Statistics

A branch of mathematics.

Foundations

• Combinations

• Correlation

• Logit

• Mahalanobis distance

• Permutations

Uncertainty

• Average absolute deviation

• Covariance

• Degrees of freedom

• Entropy

• Variance

• Pooled variance

Probability

• Bayes' rule

• Conditional probability

• Joint probability

• σ Algebra notation

• Test statistic

Prediction

• Bayesian notation

• Conditional expectations

• Expected values

• Moments

Probability distributions

• Bernoulli

• Binomial

• Chi-squared

• F

• Hotelling's T-squared

• Mills' ratio

• Normal

• Student's t

• Uniform

• Weibull

Probability tests

• Collinearity test

• Cronbach's alpha

• F test

• Granger causality test

• Hosmer-Lemeshow test

• Hotelling's t-squared test

• Kolmogorov-Smirnov test

• Lagrange multiplier test

• Likelihood-ratio test

• Mardia's test

• Pearson's chi-squared test

• Sobel test

• Student's t test

• Wald test

• Wald-Wolfowitz runs test

Samples

• Multistage sample

• Neyman allocation

• Probability proportional to size sample

• Simple random sample

• Stratification

• Survey frame

• Survey sampling

Modeling

• Analysis of variance (ANOVA)

• Bayesian hierarchical model

• Binning

• Causal inference

• Cox proportional hazards model

• Cross-validation

• Generalized estimating equation

• Generalized least squares

• Generalized linear model

• Inverse variance weights

• Iteratively reweighted least squares

• Lasso

• Logistic model

• Matching

• Maximum likelihood estimation

• Multilevel model

• Mixed model

• Multilevel regression with poststratification

• Ordinary least squares

• Post-stratification

• Standard errors

• Residuals

Econometrics

• Autoregressive models

• Censored and Truncated regression models

• Difference in differences

• Econometrics notation

• First-differenced estimator

• Fixed effects model

• Instrumental variables method

• Pooled OLS model

• Probit model

• Random effects model

• Unobserved components model

• Vector autoregression

Psychometrics

• Factor analysis

• Mediation analysis

• Structural equation modeling (and related reading notes)

Non-parametric modeling

• Bagging

• Decision trees

• Gradient boosting

• Random forest

• Support-vector machines

Survey analysis

• Calibration

• Design weights

• Double list experiment

• Experience sampling method

• Focus group

• GREG estimator

• Inverse probability weights

• Margin of error

• Nonresponse bias

• Online bulletin board

• Qualitative coding

• Response rate

• Survey disposition

• Survey inference

• Survey nonresponse (and related reading notes)

• Survey weights (and related reading notes)

• Unequal weighting and design effects

• Unexpected event during survey design framework

• Weighting class adjustment

Natural language processing

• Bag of words model

• NLP data preparation

• Word embedding

• Recursive sequencing

• Topic model

• Sentiment analysis

• Text classification

Reading Notes

Note: reading notes for the above topics are listed on the respective pages, not here.

• Estimation of Relationships for Limited Dependent Variables, James Tobin, 1958

• Multiple Frame Surveys, H.O. Hartley, 1962

• The Common Structure of Statistical Models of Truncation, Sample Selection and Limited Dependent Variables and a Simple Estimator for Such Models, James J. Heckman, 1976

• Sequential Sample Selection Methods, James R. Chromy, 1979

• The central role of the propensity score in observational studies for causal effects, Paul R. Rosenbaum and Donald B. Rubin, 1983

• Sampling Rare Populations, Graham Kalton and Dallas W. Anderson, 1986

• Measurement Error Models, Wayne A. Fuller, 1987

• Evidence on the Validity of Cross-sectional and Longitudinal Labor Market Data, John Bound, Charles Brown, Greg J. Duncan, and Willard L. Rodgers, 1994

• Statistical Modeling: The Two Cultures, Leo Breiman, 2001

• Measurement Validity: A Shared Standard for Qualitative and Quantitative Research, Robert Adcock and David Collier, 2001

• Double Sampling, Michael Hidiroglou, 2001

• Hierarchical Linear Models: Applications and Data Analysis Methods, Stephen W. Raudenbush and Anthony S. Bryk, 2002

• The influence of violations of assumptions on multilevel parameter estimates and their standard errors, Cora J.M. Maas and Joop J. Hox, 2003

• Ascertaining the validity of individual protocols from Web-based personality inventories, John A. Johnson, 2004

• A simulation study of cell collapsing in poststratification; Jay J. Kim, Linda Tompkins, Jianzhu Li, and Richard Valliant; 2005

• Is OLS with a binary dependent variable really OK?: Estimating (mostly) TSCS models with binary dependent variables and fixed effects, Nathaniel Beck, 2011

• Identifying Careless Responses in Survey Data, Andrew Meade, S. Bartholomew Craig, 2012

• Respondent use of straight-lining as a response strategy in education survey research: Prevalence and implications; James S. Cole, Alexander C. McCormick, Robert M. Gonyea; 2012

• Estimating Measurement Error in Annual Job Earnings, John M. Abowd and Martha H. Stinson, 2013

• Why ask why? Forward causal inference and reverse causal questions, Andrew Gelman and Guido Imbens, 2013

• Beyond Power Calculations: Assessing Type S (Sign) and Type M (Magnitude) Errors, Andrew Gelman and John Carlin, 2014

• How Robust Standard Errors Expose Methodological Problems They Do Not Fix, and What to Do About It, Gary King and Margaret E. Roberts, 2015

• Straightlining in Web survey panels over time, Matthias Schonlau and Vera Toepoel, 2015

• Imputation Under Informative Sampling; Emily Berg, Jae-Kwang Kim, and Chris Skinner; 2016

• Sampling-based vs. Design-based Uncertainty in Regression Analysis; Alberto Abadie, Susan Athey, Guido W. Imbens, and Jeffrey M. Wooldridge; 2017

• When Should You Adjust Standard Errors for Clustering?; Alberto Abadie, Susan Athey, Guido W. Imbens, and Jeffrey M. Wooldridge; 2017

• Why Propensity Scores Should Not Be Used for Matching, Gary King and Richard Nielsen, 2019

• Regression and Other Stories, Andrew Gelman, Jennifer Hill, and Aki Vehtari, 2020

• Unexpected Event during Surveys Design: Promise and Pitfalls for Causal Inference; Jordi Muñoz, Albert Falcó-Gimeno, and Enrique Hernández; 2020

• A Permutation Test on Complex Sample Data, Daniell Toth, 2020

• Exact Adaptive Confidence Intervals for Small Areas, Kyle C. Burris and Peter D. Hoff, 2020

• The Independent Contractor Workforce: New Evidence on Its Size and Composition and Ways to Improve Its Measurement in Household Surveys; Katharine G. Abraham, Brad J. Hershbein, Susan N. Houseman, and Beth C. Truesdale; 2023

• Using Hierarchical Models to Estimate Heterogeneous Effects, Joshua Alley, 2023

• Out of One, Many: Using Language Models to Simulate Human Samples; Lisa P. Argyle, Ethan C. Busby, Nancy Fulda, Joshua R. Gubler, Christopher Rytting, and David Wingate; 2023

• Causal Models for Longitudinal and Panel Data: A Survey, Dmitry Arkhangelsky and Guido Imbens, 2023

• Surveys of Consumers Technical Report: Technical Documentation for the 2024 Methodological Transition to Web Surveys, 2024

• The effect of online interviews on the University of Michigan Survey of Consumer Sentiment, Ryan Cummings and Ernie Tedeschi, 2024

• The micro-task market for lemons: data quality on Amazon’s Mechanical Turk; Douglas J. Ahler, Carolyn E. Roush, and Gaurav Sood; 2024

• Adapting to Misspecification; Timothy B. Armstrong, Patrick Kline, and Liyang Sun; 2024

• Linking Survey and LinkedIn Data: Understanding Usage and Consent Patterns; Tarek Al Baghal, Alexander Wenz, Paulo Serôdio, Shujin Liu, Curtis Jessop, and Luke Sloan; 2024

• Small Area Prediction for Exponential Dispersion Families Under Informative Sampling, Emily Berg and Abdulhakeem Eideh, 2024

• Measurement error when surveying issue positions: a MultiTrait MultiError approach; Kim Backström, Alexandru Cernat, Rasmus Sirén, and Peter Söderlund; 2025

• Self-Reporting News Use in Situ and in Retrospect; Danit Shalev, Teresa K Naab, and Yariv Tsfati; 2025

• Where to place sensitive questions? Experiments on survey response order and measures of discriminatory attitudes; Amanda Sahar d’Urso, Tabitha Bonilla, and Genni Bogdanowicz; 2025

• Difference-in-Differences Designs: A Practitioner’s Guide; Andrew Baker, Brantly Callaway, Scott Cunningham, Andrew Goodman-Bacon, and Pedro H. C. Sant’Anna; 2025

• Inferring a Population Composition From Survey Data With Nonignorable Nonresponse: Borrowing Information From External Sources, Veronica Ballerini and Brunero Liseo, 2025

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