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Contents Acknowledgements 1 The Scientific Study of Politics 1.1 Political Science? 1.2 Approaching politics scientifically: The search for causal explanations 1.3 Thinking about the world in terms of variables and causal explanations 1.4 Models of politics 1.5 Rules of the road to scientific knowledge about politics 1.5.1 Make your theories causal 1.5.2 Don't let data alone drive your theories 1.5.3 Consider only empirical evidence 1.5.4 Avoid normative statements 1.5.5 Pursue both generality and parsimony 1.6 A quick look ahead 2 The Art of Theory Building 2.1 Good theories corne from good theory-building strategies 2.2 Identifying interesting variation 2.2.1 Time-series example 2.2.2 Cross-sectional example 2.3 Learning to use your knowledge 2.3.1 Moving from a specific event to more general theories 2.3.2 Know local, think global: Can you drop the proper nouns? 2.4 Examine previous research 2.4.1 What did the previous researchers miss? 2.4.2 Can their theory be applied elsewhere? 2.4.3 If we believe their findings, are there further implications? 2.4.4 How might this theory work at different levels of aggregation (micromacro)? 2.5 Think formally about the causes that lead to variation in your dependent variable 2.5.1 Utility and expected utility 2.5.2 The puzzle of turnout 2.6 Think about the institutions: The rules usually matter 2.6.1 Legislative rules 2.6.2 The rules matter! 2.7 Extensions 2.8 How do I know if I have a 'good' theory? 2.8.1 Is your theory causal? 2.8.2 Can you test your theory on data that you have not yet observed? 2.8.3 How general is your theory? 2.8.4 How parsimonious is your theory? 2.8.5 How new is your theory? 2.8.6 How non-obvious is your theory? 2.9 Conclusion 3 Evaluating Causal Relationships 3.1 Causality and everyday language 3.2 Four hurdles along the route to establishing causal relationships 3.2.1 Putting it all together---adding up the answers to our four questions 3.2.2 Identifying causal claims is an essential thinking skill 3.2.3 What are the consequences of failing to control for other possible causes? 3.3 Why is studying causality so important? Three examples from political science 3.3.1 Life satisfaction and democratic stability 3.3.2 School choice and student achievement 3.3.3 Electoral systems and the number of political parties 3.4 Why is studying causality so important? Three examples from everyday life 3.4.1 Alcohol consumption and income 3.4.2 Treatment choice and breast-cancer survival 3.4.3 Explicit lyrics and teen sexual behavior 3.5 Wrapping up 4 Research Design 4.1 Comparison as the key to establishing causal relationships 4.2 Experimental research designs 4.2.1 "Random assignment" versus "Random sampling" 4.2.2 Are there drawbacks to experimental research designs? 4.3 Observational studies (in two flavors) 4.3.1 Datum, data, data set 4.3.2 Cross-sectional observational studies 4.3.3 Time-series observational studies 4.3.4 The major difficulty with observational studies 4.4 Summary 5 Measurement 5.1 Why measurement matters 5.2 Social science measurement: The varying challenges of quantifying humanity 5.3 Problems in measuring concepts of interest 5.3.1 Conceptual clarity 5.3.2 Reliability 5.3.3 Measurement Bias and Reliability 5.3.4 Validity 5.3.5 The relationship between validity and reliability 5.4 Controversy 1: Measuring democracy 5.5 Controversy 2: Measuring political tolerance 5.6 Are there consequences to poor measurement? 5.7 Conclusions 6 Descriptive Statistics and Graphs 6.1 Know your data 6.2 What is the variable's measurement metric? 6.2.1 Categorical variables 6.2.2 Ordinal variables 6.2.3 Continuous variables 6.2.4 Variable types and statistical analyses 6.3 Describing categorical variables 6.4 Describing continuous variables 6.4.1 Rank statistics 6.4.2 Moments 6.5 Limitations 7 Statistical Inference 7.1 Populations and samples 7.2 Learning about the population from a sample: The central limit theorem 7.2.1 The normal distribution 7.3 Example: Presidential approval ratings 7.3.1 What kind of sample was that? 7.3.2 A note on the effects of sample size 7.4 A look ahead: Examining relationships between variables 8 Bivariate Hypothesis Testing 8.1 Bivariate hypothesis tests and establishing causal relationships 8.2 Choosing the right bivariate hypothesis test 8.3 All roads lead to p 8.3.1 The logic of p-values 8.3.2 The limitations of p-values 8.3.3 From p-values to statistical significance 8.3.4 The null hypothesis and p-values 8.4 Three bivariate hypothesis tests 8.4.1 Example 1: Tabular analysis 8.4.2 Example 2: Difference of means 8.4.3 Example 3: Correlation coefficient 8.5 Wrapping up 9 Bivariate Regression Models 9.1 Two variable regression 9.2 Fitting a line: Population ¿ Sample 9.3 Which line fits best? Estimating the regression line 9.4 Measuring our uncertainty about the OLS regression line Goodness of fit: Root mean squared error 198 9.4.1 Goodness of fit: r-squared statistic 9.4.2 Is that a "good" goodness of fit? 9.4.3 Uncertainty about individual components of the sample regression model 9.4.4 Confidence intervals about parameter estimates 9.4.5 Hypothesis testing: Overview 9.4.6 Two-tailed hypothesis tests 9.4.7 The relationship between confidence intervals and two-tailed hypothesis tests 9.4.8 One-tailed hypothesis tests 9.5 Assumptions, more assumptions, and minimal mathematical requirements 9.5.1 Assumptions about the population stochastic component 9.5.2 Assumptions about our model specification 9.5.3 Minimal mathematical requirements 9.5.4 How can we make all of these assumptions? 10 Multiple Regression Models I: The Basics 10.1 Modeling multivariate reality 10.2 The population regression function 10.3 From two-variable to multiple regression 10.4 What happens when we fail to control for Z? 10.4.1 An additional minimal mathematical requirement in multiple regression 10.5 Interpreting multiple regression 10.6 Which effect is "biggest"? 10.7 Statistical and substantive significance 10.8 Implications 11 Multiple Regression Models II: Crucial Extensions 11.1 Extensions of OLS 11.2 Being smart with dummy independent variables in OLS 11.2.1 Using dummy variables to test hypotheses about a categorical independent variable with only two values 11.2.2 Using dummy variables to test hypotheses about a categorical independent variable with more than two values 11.3 Testing interactive hypotheses with dummy variables 11.4 Dummy dependent variables 11.4.1 The Linear Probability Model 11.4.2 Binomial Logit and Binomial Probit 11.4.3 Goodness of fit with dummy dependent variables 11.5 Outliers and influential cases in OLS 11.5.1 Identifying influential cases 11.5.2 Dealing with influential cases 11.6 Multicollinearity 11.6.1 How does multicollinearity happen? 11.6.2 Detecting multicollinearity 11.6.3 Multicollinearity: A simulated example 11.6.4 Multicollinearity: A real world example 11.6.5 Multicollinearity: What should I do? 11.7 Being careful with time series 11.7.1 Time series notation 11.7.2 Memory and lags in time series analysis 11.7.3 Trends and the spurious regression problem 11.7.4 The differenced dependent variable 11.7.5 The lagged dependent variable 11.8 Wrapping up 12 Multiple Regression Models III: Applications 12.1 Why controlling for Z matters 12.2 Example 1: The economy and presidential popularity 12.3 Example 2: Politics, economics, and public support for democracy . 12.4 Example 3: Competing theories of how politics affects international trade 12.5 Conclusions A Critical Values of Chi-square B Critical Values of t C The A Link Function for Binomial Logit Models D The $ Link Function for Binomial Probit Models

Library of Congress Subject Headings for this publication:

Political science -- Research.