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# An Introduction to Statistical Concepts, Second Edition

**by**Lomax; Richard G.

2nd

### 9780805857399

0805857397

Hardcover

4/12/2007

Lawrence Erlbau

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## Summary

Unlike many other statistics texts, this one is comprehensive and flexible enough for either a single or a two-semester course. Instructors can select only the topics that are most appropriate for their course.Its intuitive approach helps students more easily understand the concepts and interpret software results. Throughout the text, the author demonstrates how many statistical concepts relate to one another. Only the most crucial equations are included.The new edition features: SPSS sections throughout with input, output, and APA style write-ups using the book's dataset A CD with every example and problem dataset used in the text in SPSS format; More information on confidence intervals, effect size measures, power, and regression models A revised sequence of the regression and ANOVA chapters for enhanced conceptual flow De-emphasized computations to provide more discussion of concepts and software More end of chapter problems with more realistic data and a greater emphasis on interpretation Many more references An Instructor's Resource CD with all of the solutions to the problems and other teaching aids.The first five chapters cover basic descriptive statistics including ways of representing data graphically, statistical measures, the normal distribution and other standard scores, and probability and sampling.The remainder of the text covers inferential statistics involving means, proportions, variances, and correlations, basic and advanced analysis of variance (ANOVA) and regression models. It contains a number of topics not dealt with in other texts such as robust methods, multiple comparison and nonparametric procedures, and advanced ANOVA and multiple regression models.Realistic examples from education and the behavioral sciences illustrate the concepts. Each example includes an examination of the various procedures and necessary assumptions, tips on developing an APA style write-up, and sample SPSS output. Useful tables of assumptions and the effects of their violation are included, along with how to test assumptions in SPSS. Each chapter concludes with conceptual and computational problems, about a third of which are new to this edition. Answers to the odd-numbered problems are provided.Intended for a one- or a two-semester course in introductory statistics taught in education and/or behavioral science departments. Although used predominantly at the master's or doctoral level, the book is also used at the undergraduate level. Only a rudimentary knowledge of algebra is required.

## Author Biography

**Richard Lomax, Ph.D.,**is a Professor in the College of Education at The Ohio State University. He received his Ph.D. in Educational Research Methodology from the University of Pittsburgh.

## Table of Contents

Preface | p. ix |

Introduction | p. 1 |

What is the value of statistics? | p. 3 |

Brief introduction to the history of statistics | p. 5 |

General statistical definitions | p. 5 |

Types of variables | p. 7 |

Scales of measurement | p. 8 |

Summary | p. 12 |

Data Representation | p. 16 |

Tabular display of distributions | p. 18 |

Graphical display of distributions | p. 23 |

Percentiles | p. 29 |

SPSS | p. 33 |

Summary | p. 34 |

Univariate Population Parameters and Sample Statistics | p. 39 |

Summation notation | p. 40 |

Measures of central tendency | p. 41 |

Measures of dispersion | p. 45 |

SPSS | p. 53 |

Summary | p. 55 |

The Normal Distribution and Standard Scores | p. 59 |

The normal distribution | p. 60 |

Standard scores | p. 65 |

Skewness and kurtosis statistics | p. 68 |

SPSS | p. 72 |

Summary | p. 73 |

Introduction to Probability and Sample Statistics | p. 77 |

Brief introduction to probability | p. 78 |

Sampling and estimation | p. 81 |

Summary | p. 87 |

Introduction to Hypothesis Testing: Inferences About a Single Mean | p. 92 |

Types of hypotheses | p. 93 |

Types of decision errors | p. 95 |

Level of significance [Alpha] | p. 98 |

Overview of steps in the decision-making process | p. 100 |

Inferences about [Mu] when [sigma] is known | p. 101 |

Type II error [Beta] and power [1 - Beta] | p. 105 |

Statistical versus practical significance | p. 108 |

Inferences about [Mu] when [sigma] is unknown | p. 109 |

SPSS | p. 113 |

Summary | p. 114 |

Inferences About the Difference Between Two Means | p. 119 |

New concepts | p. 120 |

Inferences about two independent means | p. 122 |

Inferences about two dependent means | p. 129 |

SPSS | p. 133 |

Summary | p. 134 |

Inferences About Proportions | p. 140 |

Inferences about proportions involving the normal distribution | p. 141 |

Inferences about proportions involving the chi-square distribution | p. 151 |

SPSS | p. 156 |

Summary | p. 158 |

Inferences About Variances | p. 162 |

New concepts | p. 163 |

Inferences about a single variance | p. 164 |

Inferences about two dependent variances | p. 166 |

Inferences about two or more independent variances (homogeneity of variance tests) | p. 168 |

SPSS | p. 172 |

Summary | p. 173 |

Bivariate Measures of Association | p. 176 |

Scatterplot | p. 177 |

Covariance | p. 179 |

Pearson product-moment correlation coefficient | p. 182 |

Inferences about the Pearson product-moment correlation coefficient | p. 183 |

Some issues regarding correlations | p. 186 |

Other measures of association | p. 188 |

SPSS | p. 191 |

Summary | p. 192 |

One-Factor Analysis of Variance-Fixed-Effects Model | p. 196 |

Characteristics of the one-factor ANOVA model | p. 198 |

The layout of the data | p. 200 |

ANOVA theory | p. 201 |

The ANOVA model | p. 206 |

Assumptions and violation of assumptions | p. 210 |

The unequal n's or unbalanced design | p. 213 |

Alternative ANOVA procedures | p. 213 |

SPSS | p. 215 |

Summary | p. 217 |

Multiple Comparison Procedures | p. 222 |

Concepts of multiple comparison procedures | p. 224 |

Selected multiple comparison procedures | p. 228 |

SPSS | p. 241 |

Summary | p. 242 |

Factorial Analysis of Variance-Fixed-Effects Model | p. 247 |

The two-factor ANOVA model | p. 249 |

Three-factor and higher-order ANOVA | p. 265 |

Factorial ANOVA with unequal n's | p. 267 |

SPSS | p. 268 |

Summary | p. 269 |

Introduction to Analysis of Covariance: The One-Factor Fixed-Effects Model With a Single Covariate | p. 277 |

Characteristics of the model | p. 278 |

The layout of the data | p. 281 |

The ANCOVA model | p. 281 |

The ANCOVA summary table | p. 282 |

Partitioning the sums of squares | p. 283 |

Adjusted means and related procedures | p. 283 |

Assumptions and violation of assumptions | p. 286 |

An example | p. 289 |

ANCOVA without randomization | p. 292 |

More complex ANCOVA models | p. 293 |

Nonparametric ANCOVA procedures | p. 293 |

SPSS | p. 293 |

Summary | p. 294 |

Random-and Mixed-Effects Analysis of Variance Models | p. 301 |

The one-factor random-effects model | p. 303 |

The two-factor random-effects model | p. 306 |

The two-factor mixed-effects model | p. 309 |

The one-factor repeated measures design | p. 313 |

The two-factor split-plot or mixed design | p. 319 |

SPSS | p. 325 |

Summary | p. 331 |

Hierarchical and Randomized Block Analysis of Variance Models | p. 335 |

The two-factor hierarchical model | p. 336 |

The two-factor randomized block design for n = 1 | p. 343 |

The two-factor randomized block design for n > 1 | p. 350 |

The Friedman test | p. 350 |

Comparison of various ANOVA models | p. 351 |

SPSS | p. 353 |

Summary | p. 357 |

Simple Linear Regression | p. 361 |

The concepts of simple linear regression | p. 362 |

The population simple linear regression model | p. 364 |

The sample simple linear regression model | p. 365 |

SPSS | p. 381 |

Summary | p. 383 |

Multiple Regression | p. 387 |

Partial and semipartial correlations | p. 388 |

Multiple linear regression | p. 390 |

Other regression models | p. 403 |

SPSS | p. 408 |

What's next? | p. 408 |

Summary | p. 410 |

References | p. 415 |

Appendix Tables | p. 425 |

Answers | p. 449 |

Index | p. 463 |

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