Statistics Using Stata: An Intergrative Approach

Half title......Page 2
Title page......Page 4
Imprints page......Page 5
Dedication......Page 7
Contents......Page 8
Preface......Page 20
Acknowledgments......Page 24
Chapter One Introduction......Page 25
The Role of the Computer in Data Analysis......Page 27
Statistics: Descriptive and Inferential......Page 28
Variables and Constants......Page 30
The Measurement of Variables......Page 33
Discrete and Continuous Variables......Page 43
Setting a Context with Real Data......Page 50
Exercises......Page 55
Chapter Two Examining Univariate Distributions......Page 75
Counting the Occurrence of Data Values......Page 76
When Variables Are Measured at the Nominal Level......Page 77
Frequency and Percent Distribution Tables......Page 78
Bar Charts......Page 82
Pie Charts......Page 87
When Variables Are Measured at the Ordinal, Interval, or Ratio Level......Page 91
Frequency and Percent Distribution Tables......Page 92
Stem-and-Leaf Displays......Page 97
Histograms......Page 102
Line Graphs......Page 107
Describing the Shape of a Distribution......Page 111
Accumulating Data......Page 115
Cumulative Percent Distributions......Page 116
Ogive Curves......Page 117
Percentile Ranks......Page 120
Percentiles......Page 122
Five-Number Summaries and Boxplots......Page 129
Modifying the Appearance of Graphs......Page 140
Summary of Graphical Selection......Page 141
Summary of Stata Commands in Chapter 2......Page 142
Commands for Frequency and Percent Distribution Tables......Page 143
Bar and Pie Graphs......Page 144
Stem and Leaf Displays......Page 146
Histograms......Page 147
Line Graphs......Page 148
Percentiles......Page 149
Boxplots......Page 150
Exercises......Page 151
Chapter Three Measures of Location, Spread, and Skewness......Page 178
Characterizing the Location of a Distribution......Page 179
The Mode......Page 180
The Median......Page 188
The Arithmetic Mean......Page 192
Interpreting the mean of a dichotomous variable......Page 195
The Weighted Mean......Page 197
Comparing the Mode, Median, and Mean......Page 199
Characterizing the Spread of a Distribution......Page 204
The Range and Interquartile Range......Page 209
The Variance......Page 214
The Standard Deviation......Page 219
Characterizing the Skewness of a Distribution......Page 222
Selecting Measures of Location and Spread......Page 230
Applying What We Have Learned......Page 232
Summary of Stata Commands in Chapter 3......Page 241
The Stata Command......Page 243
Stata TIPS......Page 248
Exercises......Page 250
Chapter Four Reexpressing Variables......Page 266
Linear and Nonlinear Transformations......Page 267
Linear Transformations: Addition, Subtraction, Multiplication, and Division......Page 269
The Effect on the Shape of a Distribution......Page 274
The Effect on Summary Statistics of a Distribution......Page 276
Common Linear Transformations......Page 282
Standard Scores......Page 286
z-SCORES......Page 289
Using z-Scores to Detect Outliers......Page 294
Using z-Scores to Compare Scores in Different Distributions......Page 298
Relating z-Scores to Percentile Ranks......Page 300
Nonlinear Transformations: Square Roots and Logarithms......Page 302
Nonlinear Transformations: Ranking Variables......Page 317
Other Transformations: Recoding and Combining Variables......Page 320
Recoding Variables......Page 321
Combining Variables......Page 327
Data Management Fundamentals – the Do-File......Page 328
Summary of Stata Commands in Chapter 4......Page 332
Exercises......Page 335
Chapter Five Exploring Relationships between Two Variables......Page 349
When Both Variables Are at Least Interval-Leveled......Page 351
Scatterplots......Page 353
The Pearson Product Moment Correlation Coefficient......Page 364
Judging the Strength of the Linear Relationship.......Page 373
The Correlation Scale Itself Is Ordinal.......Page 376
Correlation Does Not Imply Causation.......Page 377
The Effect of Linear Transformations.......Page 378
Restriction of Range.......Page 379
The Reliability of the Data.......Page 380
When at Least One Variable Is Ordinal and the Other Is at Least Ordinal: The Spearman Rank Correlation Coefficient......Page 381
When at Least One Variable Is Dichotomous: Other Special Cases of the Pearson Correlation Coefficient......Page 385
The Point Biserial Correlation Coefficient: The Case of One at Least Interval and One Dichotomous Variable......Page 386
The Phi Coefficient: The Case of Two Dichotomous Variables......Page 396
Other Visual Displays of Bivariate Relationships......Page 406
Summary of Stata Commands in Chapter 5......Page 413
Exercises......Page 416
Chapter Six Simple Linear Regression......Page 439
The “Best-Fitting” Linear Equation......Page 441
The Accuracy of Prediction Using the Linear Regression Model......Page 454
The Standardized Regression Equation......Page 456
R as a Measure of the Overall Fit of the Linear Regression Model......Page 457
Simple Linear Regression When the Independent Variable Is Dichotomous......Page 466
Using r and R as Measures of Effect Size......Page 472
Emphasizing the Importance of the Scatterplot......Page 473
Summary of Stata Commands in Chapter 6......Page 476
Exercises......Page 478
Chapter Seven Probability Fundamentals......Page 494
The Discrete Case......Page 496
The Complement Rule of Probability......Page 501
The Additive Rules of Probability......Page 502
First Additive Rule of Probability......Page 503
Second Additive Rule of Probability......Page 506
The Multiplicative Rule of Probability......Page 508
The Relationship between Independence and Mutual Exclusivity......Page 514
Conditional Probability......Page 515
The Law of Large Numbers......Page 519
Exercises......Page 520
Chapter Eight Theoretical Probability Models......Page 526
The Binomial Probability Model and Distribution......Page 528
The Applicability of the Binomial Probability Model......Page 538
The Normal Probability Model and Distribution......Page 548
Summary of Chapter 8 Stata Commands......Page 561
Exercises......Page 565
Chapter Nine The Role of Sampling in Inferential Statistics......Page 577
Samples and Populations......Page 578
Random Samples......Page 581
Obtaining a Simple Random Sample......Page 584
Sampling with and without Replacement......Page 588
Sampling Distributions......Page 592
Describing the Sampling Distribution of Means Empirically......Page 593
Describing the Sampling Distribution of Means Theoretically: The Central Limit Theorem......Page 604
Central Limit Theorem (CLT)......Page 605
Estimators and BIAS......Page 614
Summary of Chapter 9 Stata Commands......Page 615
Exercises......Page 618
Chapter Ten Inferences Involving the Mean of a Single Population When σ Is Known......Page 625
Estimating the Population Mean, µ, When the Population Standard Deviation, σ, Is Known......Page 627
Interval Estimation......Page 630
Relating the Length of a Confidence Interval, the Level of Confidence, and the Sample Size......Page 637
Hypothesis Testing......Page 638
The Relationship between Hypothesis Testing and Interval Estimation......Page 655
Effect Size......Page 657
Type II Error and the Concept of Power......Page 660
Increasing the Level of Significance, α......Page 667
Increasing the Effect Size, δ......Page 668
Decreasing the Standard Error of the Mean, σx¯......Page 669
Closing Remarks......Page 671
Summary of Chapter 10 Stata Commands......Page 672
Exercises......Page 676
Chapter Eleven Inferences Involving the Mean When σ Is Not Known: One- and Two-Sample Designs......Page 684
Single Sample Designs When the Parameter of Interest Is the Mean and σ Is Not Known......Page 685
The t Distribution......Page 687
Degrees of Freedom for the One Sample t-Test......Page 689
Violating the Assumption of a Normally Distributed Parent Population in the One Sample t-Test......Page 692
Confidence Intervals for the One Sample t-Test......Page 693
Hypothesis Tests: The One Sample t-Test......Page 707
Effect Size for the One Sample t-Test......Page 712
Two Sample Designs When the Parameter of Interest Is µ, and σ Is Not Known......Page 718
Independent (or Unrelated) and Dependent (or Related) Samples......Page 720
Independent Samples t-Test and Confidence Interval......Page 723
The Assumptions of the Independent Samples t-Test......Page 727
Effect Size for the Independent Samples t-Test......Page 744
Paired Samples t-test and Confidence Interval......Page 751
The Assumptions of the Paired Samples t-Test......Page 753
Effect Size for the Paired Samples t-Test......Page 763
The Bootstrap......Page 765
Summary......Page 774
Summary of Chapter 11 Stata Commands......Page 779
Commands Involving the t-Distribution......Page 780
One Sample t-Test Commands......Page 781
Independent Samples t-Test Commands......Page 783
Paired Samples t-Test Commands......Page 784
Exercises......Page 785
Chapter Twelve Research Design: Introduction and Overview......Page 814
Questions and Their Link to Descriptive, Relational, and Causal Research Studies......Page 815
The Need for a Good Measure of Our Construct, Weight......Page 816
The Descriptive Study......Page 818
From Descriptive to Relational Studies......Page 820
From Relational to Causal Studies......Page 821
The Gold Standard of Causal Studies: The True Experiment and Random Assignment......Page 824
Comparing Two Kidney Stone Treatments using a Non-randomized Controlled Study......Page 827
Including Blocking in a Research Design......Page 830
Underscoring the Importance of Having a True Control Group Using Randomization......Page 832
Analytic Methods for Bolstering Claims of Causality from Observational Data (Optional Reading)......Page 839
Quasi-Experimental Designs......Page 843
Threats to the Internal Validity of a Quasi-Experimental Design......Page 845
Threats to the External Validity of a Quasi-Experimental Design......Page 847
Threats to the Validity of a Study: Some Clarifications and Caveats......Page 848
Threats to the Validity of a Study: Some Examples......Page 850
Exercises......Page 853
Chapter Thirteen One-Way Analysis of Variance......Page 860
The Disadvantage of Multiple t-Tests......Page 862
The One-Way Analysis of Variance......Page 865
A Graphical Illustration of the Role of Variance in Tests on Means......Page 867
ANOVA as an Extension of the Independent Samples t-Test......Page 870
Developing an Index of Separation for the Analysis of Variance......Page 872
Carrying Out the ANOVA Computation......Page 873
The Between Group Variance (MSB)......Page 875
The Within Group Variance (MSW)......Page 876
The Assumptions of the One-way ANOVA......Page 878
Testing the Equality of Population Means: The F-Ratio......Page 880
How to Read the Tables and Use Stata Functions for the F-Distribution......Page 882
ANOVA Summary Table......Page 889
Measuring the Effect Size......Page 890
Post-hoc Multiple Comparison Tests......Page 900
The Bonferroni Adjustment: Testing Planned Comparisons......Page 923
The Bonferroni Tests on Multiple Measures......Page 927
Summary of Stata Commands in Chapter 13......Page 930
Exercises......Page 933
Chapter Fourteen Two-Way Analysis of Variance......Page 942
The Two-Factor Design......Page 944
The Concept of Interaction......Page 952
The Hypotheses That Are Tested by a Two-Way Analysis of Variance......Page 961
Assumptions of the Two-Way Analysis of Variance......Page 963
Balanced versus Unbalanced Factorial Designs......Page 967
Partitioning the Total Sum of Squares......Page 968
Using the F-Ratio to Test the Effects in Two-Way ANOVA......Page 970
Carrying Out the Two-Way ANOVA Computation by Hand......Page 972
Decomposing Score Deviations about the Grand Mean......Page 982
Modeling Each Score as a Sum of Component Parts......Page 984
Explaining the Interaction as a Joint (or Multiplicative) Effect......Page 985
Measuring Effect Size......Page 987
Fixed versus Random Factors......Page 992
Post-hoc Multiple Comparison Tests......Page 994
Summary of Steps to Be Taken in a Two-Way ANOVA Procedure......Page 1003
Summary of Stata Commands in Chapter 14......Page 1009
Exercises......Page 1013
Chapter Fifteen Correlation and Simple Regression as Inferential Techniques......Page 1028
The Bivariate Normal Distribution......Page 1030
Testing Whether the Population Pearson Product Moment Correlation Equals Zero......Page 1036
Using a Confidence Interval to Estimate the Size of the Population Correlation Coefficient, ρ......Page 1043
Revisiting Simple Linear Regression for Prediction......Page 1049
Estimating the Population Standard Error of Prediction, σY|X......Page 1051
Testing the b-Weight for Statistical Significance......Page 1053
Explaining Simple Regression Using an Analysis of Variance Framework......Page 1061
Measuring the Fit of the Overall Regression Equation: Using R and R2......Page 1066
Relating R2 to σ2y|x......Page 1068
Testing R2 for Statistical Significance......Page 1070
Estimating the True Population R2: The Adjusted R2......Page 1072
Exploring the Goodness of Fit of the Regression Equation: Using Regression Diagnostics......Page 1074
Residual Plots: Evaluating the Assumptions Underlying Regression......Page 1077
Detecting Influential Observations: Discrepancy and Leverage......Page 1083
Using Stata to Obtain Leverage......Page 1087
Using Stata to Obtain Discrepancy......Page 1089
Using Stata to Obtain Influence......Page 1091
Using Diagnostics to Evaluate the Ice Cream Sales Example......Page 1094
Using the Prediction Model to Predict Ice Cream Sales......Page 1100
Simple Regression When the Predictor Is Dichotomous......Page 1101
Summary of Stata Commands in Chapter 15......Page 1103
Exercises......Page 1106
Chapter Sixteen An Introduction to Multiple Regression......Page 1128
The Basic Equation with Two Predictors......Page 1130
Equations for b, β, and Ry.12 When the Predictors Are Not Correlated......Page 1132
Equations for b, β, and Ry.12 When the Predictors Are Correlated......Page 1136
Summarizing and Expanding on Some Important Principles of Multiple Regression......Page 1140
Testing the b-Weights for Statistical Significance......Page 1152
Assessing the Relative Importance of the Independent Variables in the Equation......Page 1155
Measuring the Drop in R2 Directly: An Alternative to the Squared Semipartial Correlation......Page 1158
Evaluating the Statistical Significance of the Change in R2......Page 1159
The b-Weight as a Partial Slope in Multiple Regression......Page 1163
Multiple Regression When One of the Two Independent Variables Is Dichotomous......Page 1168
The Concept of Interaction between Two Variables That Are at Least Interval-Leveled......Page 1179
Testing the Statistical Significance of an Interaction Using Stata......Page 1183
Centering First-Order Effects to Achieve Meaningful Interpretations of b-Weights......Page 1192
Understanding the Nature of a Statistically Significant Two-Way Interaction......Page 1194
Interaction When One of the Independent Variables Is Dichotomous and the Other Is Continuous......Page 1200
Summary of Stata Commands in Chapter 16......Page 1206
Exercises......Page 1210
Chapter Seventeen Nonparametric Methods......Page 1232
Parametric versus Nonparametric Methods......Page 1233
Nonparametric Methods When the Dependent Variable Is at the Nominal Level......Page 1235
The Chi-Square Distribution (χ2)......Page 1236
The Chi-Square Goodness-of-Fit Test......Page 1241
The Chi-Square Test of Independence......Page 1251
Assumptions of the Chi-Square Test of Independence......Page 1257
Fisher’s Exact Test......Page 1262
Calculating the Fisher Exact Test by Hand Using the Hypergeometric Distribution......Page 1265
Nonparametric Methods When the Dependent Variable Is Ordinal-Leveled......Page 1272
Wilcoxon Sign Test......Page 1274
The Mann-Whitney U Test......Page 1280
The Kruskal-Wallis Analysis of Variance......Page 1289
Summary of Stata Commands in Chapter 17......Page 1293
Exercises......Page 1296
Appendices......Page 1305
Appendix A Data Set Descriptions......Page 1306
Anscombe......Page 1307
Basketball......Page 1308
Blood......Page 1309
Brainsz......Page 1310
Currency......Page 1312
Exercise, Food Intake, and Weight Loss......Page 1313
Framingham......Page 1314
Hamburg......Page 1318
Ice Cream......Page 1319
Impeach......Page 1320
Learndis......Page 1322
Mandex......Page 1324
Marijuana......Page 1325
Nels......Page 1326
States......Page 1335
Stepping......Page 1337
Temp......Page 1339
Wages......Page 1340
Appendix B Stata .do Files and Data Sets in Stata Format......Page 1342
Appendix C Statistical Tables......Page 1343
Appendix D References......Page 1376
Appendix E Solutions......Page 1384
Index......Page 1385