📚 Content

First Half Topics

Introduction: Basic Concepts

• Data
• Cases
• Value
• Unit of Analysis
• Estimator
• Two main goals of data analysis
• Hypotheses
• Dependent Variable
• Independent Variable
• Population
• Sample
• Parameters
• Statistics
• Descriptive Statistics
• Inferential Statistics

Unit I: Descriptive Statistics

• Kinds of variables
• Measurement metrics
• “Exploratory data analysis”
• Kinds of univariate graphics (histogram, box plots, etc)
• Tabulations and crosstabulations
• Shape, center, spread, skew
• Mistakes with graphics: axes, scales, etc
• Measures of central tendency
• Measures of dispersion
• Outliers
• Linear transformations
• Density curves
• Normal distribution
• Z-scores
• Cumulative probabilities

Unit II: Statistical Relationships

• Kinds of bivariate graphics (scatterplots, linear fits, smooth lines, etc)
• Scatterplot diagnoses: form, direction, strength, outliers
• Transformed data in scatterplots
• Correlation coefficients
• Sample vs. population calculation differences
• Regression
  • intercept
  • slope
  • model component
  • stochastic component
  • sources of error in modeling
  • method of least squares
  • model sum of squares
  • residual/error sum of squares
  • total sum of squares
  • \(R^2\)
  • \(\hat Y\)
  • \(Y_i\)
  • \(\bar Y\)
  • Calculating the slope (b1) from a correlation coefficient
  • Regression coefficients vs correlation coefficients
  • Residual plots
  • Effects of outliers on regression lines
  • Predicted values/expected values of Y given X
• Two-way tables for qualitative variables

Unit III: Producing Data & Research Design

• Correlation vs. causation
• Confounding variables
• Conditions for causation
  • credible causal link (theory)
  • temporal precedence (could Y cause X?)
  • covariation (do X and Y move together/covary?)
  • no plausible alternative explanations (no confounding variables)
• Simpson’s paradox
• Internal validity
• Threats to internal validity
  • History
  • Maturation/Learning
  • Testing
  • Instrumentation
  • Regression to the mean
  • Selection bias
  • Mortality
  • Social Desirability
• External validity
• Threats to external validity
  • context
  • sampling procedures
• Anecdotal data
• Survivor’s bias
• Control through randomization
• Experiments
  • treatment
  • control
  • observations
  • random assignment
• Surveys
  • Population/sample/sampling frame
  • Simple random sample
  • Stratified random sample
  • Multi-stage sampling
  • Response rate
  • Response bias
  • Question framing and ordering effects
  • Bias vs. variability (validity vs reliability)

Unit IV: Probability

• Random phenomenon
• Independence
• Probability model
• Event
• Long run
• Rules of probability
  • Range
  • Sample space
  • Addition
  • Complementarity
  • Multiplication
• Disjoint events
• Random variable
  • Discrete
  • Continuous
• Probability distribution
• Expected value (mean) of a random variable
• Law of large numbers
• Standard deviation/variance of a random variable
• Rules for means of random variables
  • Addition
  • Subtraction
  • Linear transformations
• Conditional probability
• Probability trees

Second Half Topics

Unit V: Sampling

• Sample Distribution
• Population Distribution
• Sampling Distribution
• Central Limit Theorem
• Estimators as Random Variables
• Standard Error of the Mean
• Standard Error of a Proportion
• Standard Error of a Count

Unit VI: Inference

• Confidence Intervals
  • Point Estimate
  • Margin of Error
  • Critical Values
  • Margin of Error
  • Ways to reduce margin of error
  • Statistical Power
  • Inference when \(\sigma\) is unknown
  • Student’s T distribution
  • Degrees of freedom (\(df\))

Unit VII: Hypothesis Testing

• Logic of Hypothesis testing
• Null Hypothesis (\(H_0\))
• Alternative Hypothesis (\(H_A\))
• Types of Hypothesis Test
  • Tabular Analysis
  • Difference in Means
  • Correlation Coefficient
  • Regression
• How to choose test statistic
  • Critical Values (\(Z\), \(T\), \(\chi^2\))
  • One-Tail vs Two-Tail Tests
  • P-values
  • Type I and Type II Errors

Unit VIII: Simple Linear Regression

• Bivariate Regression
• Dichotomous Dummy Variables
• Difference in Means Tests via Regression
• Statistical Significance (hypothesis testing, confidence intervals, t- and p- values, etc)
• Substantive/Practical Significance (effect magnitudes, predicted values, \(R^2\))

Unit IX: Less Simple Linear Regression

• Multiple Regression
• Confounding variables in Multiple Regression
• Multi-category Variables and Dummy Variables
• Standardized coefficients
• Simple model comparison: \(R^2\), effect magnitudes, predicted values

Stata Skills

• Be able to:

  • Load data
  • Use a .do file
  • Place comments in .do files
  • Calculate summary statistics
  • Graph scatterplots and histograms
  • Recode data
  • Tabulate and cross-tabulate data
  • Conduct difference in means tests
  • Run regressions
  • Predict values from regression results

• Selected Stata commands

   cd, use, clear, tab, sum, tabstat, gen, sort, browse, 
   twoway, scatter, histogram, graph export, corr, reg, 
   disp, bys, predict, save, keep, drop, if, recode, 
   collapse, preserve, restore, ttest