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El. knyga: Presenting Statistical Results Effectively

(University of Wisconsin - Madison, USA), (Western University, Canada)
  • Formatas: 288 pages
  • Išleidimo metai: 15-Dec-2021
  • Leidėjas: Sage Publications Ltd
  • Kalba: eng
  • ISBN-13: 9781473944176
Kitos knygos pagal šią temą:
Presenting Statistical Results EffectivelyDidesnis paveikslėlis
  • Formatas: 288 pages
  • Išleidimo metai: 15-Dec-2021
  • Leidėjas: Sage Publications Ltd
  • Kalba: eng
  • ISBN-13: 9781473944176
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Perfect for any statistics student or researcher, this book offers hands-on guidance on how to interpret and discuss your results in a way that not only gives them meaning, but also achieves maximum impact on your target audience. No matter what variables your data involves, it offers a roadmap for analysis and presentation that can be extended to other models and contexts.

Focused on best practices for building statistical models and effectively communicating their results, this book helps you: -        Find the right analytic and presentation techniques for your type of data -        Understand the cognitive processes involved in decoding information -        Assess distributions and relationships among variables -        Know when and how to choose tables or graphs -        Build, compare, and present results for linear and non-linear models -        Work with univariate, bivariate, and multivariate distributions -        Communicate the processes involved in and importance of your results. 

Recenzijos

Is your quantitative work so screamingly clear that your readers never misunderstand your figures, misread your tables, or get confused by your prose?  If so, then dont waste your time with Andersen and Armstrongs thoughtful book about the effective presentation and interpretation of statistical results. -- Gary King

List of Figures
xv
List of Tables
xix
About the Authors xxi
Preface xxiii
1 Some Foundation
1(16)
1.1 Introduction
1(3)
1.2 What is a `Model?'
4(4)
1.2.1 Mathematical notation
4(1)
1.2.2 Relationships and `effects'
5(1)
1.2.3 Types of variables
6(1)
1.2.4 There is no `true' model
7(1)
1.3 Statistical Inference
8(7)
1.3.1 The sampling distribution
9(1)
1.3.2 Bias, efficiency and consistency
10(2)
1.3.3 Hypothesis tests and confidence intervals
12(2)
1.3.4 Substantive importance and practical significance
14(1)
1.4 Layout of the Book
15(2)
Part A General Principles of Effective Presentation
17(80)
2 Best Practices for Graphs and Tables
19(18)
2.1 Introduction
19(1)
2.2 When to Use Tables and Graphs
20(2)
2.3 Constructing Effective Tables
22(5)
2.3.1 Significant digits and rounding
23(1)
2.3.2 Placement of numerical values and text
23(3)
2.3.3 Delineating information
26(1)
2.4 Constructing Clear and Informative Graphs
27(8)
2.4.1 Graphical perception
28(1)
2.4.2 Graph construction
29(2)
2.4.3 Encoding the data
31(4)
2.4.4 Grouping and ordering
35(1)
2.5 Concluding Remarks
35(2)
3 Methods for Visualizing Distributions
37(26)
3.1 Displaying Distributions of Categorical Variables
38(4)
3.2 Displaying Distributions of Quantitative Variables
42(11)
3.2.1 Histograms and density estimation
42(6)
3.2.2 Quantile comparison plots
48(4)
3.2.3 Boxplots and violin plots
52(1)
3.3 Transformations
53(8)
3.4 Concluding Remarks
61(2)
4 Exploring and Describing Relationships
63(34)
4.1 Two Categorical Variables
63(8)
4.1.1 Cross-tabulation
63(4)
4.1.2 Bar charts
67(2)
4.1.3 Mosaic plots
69(2)
4.2 Categorical Explanatory Variable and Quantitative Dependent Variable
71(7)
4.2.1 Side-by-side boxplots and violin plots
71(1)
4.2.2 Superposition of density estimates
72(2)
4.2.3 Tests of differences across groups
74(2)
4.2.4 Heatmaps
76(2)
4.3 Two Quantitative Variables
78(10)
4.3.1 Adding regression lines to scatterplots
80(1)
4.3.2 Jittering a scatterplot
81(1)
4.3.3 Encoding a control variable in a scatterplot
82(1)
4.3.4 Correlations, scatterplot matrices and linear scatterplot arrays
83(4)
4.3.5 Line plots
87(1)
4.4 Multivariate Displays
88(7)
4.4.1 Bivariate density estimation
88(3)
4.4.2 Three-dimensional density estimation
91(2)
4.4.3 Conditioning plots
93(2)
4.5 Concluding Remarks
95(2)
Part B The Linear Model
97(174)
5 The Linear Regression Model
99(36)
5.1 Introduction
99(1)
5.2 Ordinary Least Squares Regression
100(7)
5.2.1 Basics of the linear model
100(1)
5.2.2 Alternatives to minimizing the least squared residuals
101(1)
5.2.3 Ordinary least squares estimator
102(2)
5.2.4 Inference and assumptions of the linear model
104(3)
5.3 Hypothesis Tests and Confidence Intervals
107(2)
5.3.1 Individual coefficients
107(1)
5.3.2 Difference between two coefficients in the same model
108(1)
5.3.3 Difference between two coefficients from different models
109(1)
5.4 Assessing and Comparing Model Fit
109(9)
5.4.1 Residual standard error and R2 for assessing overall model fit
110(1)
5.4.2 F-tests for nested models
111(2)
5.4.3 Analysis of deviance for nested models
113(1)
5.4.4 Tests for non-nested models
114(1)
5.4.5 Using information criteria to compare models
115(2)
5.4.6 Cross-validation
117(1)
5.4.7 Some general advice
117(1)
5.5 Relative Importance of Predictors
118(4)
5.5.1 Scaling quantitative variables
119(1)
5.5.2 Standardized coefficients and related methods
120(2)
5.6 Interpreting and Presenting OLS Models: Some Empirical Examples
122(8)
5.6.1 Some general considerations
122(1)
5.6.2 General interpretation and presentation of regression models
123(3)
5.6.3 Assessing competing models
126(2)
5.6.4 Assessing relative importance
128(2)
5.7 Linear Probability Model
130(3)
5.7.1 Some basics
130(1)
5.7.2 Problems with the error distribution
130(1)
5.7.3 Problems with prediction
131(2)
5.8 Concluding Remarks
133(2)
6 Assessing the Impact and Importance of Multi-category Explanatory Variables
135(32)
6.1 Introduction
135(1)
6.2 Coding Multi-category Explanatory Variables
136(10)
6.2.1 Dummy coding
136(2)
6.2.2 Deviation or effect coding
138(1)
6.2.3 Comparing estimates from dummy and deviation coding
139(2)
6.2.4 Ordered explanatory variables
141(4)
6.2.5 The `reference category problem'
145(1)
6.3 Revisiting Statistical Significance: Multi-category Predictors
146(8)
6.3.1 Omnibus F-test for the null hypothesis that all coefficients equal zero
146(1)
6.3.2 Testing the difference between two coefficients
147(1)
6.3.3 Quasi-variances: Testing differences across all groups
148(3)
6.3.4 Comparing confidence intervals
151(3)
6.4 Relative Importance of Sets of Regressors
154(6)
6.4.1 Scaling and standardization revisited
156(1)
6.4.2 Comparing the relative importance of sets of regressors
157(3)
6.5 Graphical Presentation of Additive Effects
160(6)
6.5.1 Dot plots for comparing coefficients
161(1)
6.5.2 Fitted values and effect displays
162(1)
6.5.3 Compact letter displays for categorical variables
163(2)
6.5.4 Factorplots for the effects of categorical variables
165(1)
6.5.6 Choosing the `right' display
166(1)
6.6 Concluding Remarks
166(1)
7 Identifying and Handling Problems in Linear Models
167(36)
7.1 Introduction
167(5)
7.1.1 The importance of regression diagnostics
168(1)
7.1.2 Motivating example: Inequality and democratic history
169(3)
7.2 Nonlinearity
172(5)
7.2.1 Component-plus-residual plots (or partial-residual plots)
173(2)
7.2.2 Testing for nonlinearity
175(2)
7.3 Influential Observations
177(16)
7.3.1 Breakdown point, influence function and OLS
177(1)
7.3.2 Identifying outliers: Studentized residuals
178(1)
7.3.3 Measuring leverage: Hat values
179(1)
7.3.4 Cook's D: Overall influence of individual observations
180(1)
7.3.5 Residual-residual plots: Comparing OLS and robust regression residuals
181(3)
7.3.6 DFBETAS: Influence of individual observations on specific coefficients
184(1)
7.3.7 Partial regression plots: Joint influence
185(3)
7.3.8 How to handle outliers
188(5)
7.4 Heteroscedasticity
193(1)
7.5 Non-normality
193(2)
7.6 Other issues of concern
195(7)
7.6.1 Dependent observations
195(2)
7.6.2 Control variables, omitted-variable bias and endogeneity
197(3)
7.6.3 Collinearity
200(2)
7.7 Concluding Remarks
202(1)
8 Modelling and Presentation of Curvilinear Effects
203(36)
8.1 Introduction
203(1)
8.2 Curvilinearity in the linear model framework
204(1)
8.3 Nonlinear Transformations
205(10)
8.3.1 Fitted values and effect displays
209(1)
8.3.2 `Marginal effects'
210(3)
8.3.3 First differences: An alternative to marginal effects
213(2)
8.4 Polynomial Regression
215(4)
8.4.1 Centred and orthogonal polynomial terms
216(1)
8.4.2 Exploring the effects of polynomials: An empirical example
217(2)
8.5 Regression Splines
219(8)
8.5.1 Piecewise linear regression splines
220(3)
8.5.2 Cubic regression splines
223(1)
8.5.3 Comparing methods: An empirical example
224(3)
8.6 Nonparametric Regression
227(5)
8.6.1 Local polynomial regression
228(2)
8.6.2 Smoothing splines
230(1)
8.6.3 Comparing the LOESS and smoothing spline fits
231(1)
8.7 Generalized Additive Models
232(5)
8.7.1 The backfitting estimation procedure
233(2)
8.7.2 Plotting the fitted curve
235(1)
8.7.3 Using GAMs to test functional form
236(1)
8.8 Concluding Remarks
237(2)
9 Interaction Effects in Linear Models
239(32)
9.1 Introduction
239(1)
9.2 Understanding Interaction Effects
240(5)
9.2.1 Specifying interaction effects
240(3)
9.2.2 Necessity of statistical significance
243(1)
9.2.3 Both `sides' of the interaction and other considerations
244(1)
9.3 Interactions between Two Categorical Variables
245(4)
9.3.1 Type II tests for an overall interaction effect
245(2)
9.3.2 Effect displays based on quasi-variances using OVT confidence intervals
247(2)
9.4 Interactions between One Categorical Variable and One Quantitative Variable
249(8)
9.4.1 Calculating simple slopes
249(2)
9.4.2 Pairwise comparisons
251(2)
9.4.3 Plotting the conditional effects
253(1)
9.4.4 Assessing group differences: Subset models versus interaction effects
253(4)
9.5 Interactions between Two Continuous Variables
257(7)
9.5.1 Testing the effects of one variable at different levels of the other
259(1)
9.5.2 Marginal effect graphs
260(2)
9.5.3 Plotting fitted values
262(2)
9.6 Interaction Effects: Some Cautions and Recommendations
264(5)
9.6.1 Data density issues
265(1)
9.6.2 Assessing linearity
266(2)
9.6.3 Three-way interactions
268(1)
9.7 Concluding Remarks
269(2)
Part C The Generalized Linear Model and Extensions
271(104)
10 Generalized Linear Models
273(44)
10.1 Basics of the Generalized Linear Model
274(3)
10.1.1 Linear predictor
274(1)
10.1.2 Link function
274(2)
10.1.3 Random component and exponential family
276(1)
10.2 Maximum Likelihood Estimation
277(4)
10.2.1 Likelihood functions for some common GLMs
278(2)
10.2.2 Assumptions of the model
280(1)
10.3 Hypothesis Tests and Confidence Intervals
281(2)
10.3.1 Single-parameter tests
281(1)
10.3.2 Multiple-parameter tests
282(1)
10.3.3 Confidence intervals
282(1)
10.4 Assessing Model Fit
283(3)
10.4.1 Pseudo-R2 measures of fit
283(1)
10.4.2 Comparing models
284(2)
10.5 Empirical Example: Using Poisson Regression to Predict Counts
286(2)
10.6 Understanding Effects of Variables
288(11)
10.6.1 Marginal effects
288(2)
10.6.2 First differences
290(1)
10.6.3 `Average' case versus `observed' case approaches
291(5)
10.6.4 Hypothesis tests and confidence intervals for first differences
296(1)
10.6.5 Effect displays for GLMs
297(2)
10.7 Measuring Variable Importance
299(1)
10.8 Model Diagnostics
300(15)
10.8.1 GLM residuals
301(1)
10.8.2 Assessing the functional form: Component-plus-residual plots
302(7)
10.8.3 Assessing the appropriateness of the variance model: Residual plots
309(4)
10.8.4 Influential observations
313(2)
10.9 Concluding Remarks
315(2)
11 Categorical Dependent Variables
317(42)
11.1 Introduction
317(1)
11.2 Regression Models for Binary Outcomes
318(3)
11.2.1 Revisiting the linear probability model
318(2)
11.2.2 Logit and probit models
320(1)
11.3 Interpreting Effects in Logit and Probit Models
321(13)
11.3.1 Odds and odds ratios for the logit model
321(2)
11.3.2 Predicted and fitted probabilities
323(1)
11.3.3 Marginal effects
324(1)
11.3.4 First differences
325(3)
11.3.5 Effect displays for binary regression models
328(1)
11.3.6 Compression and interaction effects
328(1)
11.3.7 Difference in first differences
329(5)
11.4 Model Fit for Binary Regression Models
334(3)
11.4.1 Classification tables
334(1)
11.4.2 Proportional reduction in error
334(2)
11.4.3 Expected proportion correctly predicted
336(1)
11.5 Diagnostics Specific to Binary Regression Models
337(4)
11.5.1 Separation plots
337(1)
11.5.2 Empirical versus predicted probabilities
338(1)
11.5.3 Separation anxiety
338(3)
11.6 Extending the Binary Regression Model: Ordered and Multinomial Models
341(15)
11.6.1 Ordinal regression model
341(7)
11.6.2 Comparing ordered logit and linear regression models
348(3)
11.6.3 The proportional odds assumption
351(1)
11.6.4 Multinomial regression models
352(1)
11.6.5 Revisiting the reference category problem
353(3)
11.7 Concluding Remarks
356(3)
12 Conclusions and Recommendations
359(16)
12.1 Introduction
359(1)
12.2 Choosing the Right Estimator
360(3)
12.2.1 Exploratory distributions
360(2)
12.2.2 Preliminary analysis of relationships
362(1)
12.2.3 Choosing the initial regression model
362(1)
12.3 Research Design and Measurement Issues
363(4)
12.3.1 Dependent data
363(1)
12.3.2 Causation and endogeneity
364(1)
12.3.3 Omitted variables
365(1)
12.3.4 Collinearity
365(1)
12.3.5 Measurement error
366(1)
12.3.6 Missing data
366(1)
12.4 Evaluating the Model
367(4)
12.4.1 Detecting and handling nonlinearity
368(1)
12.4.2 Evaluating and handling undue influence
369(1)
12.4.3 Problems with the error distribution
370(1)
12.5 Effective Presentation of Results
371(3)
12.5.1 Simple additive effects
371(1)
12.5.2 Curvilinearity
372(1)
12.5.3 Interaction effects
373(1)
12.6 Conclusions
374(1)
Appendix: Data and Computing
375(12)
A.1 Computing
375(1)
A.2 Datasets
376(11)
References 387(20)
Index 407
Robert Andersen is Professor of Business, Economics and Public Policy, and Professor of Strategy at the Ivey Business School, Western Univeristy. He is also cross-appointed in the Departments of Sociology, Political Science, and Statistics and Actuarial Science. His previous appointments include Distinguished Professor of Social Science at the University of Toronto, Senator William McMaster Chair in Political Sociology at McMaster University, and Senior Research Fellow at the University of Oxford.

Andersens research expertise is in social statistics, social stratification, and political economy. Much of his recent research has explored the cross-national relationships between economic conditions, especially income inequality, and a wide array of attitudes and behaviours important for liberal democracy and a successful business environment, including social trust, tolerance, civic participation, support for democracy and attitudes toward public policy. His published research includes Modern Methods for Robust Regression (Sage, 2008), and more than 70 academic papers including articles in the Annual Review of Sociology, American Journal of Political Science, American Sociological Review, British Journal of Political Science, British Journal of Sociology, Journal of Politics, Journal of the Royal Statistical Society, and Sociological Methodology. Andersen has provided consulting for the United Nations, the European Commission, the Canadian Government and the Council of Ministers of Education, Canada.

Dave Armstrong is the Canada Research Chair in Political Methodology and Associate Professor of Political Science at Western University and is cross-appointed in the Department of Statistics and Actuarial Sciences.  Professor Armstrong earned a Ph.D. in Government and Politics from the University of Maryland in 2009.  Prior to arriving at Western, he had a post-doctoral position at Oxford University after which he taught in the Political Science department at the University of Wisconsin-Milwaukee.  He has been a faculty member at the Inter-university Consortium for Political and Social Research Summer Program at the University of Michigan since 2006 and has taught multiple courses at the Essex Summer School in Social Science Data Analysis at the University of Essex and the Oxford University Spring School in Quantitative Methods for Social Research. 

His current work focuses on the use of non-parametric models in conventional social scientific inference.  His work has been published in such journals as The American Political Science Review, The American Journal of Political Science, The American Sociological Review, The Annual Review of Political Science, The Journal of Peace Research, The Canadian Journal of Political Science and The R Journal.  His most recent book is Analyzing Spatial Models of Choice and Judgement with R, with Ryan Bakker, Royce Carroll, Chris Hare, Keith Poole and Howard Rosenthal (2nd ed. 2021) 

 
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