Statistics, Modeling, and Data Analysis for Social Scientists
Statistical Models as Social Representations
Modeling logic
Statistical models translate substantive assumptions into estimable relationships. In social science, the challenge is not simply fitting data but choosing specifications that respect causal structure, sampling design, and the level of aggregation at which social processes occur.
Core quantities
Interpretation matters
A statistically significant coefficient can still be substantively unimportant, while a non-significant result can still inform theory when precision is high.
Model families
| Model | Typical use | Advanced concern |
|---|---|---|
| Linear regression | Continuous outcomes | Linearity and omitted variables |
| Logistic regression | Binary outcomes | Non-collapsibility and interpretation |
| Multilevel model | Nested data | Cross-level interactions |
| Time-series model | Temporal dependence | Autocorrelation and stationarity |
What does an interaction term test?
Interactions are used to estimate conditional effects that vary across contexts, groups, or levels of another variable.
Correct answer: Whether the effect of one variable depends on another
Why are multilevel models useful for social data?
Ignoring clustering can misstate uncertainty and obscure group-level processes.
Correct answer: They account for hierarchical structure such as individuals nested in schools, neighborhoods, or countries.
Uncertainty and robustness
Advanced analysis requires sensitivity checks, alternative specifications, and explicit discussion of model dependence. Robust inference is not a mechanical output but a disciplined evaluation of whether conclusions persist under defensible changes to assumptions.
Which issue is especially important when analyzing clustered social data without multilevel methods?
When observations are not independent, standard errors can be too small if clustering is ignored.
Correct answer: Inflated type I error due to dependence
What is one reason to report confidence intervals instead of only p-values?
Intervals help evaluate magnitude, precision, and practical relevance.
Correct answer: Confidence intervals communicate both the estimated effect and its uncertainty, improving substantive interpretation.