A Guide to Doing Statistics in Second Language Research Using SPSS and R

Cover......Page 1
Half Title......Page 2
Title Page......Page 4
Copyright Page......Page 5
Dedication......Page 6
Table of Contents......Page 8
Preface......Page 16
Acknowledgments......Page 20
Part I Statistical Ideas......Page 22
1.1 Getting Started with SPSS......Page 24
1.1.2 Entering Your Own Data......Page 26
1.1.3 Application Activity for Getting Started with SPSS......Page 31
1.1.5 Saving Your Work in SPSS......Page 32
1.2.1 Downloading and Installing R......Page 34
1.2.2 Customizing R in Windows......Page 36
1.2.3 Loading Packages and R Commander......Page 38
1.3 Working with Data in R and R Commander......Page 40
1.3.1 Entering Your Own Data......Page 41
1.3.2 Importing Files into R through R Commander......Page 43
1.3.4 Saving Data and Reading It Back In......Page 46
1.3.6 Closing R and R Commander......Page 48
1.4.1 Using R as a Calculator......Page 49
1.4.2 Using R as a Calculator Practice Activities......Page 51
1.4.3 Objects in R......Page 52
1.4.4 Creating Objects in R Practice Activities......Page 53
1.4.5 Types of Data in R......Page 54
1.4.7 Functions in R......Page 56
1.4.8 Functions in R Practice Activities......Page 57
1.4.10 Specifying Variables within a Data Set, and Attaching and Detaching Data Sets......Page 58
1.5.1 Missing Data and Multiple Imputation in SPSS......Page 59
1.5.3 Missing Data and Multiple Imputation in R......Page 64
1.6.2 Getting Help with R......Page 67
1.7 Summary......Page 70
2 Some Preliminaries to Understanding Statistics......Page 71
2.1.1 Levels of Measurement of Variables......Page 72
2.1.2 Application Activity: Practice in Identifying Levels of Measurement......Page 74
2.1.3 Dependent and Independent Variables......Page 75
2.1.4 Application Activities: Practice in Identifying Variables......Page 77
2.1.6 Fixed versus Random Effects (Advanced Topic)......Page 78
2.2 Understanding Hidden Assumptions about How Statistical Testing Works......Page 79
2.2.1 Hypothesis Testing......Page 80
2.2.3 Who Gets Tested? Populations versus Samples and Inferential Statistics......Page 81
2.2.4 What Does a P-Value Mean?......Page 83
2.2.6 Understanding Statistical Reporting......Page 86
2.2.7 Application Activities: Understanding Statistical Reporting......Page 90
2.2.8 The Inner Workings of Statistical Testing......Page 91
2.3 Parametric and Non-Parametric Statistics......Page 94
2.3.1 Why Robust Statistics?......Page 95
2.4 Summary......Page 97
3.1 Numerical Summaries of Data......Page 98
3.1.1 The Mean, Median and Mode......Page 99
3.1.2 Standard Deviation, Variance and Standard Error......Page 101
3.1.3 Confidence Intervals......Page 106
3.1.5 Reporting Numerical Summaries......Page 110
3.1.6 Data for this Chapter......Page 111
3.2.1 Obtaining Numerical Summaries with SPSS and Splitting Groups......Page 112
3.2.2 Application Activities for Numerical Summaries in SPSS......Page 115
3.3.1 Basic Descriptive Statistics in R......Page 116
3.4 Satisfying Assumptions for Parametric Tests......Page 120
3.5 Graphic Summaries of Data: Examining the Shape of Distributions for Normality......Page 121
3.5.1 Histograms......Page 122
3.5.2 Skewness and Kurtosis......Page 125
3.5.3 Stem and Leaf Plots......Page 127
3.6 Obtaining Exploratory Visual Summaries in SPSS......Page 128
3.7 Obtaining Exploratory Visual Summaries in R......Page 133
3.7.1 Creating Histograms with R......Page 134
3.7.2 Creating Stem and Leaf Plots with R......Page 136
3.7.3 Creating Q-Q Plots with R......Page 138
3.7.4 Testing for Normality with R......Page 140
3.7.5 Application Activities: Looking at Normality Assumptions with R......Page 141
3.8 Examining the Shape of Distributions: The Assumption of Homogeneity......Page 142
3.8.1 Checking Homogeneity of Variance (with SPSS or R)......Page 144
3.9.2 Transforming Data......Page 145
3.10 Summary......Page 147
4 Changing the Way We Do Statistics: The New Statistics......Page 149
4.1 Introduction to Confidence Intervals......Page 151
4.1.1 Application Activity for ESCI and Confidence Intervals......Page 152
4.1.2 Interpreting Confidence Intervals......Page 154
4.1.3 Application Activities with Confidence Intervals......Page 158
4.1.4 Confidence Intervals and the Imprecision of P-Values......Page 160
4.2 Introduction to Effect Sizes......Page 162
4.2.1 Understanding Effect Size Measures......Page 164
4.2.2 Interpreting Effect Sizes......Page 165
4.2.3 Calculating Effect Sizes Summary......Page 167
4.2.4 Effect Size Confidence Intervals......Page 170
4.3.1 Null Hypothesis Significance Tests......Page 172
4.3.2 One-Tailed versus Two-Tailed Tests of Hypotheses......Page 175
4.3.3 Outcomes of Null Hypothesis Significance Testing......Page 177
4.3.4 Power Analysis......Page 178
4.3.6 Examples of Power Analyses......Page 179
4.3.7 Application Activities with Power Calculation......Page 183
4.4 Precision instead of Power......Page 184
4.4.1 Application Activities with Precision Calculation......Page 186
4.5.1 Power through Replication and Belief in the “Law of Small Numbers”......Page 187
Part II Statistical Tests......Page 190
5.1 Statistical Tests that are Covered in this Book......Page 192
5.2.1 Correlation: A Test of Relationships......Page 193
5.4.1 Multiple Regression: A Test of Relationships......Page 195
5.5.1 Chi-Square: A Test of Relationships......Page 197
5.6.1 T-Test: A Test of Group Differences......Page 198
5.6.2 A Brief Overview of the Independent Samples T-Test......Page 199
5.6.3 A Brief Overview of the Paired Samples T-Test......Page 200
5.7.1 One-Way Analysis of Variance: A Test of Group Differences......Page 201
5.8.1 Factorial Analysis of Variance: A Test of Group Differences......Page 202
5.9.1 Analysis of Covariance: A Test of Group Differences......Page 204
5.10.1 Repeated-Measures Analysis of Variance: A Test of Group Differences......Page 205
5.12 Application Activities for Choosing a Statistical Test......Page 206
6 Finding Relationships Using Correlation: Age of Learning......Page 209
6.2 Creating Scatterplots in SPSS......Page 211
6.2.1 Adding a Regression or Loess Line......Page 213
6.2.2 Viewing Simple Scatterplot Data by Categories......Page 216
6.3 Creating Scatterplots in R......Page 217
6.3.1 Modifying a Scatterplot in R Console......Page 218
6.3.2 Viewing Simple Scatterplot Data by Categories......Page 221
6.3.3 Application Activities with Scatterplots......Page 223
6.3.5 Creating Multiple Scatterplots with SPSS......Page 224
6.3.6 Creating Multiple Scatterplots with R......Page 225
6.3.7 Interpreting Multiple Scatterplots......Page 226
6.4 Assumptions of Parametric Statistics for Correlation......Page 227
6.4.1 Effect Size for Correlation......Page 229
6.5 Calculating Correlation Coefficients and Confidence Intervals......Page 231
6.5.1 Calculating Correlation Coefficients and Confidence Intervals in SPSS......Page 232
6.5.2 Calculating Correlation Coefficients and Confidence Intervals in R......Page 234
6.5.3 Robust Correlations......Page 239
6.5.4 Application Activities for Correlation......Page 242
6.6 Summary......Page 243
7 Looking for Groups of Explanatory Variables through Multiple Regression: Predicting Important Factors in First Grade Reading......Page 245
7.1 Understanding Regression Design......Page 246
7.1.1 Standard Multiple Regression......Page 248
7.1.3 Data Used in this Chapter......Page 249
7.2 Visualizing Multiple Relationships......Page 250
7.2.1 Graphs in R for Understanding Complex Relationships: Conditioning Plots......Page 251
7.2.2 Graphs in R for Understanding Complex Relationships: 3-D Graphs......Page 255
7.2.3 Graphs in R for Understanding Complex Relationships: Tree Models......Page 256
7.2.4 Application Activities in R with Graphs for Understanding Complex Relationships......Page 258
7.3.1 Assumptions about Sample Size......Page 259
7.4 Performing a Multiple Regression......Page 261
7.4.1 Starting the Multiple Regression in SPSS......Page 262
7.4.2 Regression Output in SPSS......Page 263
7.4.3 Examining Regression Assumptions Using SPSS......Page 270
7.4.4 Robust Regression with SPSS......Page 271
7.4.5 Linear Regression in R: Doing the Same Type of Regression as in SPSS......Page 273
7.4.6 Examining Regression Assumptions in R......Page 280
7.4.7 Robust Linear Regression in R......Page 284
7.4.8 Reporting the Results of a Regression Analysis......Page 285
7.4.9 Application Activities: Multiple Regression......Page 287
7.5 Summary......Page 289
8.1 Types of T-Tests......Page 290
8.1.1 Application Activity: Choosing a T-Test......Page 292
8.2 Data Summaries and Numerical Inspection......Page 293
8.2.1 Visual Inspection: Box Plots......Page 294
8.2.2 Box Plots for One Variable Separated by Groups in SPSS......Page 296
8.2.3 Box Plots for One Variable Separated by Groups in R......Page 297
8.2.4 Box Plots for More than One Variable Plotted on the Same Graph in SPSS......Page 301
8.2.5 Box Plots for More than One Variable Plotted on the Same Graph in R......Page 302
8.2.6 Box Plots for More than One Variable Separated by Groups in SPSS and R......Page 304
8.2.7 Application Activities with Box Plots......Page 306
8.3 Assumptions of T-Tests......Page 307
8.3.2 Data Formatting for Tests of Group Differences (the “Wide Form” and “Long Form”)......Page 308
8.4 The Independent Samples T-Test......Page 310
8.4.1 Performing an Independent Samples T-Test in SPSS......Page 311
8.4.2 Performing an Independent Samples T-Test in R......Page 314
8.4.3 Performing a Bootstrapped Independent Samples T-Test in R......Page 316
8.4.4 Performing a Bootstrapped, 20% Trimmed Means, Independent Samples T-Test in R......Page 317
8.4.5 Effect Sizes for Independent Samples T-Tests......Page 319
8.4.6 Reporting the Results of an Independent Samples T-Test......Page 320
8.4.7 Application Activities for the Independent Samples T-Test......Page 321
8.5.1 Performing a Paired Samples T-Test in SPSS......Page 322
8.5.2 One-Sided versus Two-Sided Confidence Intervals......Page 325
8.5.3 Performing a Paired Samples T-Test in R......Page 326
8.5.4 Performing a Robust Paired Samples T-Test in R......Page 327
8.5.6 Application Activities with Paired Samples T-Tests......Page 329
8.5.7 Reporting the Results of a Paired Samples T-Test......Page 330
8.8 Summary of T-Tests......Page 331
9 Looking for Group Differences with a One-Way Analysis of Variance: Effects of Planning Time......Page 332
9.1 Understanding the Analysis Of Variance Design......Page 334
9.2 The Topic of Chapter 9......Page 336
9.2.1 Numerical and Visual Inspection of the Data in this Chapter......Page 337
9.4.1 Omnibus Tests with Post-Hoc Tests or Planned Comparisons......Page 339
9.4.2 Testing for Group Equivalence before an Experimental Procedure......Page 340
9.4.3 Performing an Omnibus One-Way Analysis of Variance Test in SPSS with Subsequent Post-Hoc Tests......Page 342
9.4.4 Performing an Omnibus One-Way Analysis of Variance in R with Subsequent Post-Hoc Tests......Page 347
9.4.5 Performing a Bootstrapped One-Way Analysis of Variance in R......Page 352
9.4.6 Conducting a One-Way Analysis of Variance Using Planned Comparisons......Page 354
9.4.7 Conducting Planned Comparisons in SPSS......Page 355
9.4.8 Conducting Planned Comparisons in R......Page 357
9.4.9 Effect Sizes in One-Way Analysis of Variance......Page 359
9.4.10 Application Activities with One-Way Analysis of Variance......Page 362
9.4.11 Reporting the Results of a One-Way Analysis of Variance......Page 364
9.5 Summary of One-Way Analysis of Variance......Page 365
10 Looking for Group Differences with Factorial Analysis of Variance When there is More than One Independent Variable: Learning with Music......Page 366
10.1.1 Analysis of Variance Design: Interaction......Page 368
10.1.2 Application Activity in Understanding Interaction......Page 369
10.1.4 Analysis of Variance Design: Variable or Level?......Page 373
10.1.5 Application Activity: Identifying Independent Variables and Levels......Page 374
10.2 Numerical and Visual Inspection......Page 376
10.2.1 Creating a Combination Box Plot and Means Plot in R......Page 379
10.3 Assumptions of a Factorial Analysis of Variance......Page 382
10.4.1 Making Sure Your Data is in the Correct Format for a Factorial Analysis of Variance......Page 383
10.4.2 Rearranging Data for a Factorial Analysis of Variance Using SPSS......Page 385
10.4.3 Rearranging Data for a Factorial Analysis of Variance Using R......Page 387
10.4.4 Excursus on Type II vs. Type III Sums of Squares (Advanced Topic)......Page 389
10.5.1 Performing a Three-Way Factorial Analysis of Variance with SPSS......Page 390
10.5.2 Performing a Three-Way Factorial Analysis of Variance Using R......Page 403
10.5.3 A Confidence Interval Approach to Factorial ANOVA (Advanced Topic)......Page 406
10.5.4 Planned Comparisons in a Factorial Analysis of Variance......Page 415
10.5.5 Performing Planned Comparisons in a Factorial Analysis of Variance for SPSS and R......Page 416
10.5.6 Effect Sizes for Factorial Analysis of Variance......Page 417
10.5.8 Reporting the Results of a Factorial Analysis of Variance......Page 418
10.6 Summary......Page 420
11 Looking for Group Differences When the Same People are Tested More than Once: Repeated-Measures Analysis of Variance with Wug Tests and Instruction on French Gender......Page 422
11.1 Understanding Repeated-Measures Analysis of Variance Designs......Page 424
11.1.1 Repeated-Measures Analysis of Variance Design of the Murphy (2004) Study......Page 426
11.1.3 Application Activity: Identifying Between-Groups and Within-Groups Variables to Decide between Repeated-Measures and Factorial Analysis of Variance Designs......Page 427
11.2.1 Arranging the Data for Repeated-Measures Analysis of Variance in SPSS......Page 431
11.2.2 Changing from Wide Form to Long Form in SPSS......Page 432
11.2.3 Arranging the Data for a Repeated-Measures Analysis of Variance in R......Page 434
11.2.4 Application Activities for Changing Data from the Wide to the Long Form (Necessary for Use with the R Program Only)......Page 437
11.3.1 Exploring the Murphy (2004) and Lyster (2004) Data with the Combination Interaction Plot and Box Plot......Page 438
11.3.2 Parallel Coordinate Plots......Page 440
11.3.3 Creating a Parallel Coordinate Plot in SPSS......Page 441
11.3.4 Creating a Parallel Coordinate Plot in R......Page 443
11.4.1 Exploring Model Assumptions......Page 445
11.5 Performing a Repeated-Measures Analysis of Variance with the Least-Squares Approach......Page 447
11.5.1 Least-Squares Repeated-Measures Analysis of Variance in SPSS......Page 448
11.5.2 Repeated-Measures Analysis of Variance Output......Page 449
11.5.3 Least-Squares Repeated-Measures Analysis of Variance in R......Page 456
11.5.4 Application Activities with Least-Squares, Repeated-Measures Analysis of Variance......Page 461
11.6.1 Exploring Simple Interaction Effects and Simple Main Effects in the Murphy (2004) Data (SPSS and R)......Page 462
11.6.2 Reporting the Results of a Repeated-Measures Analysis of Variance......Page 468
11.6.3 Application Activities with Further Exploration of Repeated-Measures Analysis of Variance Using Simple Interaction Effects and Simple Main Effects......Page 470
11.7 Summary......Page 471
Appendix A: Doing Things in R......Page 474
Glossary......Page 494
Bibliography......Page 507
Author index......Page 518
R commands......Page 521
Subject index......Page 523