variance Summary 
Part III. The Normal Curve and Standard Scores 
Chapter 6: The Normal Curve and Standard Scores The Normal Curve Standard Scores Summary 
Chapter 7: Interpreting Test Scores Norm-Referenced Tests Criterion-Referenced Tests Summary 
Part IV. Measuring Relationships 
Chapter 8: Correlation Pearson Product Moment Factors Affecting the Correlation The Coefficient of Determination and Effect Size Intercorrelation Tables Correlation Tables Summary 
Chapter 9: Prediction and Regression Simple Regression Multiple Regression Summary 
Part V. Inferential Statistics 
Chapter 10: t test Hypotheses for t Tests Independent-Samples t Test An Example of a t Test for Independent Samples t Test for Paired Samples An Example of a t Test for Paired Samples t Test for a Single Sample An Example of a t Test for a Single Sample Summary 
Chapter 11: Analysis of Variance One-Way ANOVA Conceptualizing the One-Way ANOVA Hypotheses for a One-Way ANOVA The ANOVA Summary Table Further Interpretation of the F Ratio An Example of a One-Way ANOVA Post Hoc Comparisons Two-Way ANOVA Conceptualizing the Two-Way ANOVA Hypotheses for the Two-Way ANOVA Graphing the Interaction The Two-Way ANOVA Summary Table An Example of a Two-Way ANOVA Summary 
Chapter 12: Chi Square Test Assumptions for the Chi Square Test The Chi Square Test of Independence Summary 
Part VI. Reliability and Validity 
Chapter 13: Reliability Understanding the Theory of Reliability Methods of Assessing Reliability The Standard Error of Measurement Factors Affecting Reliability How High Should the Reliability Be? Summary 
Chapter 14: Validity Content Validity Criterion-Related Validity Concurrent Validity Predictive Validity Construct Validity Face Validity Assessing Validity Test Bias Summary Part Seven: Conducting Your Own Research 
Chapter 15: Planning and Conducting Research Studies Research Ethics The Research Proposal Introduction Literature Review Methodology References The Research Report Results Discussion Summary 
Chapter 16: Choosing the Right Statistical Test Choosing a Statistical Test: A Decision Flowchart Examples Scenarios 

Games and Mathematics: Subtle Connections

David Wells

 Cambridge University Press |  2012 | 258 páginas | rar - pdf |1 Mb

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epub - 3 Mb
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mobi - 3,8 Mb - link

The appeal of games and puzzles is timeless and universal. In this unique book, David Wells explores the fascinating connections between games and mathematics, proving that mathematics is not just about tedious calculation but imagination, insight and intuition. The first part of the book introduces games, puzzles and mathematical recreations, including knight tours on a chessboard. The second part explains how thinking about playing games can mirror the thinking of a mathematician, using scientific investigation, tactics and strategy, and sharp observation. Finally the author considers game-like features found in a wide range of human behaviours, illuminating the role of mathematics and helping to explain why it exists at all. This thought-provoking book is perfect for anyone with a thirst for mathematics and its hidden beauty; a good high school grounding in mathematics is all the background that is required, and the puzzles and games will suit pupils from 14 years.

Contents
PART I: Mathematical recreations and abstract games
Introduction; Everyday puzzles;
1 Recreations from Euler to Lucas;
Euler and the Bridges of Königsberg; Euler and knight tours; Lucas and mathematical recreations; Lucass game of solitaire calculation;
2 Four abstract games;
From Dudeneys puzzle to Golombs Game; Nine Mens Morris; Hex; Chess; Go;
3 Mathematics and games: mysterious connections;
Games and mathematics can be analysed in the head; Can you -look ahead'?; A novel kind of object; They are abstract. They are difficultRules; Hidden structures forced by the rules; Argument and proof; Certainty, error and truth; Players make mistakes; Reasoning, imagination and intuition; The power of analogy; Simplicity, elegance and beauty; Science and games: lets go exploring;
4 Why chess is not mathematics;
Competition; Asking questions about; Metamathematics and game-like mathematics; Changing conceptions of problem solving; Creating new concepts and new objects; Increasing abstraction; Finding common structures; The interaction between mathematics and sciences;
5 Proving versus checking.
The limitations of mathematical recreationsAbstract games and checking solutions; How do you `prove' that 11 is prime?; Is `5 is prime' a coincidence?; Proof versus checking; Structure, pattern and representation; Arbitrariness and un-manageability; Near the boundary;
PART II: Mathematics: game-like, scientific and perceptual
Introduction;
6 Game-like mathematics;
Introduction; Tactics and strategy; Sums of cubes and a hidden connection; A masterpiece by Euler;
7 Euclid and the rules of his geometrical game;
Cevas theorem; Simsons line; The parabola and its geometrical properties. Dandelins spheres
8 New concepts and new objects;
Creating new objects; Does it exist?; The force of circumstance; Infinity and infinite series; Calculus and the idea of a tangent; What is the shape of a parabola?;
9 Convergent and divergent series;
The pioneers; The harmonic series diverges; Weird objects and mysterious situations; A practical use for divergent series;
10 Mathematics becomes game-like; Eulers relation for polyhedra;
The invention-discovery of groups; Atiyah and MacLane disagree; Mathematics and geography;
11 Mathematics as science;
Introduction. Triangle geometry: the Euler line of a triangleModern geometry of the triangle; The Seven-Circle Theorem, and other New Theorems;
12 Numbers and sequences;
The sums of squares; Easy questions, easy answers; The prime numbers; Prime pairs; The limits of conjecture; A Polya conjecture and refutation; The limitations of experiment; Proof versus intuition;
13 Computers and mathematics;
Hofstadter on good problems; Computers and mathematical proof; Computers and 'proof'; Finally: formulae and yet more formulae;
14 Mathematics and the sciences;
Scientists abstract.

Statistics on the Table: The History of Statistical Concepts and Methods

Stephen M. Stigler

Harvard University Press | 2002 | 499 páginas | djvu | 5 Mb

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This lively collection of essays examines in witty detail the history of some of the concepts involved in bringing statistical argument "to the table," and some of the pitfalls that have been encountered. The topics range from seventeenth-century medicine and the circulation of blood, to the cause of the Great Depression and the effect of the California gold discoveries of 1848 upon price levels, to the determinations of the shape of the Earth and the speed of light, to the meter of Virgil's poetry and the prediction of the Second Coming of Christ. The title essay tells how the statistician Karl Pearson came to issue the challenge to put "statistics on the table" to the economists Marshall, Keynes, and Pigou in 1911. The 1911 dispute involved the effect of parental alcoholism upon children, but the challenge is general and timeless: important arguments require evidence, and quantitative evidence requires statistical evaluation. Some essays examine deep and subtle statistical ideas such as the aggregation and regression paradoxes; others tell of the origin of the Average Man and the evaluation of fingerprints as a forerunner of the use of DNA in forensic science. Several of the essays are entirely nontechnical; all examine statistical ideas with an ironic eye for their essence and what their history can tell us about current disputes.

Contents
Acknowledgments IX
Introduction 1
I. Statistics and Social Science
1 Karl Pearson and the Cambridge Economists 13
2 The Average Man Is 168 Years Old 51
3 Jevons as Statistician 66
4 Jevons on the King-Davenant Law of Demand 80
5 Francis Ysidro Edgeworth, Statistician 87
II. Galtonian Ideas
6 Galton and Identification by Fingerprints 131
7 Stochastic Simulation in the Nineteenth Century 141
8 The History of Statistics in 1933 157
9 Regression toward the Mean 173
10 Statistical Concepts in Psychology 189
III. Some Seventeenth-Century Explorers
11 Apollo Mathematicus 203
12 The Dark Ages of Probability 239
13 John Craig and the Probability of History 252
IV Questions of Discovery
14 Stigler's Law of Eponymy 277
15 Who Discovered Bayes's Theorem? 291
16 Daniel Bernoulli, Leonhard Euler, and Maximum Likelihood 302
17 Gauss and the Invention of Least Squares 320
18 Cauchy and the Witch of Agnesi 332
19 Karl Pearson and Degrees of Freedom 338
V Questions of Standards
20 Statistics and Standards
21 The Trial of the Pyx
22 Normative Terminology
with H. Kruskal

Mathematicians and their times: History of mathematics and mathematics of history

Laurence Young 

Academic Press, Elsevier | 1981 | 348 páginas | pdf | 5,4 Mb

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Contents

Preface

Introduction

Early History; The Slow Renaissance; The New Beginning of analiysis

Chapter I The Romantic Period

The Flouting of Arithmetic; The Founding of the Ecole Polytechnique; Gauss; The First Romantics;  Riemann and Weierstrass; Between Two Worlds

Chapter II The Dream of a Conceptual Age, and the Hard Reality of Struggle for Existence

The unprized heritage; The significance of  Plato for mathematics; Cantor and Sets; Goettingen 

Chapter III The Age of Contradictions, and of Great Question Marks

The art of the possible;The expansion of mathematics; Cambridge; The Hardy-Littlewood era; The battle ground of ideas; The  uncertain further blooming

Index of Persons

Philosophy of Mathematics in the Twentieth Century: Selected Essays

Charles Parsons

Harvard University Press | 2014 | 365 páginas | rar - pdf |950 kb

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In this illuminating collection, Charles Parsons surveys the contributions of philosophers and mathematicians who shaped the philosophy of mathematics over the course of the past century.
Parsons begins with a discussion of the Kantian legacy in the work of L. E. J. Brouwer, David Hilbert, and Paul Bernays, shedding light on how Bernays revised his philosophy after his collaboration with Hilbert. He considers Hermann Weyl's idea of a "vicious circle" in the foundations of mathematics, a radical claim that elicited many challenges. Turning to Kurt Gödel, whose incompleteness theorem transformed debate on the foundations of mathematics and brought mathematical logic to maturity, Parsons discusses his essay on Bertrand Russell's mathematical logic--Gödel's first mature philosophical statement and an avowal of his Platonistic view.
Philosophy of Mathematics in the Twentieth Century insightfully treats the contributions of figures the author knew personally: W. V. Quine, Hilary Putnam, Hao Wang, and William Tait. Quine's early work on ontology is explored, as is his nominalistic view of predication and his use of the genetic method of explanation in the late work The Roots of Reference. Parsons attempts to tease out Putnam's views on existence and ontology, especially in relation to logic and mathematics. Wang's contributions to subjects ranging from the concept of set, minds, and machines to the interpretation of Gödel are examined, as are Tait's axiomatic conception of mathematics, his minimalist realism, and his thoughts on historical figures

Contents
Preface
Introduction
Part I: Some Mathematicians as Philosophers
1. The Kantian Legacy in Twentieth-Century Foundations of Mathematics
2. Realism and the Debate on Impredicativity, 1917–1944 
Postscript to Essay 2
3. Paul Bernays’ Later Philosophy of Mathematics
4. Kurt Gödel
5. Gödel’s “Russell’s Mathematical Logic” ~
Postscript to Essay 5
6. Quine and Gödel on Analyticity
Postscript to Essay 6
7. Platonism and Mathematical Intuition in Kurt Gödel’s Thought
Postscript to Essay 7
Part II: Contemporaries
8. Quine’s Nominalism
9. Genetic Explanation in The Roots of Reference
10. Hao Wang as Philosopher and Interpreter of Gödel
11. Putnam on Existence and Ontology
12. William Tait’s Philosophy of Mathematics
Bibliography
Copyright Acknowledgments
Index

Windows, Rings, and Grapes — A Look at Different Shapes

(Math Is Categorical)

Brian P. Cleary e Brian Gable 

 Millbrook Pr Trade | 2009 | 36 páginas | rar - pdf | Mb

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In this humorous look at shapes, Brian P. Cleary and Brian Gable introduce circles, ovals, triangles, squares, and rectangles. The comical cats of the wildly popular Words Are CATegorical®series explain how to identify each shape and provide loads of examples. Peppy rhymes, goofy illustrations, and kid-friendly examples make shaping up a snap!