An Introduction to Statistical Concepts for Education and Behavioral Sciences

by Lomax, Richard G.

• ISBN13: 9780805827491
• ISBN10: 0805827498
• Format: Hardcover
• Copyright: 2000-01-01
• Publisher: LEA, Inc.

Summary

This book provides comprehensive coverage so that it can be used in a single- or two-course sequence in statistics. It provides greater flexibility because it contains many topics not dealt with in other introductory texts. Its conceptual, intuitive approach allows for concepts to be easily stated and related to real-life examples. Throughout the text the author demonstrates how many statistical concepts can be related to one another. Unlike other texts, this book includes the following topics: * skewness and kurtosis measures; * inferences about two dependent proportions and two independent means with unequal variances; * homogeneity of variance tests; * layout of the data in ANOVA models; * the ANOVA linear model; * a wide variety of multiple comparison procedures; * significance tests in multiple linear regression; and * extensive discussion of assumptions and how to deal with assumption violations. Numerous tables and figures help illustrate concepts and present examples within the text. An extensive bibliography is included. A number of pedagogical devices are included to increase the reader's conceptual understanding of statistics: chapter outlines; list of key concepts for each chapter; chapter objectives; numerous realistic examples; summary tables of statistical assumptions; extensive references; and end of chapter conceptual and computational problems. An instructor's manual is available containing answers to all of the problems, as well as a collection of statistical humor designed to be an instructional aid. This book is intended for introductory statistics courses for students in education and behavioral sciences.

Author Biography

Richard G. Lomax is Associate Professor of Educational Research and Applied Statistics in the Colleges of Education and Arts and Sciences at the University of Alabama

Table of Contents

Preface	xiii
Introduction	1	(13)
What Is the Value of Statistics?	3	(1)
Brief Introduction to the History of Statistics	4	(1)
General Statistical Definitions	5	(2)
Types of Variables	7	(1)
Scales of Measurement	8	(3)
Summary	11	(1)
Problems	12	(2)
Data Representation	14	(24)
Tabular Display of Distributions	16	(5)
Graphical Display of Distributions	21	(6)
Percentiles	27	(6)
Summary	33	(1)
Problems	34	(4)
Univariate Population Parameters and Sample Statistics	38	(22)
Rules of Summation	39	(3)
Measures of Central Tendency	42	(4)
Measures of Dispersion	46	(10)
Summary	56	(2)
Problems	58	(2)
The Normal Distribution and Standard Scores	60	(18)
The Normal Distribution	61	(6)
Standard Scores	67	(3)
Skewness and Kurtosis Statistics	70	(5)
Summary	75	(1)
Problems	75	(3)
Introduction to Probability and Sample Statistics	78	(16)
Introduction to Probability	79	(3)
Sampling and Estimation	82	(9)
Summary	91	(1)
Problems	91	(3)
Introduction to Hypothesis Testing: Inferences About a Single Mean	94	(26)
Types of Hypotheses	95	(2)
Types of Decision Errors	97	(3)
Level of Significance (α)	100	(3)
Overview of Steps in the Decision-Making Process	103	(1)
Inferences About μ When σ Is Known	104	(4)
Type II Error (β) and Power (1-β)	108	(3)
Statistical Versus Practical Significance	111	(1)
Inferences About μ When σ Is Unknown	112	(4)
Summary	116	(1)
Problems	117	(3)
Inferences About the Difference Between Two Means	120	(19)
New Concepts	121	(2)
Inferences about Two Independent Means	123	(7)
Inferences about Two Dependent Means	130	(4)
Summary	134	(1)
Problems	135	(4)
Inferences About Proportions	139	(20)
Inferences About Proportions Involving the Normal Distribution	140	(10)
Inferences About Proportions Involving the Chi-Square Distribution	150	(6)
Summary	156	(1)
Problems	157	(2)
Inferences About Variances	159	(14)
New Concepts	160	(1)
Inferences About a Single Variance	161	(3)
Inferences About Two Dependent Variances	164	(2)
Inferences About Two or More Independent Variances (Homogeneity of Variance Tests)	166	(4)
Summary	170	(1)
Problems	171	(2)
Bivariate Measures of Association	173	(18)
Scatterplot	174	(2)
Covariance	176	(3)
Pearson Product---Moment Correlation Coefficient	179	(1)
Inferences About the Pearson Product--Moment Correlation Coefficient	180	(2)
Some Issues Regarding Correlations	182	(3)
Other Measures of Association	185	(3)
Summary	188	(1)
Problems	189	(2)
Simple Linear Regression	191	(40)
Introduction to the Concepts of Simple Linear Regression	192	(3)
The Population Simple Linear Regression Equation	195	(1)
The Sample Simple Linear Regression Equation	196	(30)
Summary	226	(1)
Problems	227	(4)
Multiple Regression	231	(35)
Partial and Semipartial Correlations	232	(3)
Multiple Linear Regression	235	(18)
Variable Selection Procedures	253	(7)
Nonlinear Regression	260	(2)
Summary	262	(1)
Problems	262	(4)
One-Factor Analysis of Variance---Fixed-Effects Model	266	(32)
Characteristics of the One-Factor ANOVA Model	268	(3)
The Layout of the Data	271	(1)
ANOVA Theory	271	(6)
The ANOVA Model	277	(6)
Expected Mean Squares	283	(2)
Assumptions and Violation of Assumptions	285	(3)
The Unequal ns or Unbalanced Procedure	288	(1)
The Kruskal---Wallis One-Factor Analysis of Variance	289	(3)
The Relationship of ANOVA to Regression Analysis	292	(1)
Summary	293	(1)
Problems	294	(4)
Multiple-Comparison Procedures	298	(30)
Concepts of Multiple-Comparison Procedures	300	(6)
Selected Multiple-Comparison Procedures	306	(17)
Summary	323	(2)
Problems	325	(3)
Factorial Analysis of Variance---Fixed-Effects Model	328	(36)
The Two-Factor ANOVA Model	330	(23)
Three-Factor and Higher Order ANOVA	353	(3)
Factorial ANOVA with Unequal ns	356	(3)
Summary	359	(1)
Problems	359	(5)
Introduction to Analysis of Covariance: The One-Factor Fixed-Effects Model With a Single Covariate	364	(29)
Characteristics of the Model	366	(2)
The Layout of the Data	368	(1)
The ANCOVA Model	368	(2)
The ANCOVA Summary Table	370	(1)
Computation of Sums of Squares	371	(1)
Adjusted Means and Multiple-Comparison Procedures	372	(4)
Assumptions and Violation of Assumptions	376	(5)
An Example	381	(5)
Relationship of ANCOVA and Regression Analysis	386	(1)
Using Statistical Packages	387	(1)
ANCOVA Without Randomization	387	(1)
More Complex ANCOVA Models	388	(1)
Nonparametric ANCOVA Procedures	389	(1)
Summary	389	(1)
Problems	390	(3)
Random- and Mixed-Effects Analysis of Variance Models	393	(45)
The One-Factor Random-Effects Model	395	(7)
The Two-Factor Random-Effects Model	402	(6)
The Two-Factor Mixed-Effects Model	408	(7)
The One-Factor Repeated Measures Design	415	(10)
The Two-Factor Split-Plot or Mixed Design	425	(10)
Summary	435	(1)
Problems	435	(3)
Hierarchical and Randomized Block Analysis of Variance Models	438	(29)
The Two-Factor Hierarchical Model	439	(10)
The Two-Factor Randomized Block Design for n = 1	449	(10)
The Two-Factor Randomized Block Design for n > 1	459	(1)
The Friedman Test	459	(2)
Comparison of Various ANOVA Models	461	(1)
Summary	462	(1)
Problems	463	(4)
References	467	(8)
Appendix Tables	475	(26)
Answers to Selected Chapter Problems	501	(10)
Index	511