Statistics Using Stata: An Integrative Approach, Second Edition 

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Comment from the Stata technical groupStatistics Using Stata: An Integrative Approach, Second Edition, by Sharon Lawner Weinberg and Sarah Knapp Abramowitz, is an excellent introduction to applied statistics and its implementation in Stata. The authors cover essential topics from exploratory data analysis to multiple regression, interweaving statistical concepts and their application in Stata. Their repeated use of real data throughout the book clearly connects the statistical concepts to realworld applications. Designed for teaching graduate and undergraduate students from the behavioral, social, and health sciences, this text is accompanied by additional resources online such as Powerpoint slides and Stata dofiles. Each chapter concludes with exercises and a review of Stata code used in the examples, allowing readers to test their knowledge and refer back to Stata commands. The authors guide the reader from basic statistical concepts to more advanced material, tying concepts together to emphasize the overarching ideas. They begin with descriptive statistics, discussing the different variable types and the corresponding graphs and statistics used to examine their distribution and relationship with other variables. Then, they discuss the law of large numbers, theoretical probability distributions, and sampling, preparing the reader to dive into inferential statistics. The authors then present ANOVA, simple and multiple regression, and nonparametric methods. They carefully explain what the values represent in context of the data and how the methods relate to one another, allowing readers to really grasp the meaning behind the analyses. Weinberg and Abramowitz are just as careful when teaching the reader how to implement statistical methods in Stata. First, they introduce the reader to Stata's interface and the general syntax of Stata’s commands. Then, they explain the importance of dofiles for reproducing one’s work and encourage the reader to work alongside the text with the dofiles provided at the companion website. Readers can then use these dofiles as a starting point when performing analyses on their own data. The authors have updated the second edition based on the most recent version of Stata, version 16. Building on the concept of power discussed in the first edition, they use the power suite to demonstrate how to perform power analysis for the inferential methods discussed. Additionally, an entirely new chapter is devoted to understanding and visualizing statistical interactions, providing much needed clarity on a topic that has confused many students in the past. And, reflecting on the importance of creating publicationquality reports that can be easily reproduced, the authors have added a new chapter demonstrating how to embed Stata results in Excel files.  
Table of contentsView table of contents >> Preface
New to the Second Edition
Guiding Principles Underlying Our Approach Overview of Content Coverage and Intended Audience Acknowledgments
1 INTRODUCTION
The Role of Statistical Software in Data Analysis
Statistics: Descriptive and Inferential Variables and Constants The Measurement of Variables
Nominal Level
Discrete and Continuous VariablesOrdinal Level Interval Level Ratio Level Choosing a Scale of Measurement Setting a Context with Real Data Exercises 2 EXAMINING UNIVARIATE DISTRIBUTIONS
Counting the Occurrence of Data Values
When Variables are Measured at the Nominal Level
Frequency and Percent Distribution Tables
When Variables are Measured at the Ordinal, Interval, or Ratio LevelBar Charts Pie Charts
Frequency and Percent Distribution Tables
Describing the Shape of a DistributionStemandLeaf Displays Histograms Line Graphs Accumulating Data
Cumulative Percent Distributions
Summary of Graphical SelectionOgive Curves Percentile Ranks Percentiles FiveNumber Summaries and Boxplots Modifying the Appearance of Graphs Summary of Stata Commands Exercises 3 MEASURES OF LOCATION, SPREAD, AND SKEWNESS
Characterizing the Location of a Distribution
The Mode
Characterizing the Spread of a DistributionThe Median The Arithmetic Mean
Interpreting the Mean of a Dichotomous Variable
Comparing the Mode, Median, and MeanThe Weighted Mean
The Range and Interquartile Range
Characterizing the Skewness of a DistributionThe Variance The Standard Deviation Selecting Measures of Location and Spread Applying What We Have Learned Summary of Stata Commands
Helpful Hints When Using Stata
Exercises
Online Resources
The Stata Command Stata Tips 4 RE–EXPRESSING VARIABLES
Linear and Nonlinear Transformations
Linear Transformations: Addition, Subtraction, Multiplication, and Division
The Effect on the Shape of a Distribution
Nonlinear Transformations: Square Roots and LogarithmsThe Effect on Summary Statistics of a Distribution Common Linear Transformations Standard Scores zScores
Using zScores to Detect Outliers
Using zScores to Compare Scores in Different Distributions Relating zScores to Percentile Ranks Nonlinear Transformations: Ranking Variables Other Transformations: Recoding and Combining Variables
Recoding Variables
Data Management Fundamentals: The DoFileCombining Variables Summary of Stata Commands Exercises 5 EXPLORING RELATIONSHIPS BETWEEN TWO VARIABLES
When Both Variables are at Least IntervalLeveled
Scatterplots
When at Least One Variable Is Ordinal and the Other Is at Least Ordinal: The
Spearman Rank Correlation CoefficientThe Pearson Product–Moment Correlation Coefficient
Interpreting the Pearson Correlation Coefficient
Judging the Strength of the Linear Relationship
The Correlation Scale Itself Is Ordinal Correlation Does Not Imply Causation The Effect of Linear Transformations Restriction of Range The Shape of the Underlying Distributions The Reliability of the Data When at Least One Variable Is Dichotomous: Other Special Cases of the Pearson Correlation Coefficient
The Point Biserial Correlation Coefficient: The Case of One at Least
Interval and One Dichotomous Variable
Other Visual Displays of Bivariate RelationshipsThe Phi Coefficient: The Case of Two Dichotomous Variables Selection of Appropriate Statistic or Graph to Summarize a Relationship Summary of Stata Commands Exercises 6 SIMPLE LINEAR REGRESSION
The “BestFitting” Linear Equation
The Accuracy of Prediction Using the Linear Regression Model The Standardized Regression Equation R As a Measure of the Overall Fit of the Linear Regression Model Simple Linear Regression When the Independent Variable Is Dichotomous Using r and R As Measures of Effect Size Emphasizing the Importance of the Scatterplot Summary of Stata Commands Exercises 7 PROBABILITY FUNDAMENTALS
The Discrete Case
The Complement Rule of Probability The Additive Rules of Probability
First Additive Rule of Probability
The Multiplicative Rule of ProbabilitySecond Additive Rule of Probability The Relationship between Independence and Mutual Exclusivity Conditional Probability The Law of Total Probability Bayes' Theorem The Law of Large Numbers Exercises 8 THEORETICAL PROBABILITY MODELS
The Binomial Probability Model and Distribution
The Applicability of the Binomial Probability Model
The Normal Probability Model and DistributionUsing the Normal Distribution to Approximate the Binomial Distribution Summary of Stata Commands Exercises 9 THE ROLE OF SAMPLING IN INFERENTIAL STATISTICS
Samples and Populations
Random Samples
Obtaining a Simple Random Sample
Sampling with and without ReplacementSampling Distributions Describing the Sampling Distribution of Means Empirically Describing the Sampling Distribution of Means Theoretically
Central Limit Theorem
Estimators and BIASSummary of Stata Commands Exercises 10 INFERENCES INVOLVING THE MEAN OF A SINGLE POPULATION
WHEN σ IS KNOWN
Estimating the Population Mean, μ, When the Population Standard Deviation,
σ, Is Known
Interval Estimation Relating the Length of a Confidence Interval, the Level of Confidence, and the Sample Size Hypothesis Testing The Relationship between Hypothesis Testing and Interval Estimation Effect Size Type II Error and the Concept of Power
Increasing the Level of Significance, α
Closing RemarksIncreasing the Effect Size, δ Decreasing the Standard Error of the Mean, σ_{𝓍̅} Summary of Stata Commands Exercises 11 INFERENCES INVOLVING THE MEAN WHEN σ IS NOT
KNOWN: ONE AND TWOSAMPLE DESIGNS
Single Sample Designs When the Parameter of Interest Is the Mean and σ
Is Not Known
The t Distribution
TwoSample Designs When the Parameter of Interest Is μ, and σ Is
Not KnownDegrees of Freedom for the OneSample tTest Violating the Assumption of a Normally Distributed Parent Population in the OneSample tTest Confidence Intervals for the OneSample tTest Hypothesis Tests: The OneSample tTest Effect Size for the OneSample tTest
Independent (or Unrelated) and Dependent (or Related) Samples
The BootstrapIndependent Samples tTest and Confidence Interval The Assumptions of the Independent Samples tTest Effect Size for the Independent Samples tTest Paired Samples tTest and Confidence Interval The Assumptions of the Paired Samples tTest Effect Size for the Paired Samples tTest Conducting Power Analyses for tTests on Means Summary Summary of Stata Commands Exercises 12 RESEARCH DESIGN: INTRODUCTION AND OVERVIEW
Questions and their Link to Descriptive, Relational, and Causal Research
Studies
The Need for a Good Measure of Our Construct: Weight
The Gold Standard of Causal Studies: The True Experiment and Random AssignmentThe Descriptive Study From Descriptive to Relational Studies From Relational to Causal Studies Comparing Two Kidney Stone Treatments Using a NonRandomized Controlled Study Including Blocking in a Research Design Underscoring the Importance of Having a True Control Group Using Randomization Analytic Methods for Bolstering Claims of Causality from Observational Data QuasiExperimental Designs Threats to the Internal Validity of a QuasiExperimental Design Threats to the External Validity of a QuasiExperimental Design Threats to the Validity of a Study: Some Clarifications and Caveats Threats to the Validity of a Study: Some Examples Exercises 13 ONEWAY ANALYSIS OF VARIANCE
The Disadvantage of Multiple tTests
The OneWay Analysis of Variance
A Graphical Illustration of the Role of Variance in Tests on Means
Measuring the Effect SizeANOVA As an Extension of the Independent Samples tTest Developing an Index of Separation for the Analysis of Variance Carrying Out the ANOVA Computation
The Between Group Variance (MS_{B})
The Assumptions of the OneWay ANOVAThe Within Group Variance (MS_{W}) Testing the Equality of Population Means: The FRatio How to Read the Tables and Use Stata Functions for the FDistribution ANOVA Summary Table PostHoc Multiple Comparison Tests The Bonferroni Adjustment: Testing Planned Comparisons The Bonferroni Tests on Multiple Measures Conducting Power Analyses for OneWay ANOVA Summary of Stata Commands Exercises 14 TWOWAY ANALYSIS OF VARIANCE
The TwoFactor Design
The Concept of Interaction The Hypotheses That are Tested by a TwoWay Analysis of Variance Assumptions of the TwoWay Analysis of Variance Balanced versus Unbalanced Factorial Designs Partitioning the Total Sum of Squares Using the FRatio to Test the Effects in TwoWay ANOVA Carrying Out the TwoWay ANOVA Computation by Hand Decomposing Score Deviations about the Grand Mean Modeling Each Score as a Sum of Component Parts Explaining the Interaction As a Joint (or Multiplicative) Effect Measuring Effect Size Fixed versus Random Factors Posthoc Multiple Comparison Tests
Simple Effects and Pairwise Comparisons
Summary of Steps to Be Taken in a TwoWay ANOVA ProcedureConducting Power Analyses for TwoWay ANOVA Summary of Stata Commands Exercises 15 CORRELATION AND SIMPLE REGRESSION AS INFERENTIAL
TECHNIQUES
The Bivariate Normal Distribution
Testing whether the Population Pearson ProductMoment Correlation Equals Zero Using a Confidence Interval to Estimate the Size of the Population Correlation Coefficient, ρ Revisiting Simple Linear Regression for Prediction
Estimating the Population Standard Error of Prediction, σ_{ΥΧ}
Exploring the Goodness of Fit of the Regression Equation: Using Regression
DiagnosticsTesting the bWeight for Statistical Significance Explaining Simple Regression Using an Analysis of Variance Framework Measuring the Fit of the Overall Regression Equation: Using R and R^{2} Relating R^{2} to σ^{2}_{ΥΧ } Testing R^{2} for Statistical Significance Estimating the True Population R^{2}: The Adjusted R^{2}
Residual Plots: Evaluating the Assumptions Underlying Regression
Using the Prediction Model to Predict Ice Cream SalesDetecting Influential Observations: Discrepancy and Leverage Using Stata to Obtain Leverage Using Stata to Obtain Discrepancy Using Stata to Obtain Influence Using Diagnostics to Evaluate the Ice Cream Sales Example Simple Regression When the Predictor is Dichotomous Conducting Power Analyses for Correlation and Simple Regression Summary of Stata Commands Exercises 16 AN INTRODUCTION TO MULTIPLE REGRESSION
The Basic Equation with Two Predictors
Equations for b, β, and R_{Υ.12} When the Predictors Are Not Correlated Equations for b, β, and R_{Υ.12} When the Predictors Are Correlated Summarizing and Expanding on Some Important Principles of Multiple Regression Testing the bWeights for Statistical Significance Assessing the Relative Importance of the Independent Variables in the Equation Measuring the Drop in R^{2} Directly: An Alternative to the Squared Semipartial Correlation Evaluating the Statistical Significance of the Change in R^{2} The bWeight As a Partial Slope in Multiple Regression Multiple Regression When One of the Two Independent Variables is Dichotomous Controlling Variables Statistically: A Closer Look
A Hypothetical Example
Conducting Power Analyses for Multiple RegressionSummary of Stata Commands Exercises 17 TWOWAY INTERACTIONS IN MULTIPLE REGRESSION
Testing the Statistical Significance of an Interaction Using Stata
Comparing the YHat Values from the Additive and Interaction Models Centering FirstOrder Effects if the Equation Has an Interaction Probing the Nature of a TwoWay Interaction Interaction When One of the Independent Variables Is Dichotomous and the Other Is Continuous Methods Useful for Model Selection Conducting a Power Analysis to Detect an Interaction Summary of Stata Commands Exercises 18 NONPARAMETRIC METHODS
Parametric versus Nonparametric Methods
Nonparametric Methods When the Dependent Variable Is at the Nominal Level The ChiSquare Distribution (Χ^{2})
The ChiSquare GoodnessofFit Test
Nonparametric Methods When the Dependent Variable Is OrdinalLeveledThe ChiSquare Test of Independence
Assumptions of the ChiSquare Test of Independence
Fisher’s Exact Test
Calculating the Fisher is Exact Test by Hand Using the Hypergeometric
Distribution
Wilcoxon Sign Test
The Mann–Whitney U Test or Wilcoxon's RankSum Test
The Kruskal–Wallis Analysis of Variance
Summary of Stata CommandsExercises 19 COMMUNICATING YOUR STATA RESULTS VIA EXCEL
Setting the Working Directory
Reproducing a Table of Univariate Summary Statistics in Excel
Using estpost and esttab
Reproducing a Correlation Matrix As a Table in ExcelUsing putexcel
Using estpost and esttab
Reproducing Regression Output As a Table in ExcelUsing putexcel
Using outreg^{2} to obtain a table of model statistics in Excel
Reproducing a Graph in Excel (Using putexcel)Using eststo and esttab to obtain a table of model statistics in Excel Using putexcel to reproduce a table of regression coefficients in Excel Conclusion Summary of Stata Commands Exercises Appendix A Data Set Descriptions
Appendix B Stata .Dofiles and Data Sets in Stata Format
Appendix C Statistical Tables
Appendix D Solutions
References
Index

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