Statistics in Plain English

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