Quantitative and Statistical Research Methods: From Hypothesis to Results......Page 3
Contents......Page 5
Tables and Figures......Page 11
Preface......Page 19
Acknowledgments......Page 20
The Authors......Page 21
Chapter 1: Introduction and Overview......Page 23
Independent, Dependent, and Extraneous Variables......Page 25
Scales of Measurement of Variables......Page 27
Measures of Central Tendency......Page 28
Variance of the Sample (s2)......Page 30
Standard Deviation of the Sample (s)......Page 31
Visual Representations of a Data Set......Page 32
The Normal Distribution......Page 36
Characteristics of the Normal Distribution......Page 37
Descriptive Statistical Applications of the Normal Distribution......Page 39
Inferential Statistical Applications of the Normal Distribution......Page 40
Summary......Page 48
Key Terms......Page 49
Chapter 2: Logical Steps of Conducting Quantitative Research: Hypothesis-Testing Process......Page 51
Hypothesis-Testing Process......Page 52
Problem Assignment......Page 59
Key Terms......Page 60
Chapter 3: Maximizing Hypothesis Decisions Using Power Analysis......Page 61
Illustration of Avoiding Making a Type I (Alpha) Error......Page 63
Illustration of Avoiding Making a Type II (Alpha) Error......Page 65
A Priori Power Analysis......Page 66
Key Terms......Page 74
Chapter 4: Research and Statistical Designs......Page 75
Formulating Experimental Conditions......Page 76
Sampling Error......Page 77
Error of Measurement......Page 78
Methods of Controlling Extraneous Variables......Page 79
Internal Validity......Page 81
Experimental Designs......Page 83
Randomized Multiple Treatments and Control with Posttest-Only Design......Page 84
Randomized Multiple Treatments and Control with Pretest and Posttest Design......Page 85
Quasi-Experimental Designs......Page 86
Repeated-Treatment Design with One Group......Page 87
Correlational Research Methods......Page 88
Choosing a Statistic to Use for an Analysis......Page 89
Key Terms......Page 96
Chapter 5: Introduction to IBM SPSS 20......Page 99
Entering Variables......Page 102
Entering Data......Page 108
Examples of Basic Analyses......Page 109
Examples of Modifying Data Procedures......Page 118
Summary......Page 119
Key Terms......Page 120
Chapter 6: Diagnosing Study Data for Inaccuracies and Assumptions......Page 121
Detecting Erroneous Data Entries......Page 122
Identifying and Dealing with Missing Data......Page 125
Identifying and Assessing Univariate Outliers......Page 128
Screening and Making Decisions about Univariate Assumptions......Page 130
Skewness and Kurtosis......Page 131
Skewness Screening......Page 132
Kurtosis Screening......Page 135
Assessing Normal Q-Q Plots for Normality......Page 136
Screening for Homogeneity of Variance......Page 137
Levene's Test......Page 139
One-Way Analysis of Variance Results......Page 140
Transformed Screening and One-Way ANOVA Results......Page 141
Key Terms......Page 150
Chapter 7: Randomized Design Comparing Two Treatments and a Control Using a One-Way Analysis of Variance......Page 151
Research Problem......Page 152
Independent Variable......Page 153
Dependent Variable......Page 154
Statistical Analysis: One-Way Analysis of Variance (ANOVA)......Page 155
Stating the Omnibus (Comprehensive) Research Question......Page 157
Omnibus Narrative Alternative Hypothesis (Ha)......Page 158
Hypothesis Testing Step 2: Establish the Null Hypothesis (H0)......Page 159
Selecting Alpha (α) Considering Type I and Type II Errors......Page 160
A Priori Power Analysis......Page 161
Hypothesis Testing Step 4: Choose Appropriate Statistic and Its Sampling Distribution to Test the H0 Assuming H0 is True......Page 165
Sample Selection and Assignment......Page 166
Study Data Diagnostics......Page 167
One-Way Analysis of Variance of the Omnibus H0......Page 181
One-Way ANOVA Results......Page 182
Magnitude of Treatment Effect—Post Hoc Effect Size......Page 184
Post Hoc Multiple Comparisons of Means......Page 185
Confidence Intervals of Mean Differences......Page 187
One-Way ANOVA Formula Calculations......Page 188
Post Hoc Effect Sizes......Page 194
Confidence Intervals (.95) for Mean Differences of Significant Pairs......Page 196
ANOVA Study Results......Page 197
Problem Assignment......Page 199
Key Terms......Page 203
Chapter 8: Repeated-Treatment Design Using a Repeated-Measures Analysis of Variance......Page 205
Research Problem......Page 206
Independent Variable......Page 207
Statistical Analysis: Repeated-Measures Analysis of Variance......Page 208
Omnibus Research Question (RQ)......Page 211
Hypothesis Testing Step 1: Establish the Alternative (Research) Hypothesis (Ha)......Page 212
Omnibus Narrative Null Hypothesis (H0)......Page 213
A Priori Power Analysis......Page 214
Hypothesis Testing Step 4: Choose Appropriate Statistic and Its Sampling Distribution to Test the H0 Assuming H0 Is True......Page 217
Study Data Diagnostics......Page 218
Repeated-Measures Analysis of Variance of the Omnibus H0......Page 227
RM-ANOVA Results......Page 232
Post Hoc Multiple Comparisons of Pairs of Means......Page 234
Trend Analysis......Page 235
Post Hoc Power......Page 238
Confidence Intervals of Mean Differences......Page 239
Formula Calculations of the Study Results......Page 240
Calculation of Sums of Squares......Page 242
Post Hoc Effect Size—Partial Eta-Squared......Page 243
Post Hoc Paired-Means Comparisons......Page 244
Study Results......Page 249
Summary......Page 250
Key Terms......Page 252
Chapter 9: Randomized Factorial Experimental Design Using a Factorial ANOVA......Page 253
Independent Variables......Page 254
Research Design......Page 255
Statistical Analysis: Factorial Analysis of Variance......Page 257
Omnibus Research Questions (RQs)......Page 259
Hypothesis Testing Step 1: Establish the Alternative (Research) Hypothesis (Ha)......Page 260
Jones and Tukey (2000) Recommended Process to Reach Conclusions......Page 261
Omnibus Narrative Null Hypotheses (H0)......Page 262
Selecting Alpha (α) Considering Type I and Type II Errors......Page 263
A Priori Power Analysis......Page 264
Hypothesis Testing Step 4: Choose Appropriate Statistic and Its Sampling Distribution to Test the H0 Assuming H0 Is True......Page 269
Sample Selection and Assignment......Page 270
Study Data Diagnostics......Page 271
Assessing for Underlying Assumptions......Page 272
Two-Way Analysis of Variance of the Omnibus H0's......Page 286
Two-Way ANOVA Computer Analysis Results......Page 287
Hypothesis Testing Step 6: Make Decision Regarding the H0 and Interpret Post Hoc Effect Sizes and Confidence Intervals......Page 293
Magnitude of Treatment Effect—Post Hoc Effect Sizes......Page 294
Confidence Intervals of Mean Differences......Page 295
Two-Way ANOVA Formula Calculations......Page 300
Post Hoc Effect Sizes......Page 306
Confidence Intervals (.99) for Mean Differences......Page 309
Study Results......Page 311
Problem Assignment......Page 313
Key Terms......Page 317
Chapter 10: Analysis of Covariance......Page 319
Research Problem......Page 320
Covariate......Page 321
Statistical Analysis: Analysis of Covariance (ANCOVA)......Page 322
Hypothesis Testing Step 1: Establish the Alternative (Research) Hypothesis (Ha)......Page 323
Hypothesis Testing Step 3: Decide on a Risk Level (Alpha) of Rejecting the True H0 Considering Type I and II Errors and Power......Page 324
A Priori Power Analysis......Page 325
Hypothesis Testing Step 4: Choose Appropriate Statistic and Its Sampling Distribution to Test the H0 Assuming H0 Is True......Page 328
Exploratory Data Analysis......Page 329
Analysis of Covariance of the Omnibus H0......Page 342
ANCOVA Results......Page 343
Estimated Marginal Means......Page 345
Magnitude of Treatment Effect—Post Hoc Effect Size......Page 346
Confidence Intervals of Mean Differences......Page 347
Step 1: Calculations for the Dependent Variable LDA (Y)......Page 349
Step 2: Calculations for the Covariate Age (X)......Page 352
Step 3: Calculations of Covariance of Age X LDA......Page 354
Step 4: Adjustment of LDA (DV, Y) Based on the Covariate of Age (X)......Page 357
Step 5: Calculation of Adjusted Means......Page 359
ANCOVA Study Results......Page 361
Summary......Page 362
Key Terms......Page 365
Chapter 11: Randomized Control Group and Repeated-Treatment Designs and Nonparametics......Page 367
Study Variables......Page 368
Research Design......Page 369
Statistical Analyses......Page 370
Hypothesis Testing Step 1: Establish the Alternative (Research) Hypothesis (Ha)......Page 371
Hypothesis Testing Step 3: Decide on a Risk Level (Alpha) of Rejecting the True H0 Considering Type I and II Errors and Power......Page 372
A Priori Power Analysis......Page 373
Hypothesis Testing Step 4: Choose Appropriate Statistic and Its Sampling Distribution to Test the H0 Assuming H0 Is True......Page 376
Study Data Diagnostics......Page 377
Summary of Underlying Assumptions Findings......Page 390
K-W One-Way ANOVA Results......Page 391
Hypothesis Testing Step 6: Make Decision Regarding the H0 and Interpret Post Hoc Effect Sizes......Page 392
Mann-Whitney U Statistical Analysis......Page 393
Magnitude of Treatment Effect—Post Hoc Effect Size and Post Hoc Power......Page 395
Formula Calculations......Page 398
Study Results......Page 403
Nonparametric Research Problem Two: Friedman's Rank Test for Correlated Samples and Wilcoxon's Matched-Pairs Signed-Ranks Test......Page 404
Friedman's Repeated Measures Analysis of Variance of the Omnibus H0......Page 406
Wilcoxon's Statistical Analysis......Page 409
Magnitude of Treatment Effect—Post Hoc Effect Size and Post Hoc Power for Nonparametric Research Problem 2......Page 411
Formula Calculations for Friedman's Rank Test and Wilcoxon's Matched-Pairs Signed-Ranks Test......Page 417
Summary......Page 420
Key Terms......Page 421
Chapter 12: Bivariate and Multivariate Correlation Methods Using Multiple Regression Analysis......Page 423
Study Variables......Page 424
Research Method......Page 425
Statistical Analysis: Bivariate Correlation and Multiple Regression......Page 426
Hypothesis Testing Step 1: Establish the Alternative (Research) Hypothesis (Ha)......Page 427
A Priori Power Analysis......Page 428
Hypothesis Testing Step 5: Select Sample, Collect Data, Screen Data, Compute Statistic, and Determine Probability Estimates......Page 429
Sample Selection and Assignment......Page 430
Univariate Outlier Analysis......Page 431
Multivariate Outlier Analysis......Page 432
General Screening of Correlation Coefficients......Page 434
Assessment of Multicollinearity and Singularity......Page 436
Assessment of Normality, Linearity, and Homoscedasticity of Residuals......Page 437
Sequential Multiple Regression Analysis......Page 439
SPIScient and DSI Pearson Product-Moment Correlation......Page 445
SPIPract and DSI Pearson Product-Moment Correlation......Page 449
Partial Regression Coefficients......Page 453
F-Test of Change in R2......Page 454
Study Results......Page 455
Problem Assignment......Page 456
Key Terms......Page 460
Chapter 13: Understanding Quantitative Literature and Research......Page 461
Interpretation of a Quantitative Research Article......Page 462
Identify the Research Questions in the Study......Page 473
Problem Assignment......Page 482
References......Page 483
Index......Page 487
