Statistics In Plain English

Description

This introductory textbook provides an inexpensive, brief overview of statistics to help readers gain a better understanding of how statistics work and how to interpret them correctly. Each chapter describes a different statistical technique, ranging from basic concepts like central tendency and describing distributions to more advanced concepts such as t tests, regression, repeated measures ANOVA, and factor analysis. Each chapter begins with a short description of the statistic and when it should be used. This is followed by a more in-depth explanation of how the statistic works. Finally, each chapter ends with an example of the statistic in use, and a sample of how the results of analyses using the statistic might be written up for publication. A glossary of statistical terms and symbols is also included. Using the author’s own data and examples from published research and the popular media, the book is a straightforward and accessible guide to statistics. New features in the fourth edition include: sets of work problems in each chapter with detailed solutions and additional problems online to help students test their understanding of the material, new "Worked Examples" to walk students through how to calculate and interpret the statistics featured in each chapter, new examples from the author’s own data and from published research and the popular media to help students see how statistics are applied and written about in professional publications, many more examples, tables, and charts to help students visualize key concepts, clarify concepts, and demonstrate how the statistics are used in the real world. a more logical flow, with correlation directly preceding regression, and a combined glossary appearing at the end of the book, a Quick Guide to Statistics, Formulas, and Degrees of Freedom at the start of the book, plainly outlining each statistic and when students should use them, greater emphasis on (and description of) effect size and confidence interval reporting, reflecting their growing importance in research across the social science disciplines an expanded website at www.routledge.com/cw/urdan with PowerPoint presentations, chapter summaries, a new test bank, interactive problems and detailed solutions to the text’s work problems, SPSS datasets for practice, links to useful tools and resources, and videos showing how to calculate statistics, how to calculate and interpret the appendices, and how to understand some of the more confusing tables of output produced by SPSS. Statistics in Plain English, Fourth Edition is an ideal guide for statistics, research methods, and/or for courses that use statistics taught at the undergraduate or graduate level, or as a reference tool for anyone interested in refreshing their memory about key statistical concepts. The research examples are from psychology, education, and other social and behavioral sciences. Cover......Page 1 Half Title......Page 3 Series page......Page 4 Title Page......Page 5 Copyright Page......Page 6 Brief Contents......Page 7 Table of Contents......Page 9 Preface......Page 13 Acknowledgments......Page 17 About the Author......Page 19 Quick Guide to Statistics, Formulas, and Degrees of Freedom......Page 21 Populations, Samples, Parameters, and Statistics......Page 23 Inferential and Descriptive Statistics......Page 24 Sampling Issues......Page 25 Types of Variables and Scales of Measurement......Page 26 Research Designs......Page 27 Making Sense of Distributions and Graphs......Page 29 Note......Page 34 2 Measures of Central Tendency......Page 35 Measures of Central Tendency in Depth......Page 36 Example: The Mean, Median, and Mode of Skewed Distributions......Page 37 Wrapping Up and Looking Forward......Page 41 Note......Page 42 Range......Page 43 Calculating the Variance and Standard Deviation......Page 44 Why Have Variance?......Page 48 Examples: Examining the Range, Variance, and Standard Deviation......Page 49 Worked Examples......Page 52 Notes......Page 54 Why Is the Normal Distribution So Important?......Page 55 The Normal Distribution in Depth......Page 56 The Relationship Between the Sampling Method and the Normal Distribution......Page 57 Skew and Kurtosis......Page 58 Example 1: Applying Normal Distribution Probabilities to a Normal Distribution......Page 59 Example 2: Applying Normal Distribution Probabilities to a Nonnormal Distribution......Page 61 Work Problems......Page 62 Standardization and z Scores in Depth......Page 65 Interpreting z Scores......Page 66 Examples: Comparing Raw Scores and z Scores......Page 73 Worked Examples......Page 75 Work Problems......Page 76 What Is a Standard Error?......Page 79 The Conceptual Description of the Standard Error of the Mean......Page 80 How to Calculate the Standard Error of the Mean......Page 82 The Central Limit Theorem......Page 83 The Normal Distribution and t Distributions: Comparing z Scores and t Values......Page 84 The Use of Standard Errors in Inferential Statistics......Page 87 Example: Sample Size and Standard Deviation Effects on the Standard Error......Page 88 Worked Examples......Page 90 Work Problems......Page 92 7 Statistical Significance, Effect Size, and Confidence Intervals......Page 95 Probability......Page 96 Hypothesis Testing and Type I Errors......Page 99 Limitations of Statistical Significance Testing......Page 102 Effect Size in Depth......Page 104 Confidence Intervals in Depth......Page 106 Example: Statistical Significance, Confidence Interval, and Effect Size for a One-Sample t Test of Motivation......Page 108 Work Problems......Page 112 Notes......Page 113 The One-Sample t Test......Page 115 Dependent (Paired) Samples t Test......Page 116 Conceptual Issues with the Independent Samples t Test......Page 117 The Standard Error of the Difference between Independent Sample Means......Page 118 Determining the Significance of the t Value for an Independent Samples t Test......Page 120 Paired or Dependent Samples t Tests in Depth......Page 122 Example 1: Comparing Boys’ and Girls’ Grade Point Averages......Page 124 Example 2: Comparing Fifth- and Sixth-Grade GPAs......Page 125 Writing it Up......Page 126 One-Sample t Test......Page 127 Independent Samples t Test......Page 128 Dependent/Paired t Test......Page 130 Work Problems......Page 132 Note......Page 133 ANOVA vs. Independent t Tests......Page 135 One-Way ANOVA in Depth......Page 136 Deciding if the Group Means Are Significantly Different......Page 139 Post-Hoc Tests......Page 140 Effect Size......Page 142 Example: Comparing the Sleep of 5-, 8-, and 12-Year-Olds......Page 144 Worked Example......Page 148 Wrapping Up and Looking Forward......Page 151 Work Problems......Page 152 Notes......Page 153 When to Use Factorial ANOVA......Page 155 Factorial ANOVA in Depth......Page 156 Main Effects and Controlled or Partial Effects......Page 157 Interactions......Page 158 Interpreting Main Effects in the Presence of an Interaction Effect......Page 160 Analysis of Covariance......Page 162 Illustration of Factorial ANOVA, ANCOVA, and Effect Size with Real Data......Page 163 Example: Performance, Choice, and Public vs. Private Evaluation......Page 165 Wrapping Up and Looking Forward......Page 167 Work Problems......Page 168 When to Use Each Type of Repeated-Measures Technique......Page 171 Repeated-Measures ANOVA in Depth......Page 173 Repeated-Measures Analysis of Covariance (ANCOVA)......Page 176 Adding an Independent Group Variable......Page 178 Example: Changing Attitudes about Standardized Tests......Page 180 Wrapping Up and Looking Forward......Page 184 Work Problems......Page 185 When to Use Correlation and What it Tells Us......Page 187 What the Correlation Coefficient Does, and Does Not, Tell Us......Page 189 The Coefficient of Determination......Page 194 Statistically Significant Correlations......Page 195 Example: The Correlation Between Grades and Test Scores......Page 199 Worked Example: Statistical Significance and Confidence Interval......Page 200 Writing it Up......Page 201 Work Problems......Page 202 Notes......Page 203 Simple vs. Multiple Regression......Page 205 Regression in Depth......Page 206 Multiple Regression......Page 212 An Example Using SPSS......Page 213 Example: Predicting the Use of Self-Handicapping Strategies......Page 219 Writing it Up......Page 221 Worked Examples......Page 222 Wrapping Up and Looking Forward......Page 224 Notes......Page 225 14 The Chi-Square Test of Independence......Page 227 Chi-Square Test of Independence in Depth......Page 228 Example: Generational Status and Grade Level......Page 231 Worked Example......Page 232 Work Problems......Page 234 Factor Analysis in Depth......Page 235 A More Concrete Example of Exploratory Factor Analysis......Page 238 Confirmatory Factor Analysis: A Brief Introduction......Page 242 Reliability Analysis in Depth......Page 243 Work Problems......Page 246 Notes......Page 248 Appendices......Page 249 Appendix A: Area Under the Normal Curve Beyond z......Page 251 Appendix B: Critical Values of the t Distributions......Page 253 Appendix C: Critical Values of the F Distributions......Page 255 Appendix D: Critical Values of the Studentized Range Statistic (For Tukey HSD Tests)......Page 261 Appendix E: Critical Values Of The χ2 Distributions......Page 265 Bibliography......Page 267 Glossary of Terms......Page 269 Glossary of Symbols......Page 279 Index......Page 281