Estimate weather’s effect on mental health
Company: Google
Role: Data Scientist
Category: Statistics & Math
Difficulty: easy
Interview Round: HR Screen
## Scenario
You are studying whether **weather** (e.g., temperature, precipitation, sunlight, air pressure) affects **mental health outcomes** (e.g., depression score, anxiety index, crisis hotline calls, therapy app usage).
You have observational data at either the **person-day** level or **region-day** level.
## Task
Describe how you would estimate the **causal effect** of weather on mental health while addressing confounding.
Your answer should include:
1. **Define the outcome and treatment**
- What is the outcome variable (continuous score vs binary event)?
- What is the “treatment” (e.g., +5°C temperature shock, rainy day indicator, hours of sunlight)?
- Consider possible **lagged effects** (weather today impacts mental health over the next few days).
2. **Confounders & biases**
- List plausible confounders (seasonality, holidays, location, socioeconomic status, pollution, day-of-week, long-term trends).
- Discuss selection bias (who appears in the dataset) and measurement error.
3. **Identification strategy**
- Propose an approach to identify a causal effect (e.g., fixed effects, difference-in-differences/event study, instrumental variables, propensity scores), and state assumptions.
4. **Model specification and checks**
- Provide a concrete regression / model form.
- How would you test key assumptions (parallel trends, no unobserved time-varying confounders, SUTVA)?
5. **Interpretation**
- How would you interpret the effect size?
- What sensitivity analyses would you run to assess robustness?
## Output
Provide a structured plan and at least one model equation (LaTeX is OK).
Quick Answer: This question evaluates causal inference and applied statistical modeling skills—specifically defining outcomes and treatments, addressing confounding and selection biases, choosing identification strategies, and conducting robustness checks with observational data.