| date | sample_size | margin |
|---|---|---|
| September 24 | 760 | - |
| September 24 | 582 | +3.1% |
| September 23 | 601 | +2.2% |
| September 23 | 384 | - |
| September 22 | 644 | - |
| September 20 | 768 | - |
| September 20 | 760 | +1.1% |
| September 19 | 1,020 | - |
| September 19 | 432 | - |
| September 19 | 752 | +2.1% |
Weighting and Its Consequences
Variance Reduction in Discrete Outcomes and Its Implications for Survey Aggregation
Mark Rieke
May 15, 2025
Disclaimer
The views and opinions expressed in this presentation are wholly my own and do not necessarily represent that of my employer, Game Data Pros, Inc (GDP).
Outline
- Setting the Stage
- Recreating Results
- Extending the Example
- Adjustments for Aggregators
Setting the Stage
Setting the Stage: About Me
- Bayesian Data Scientist at Game Data Pros
- Previously: Senior CX Analyst at Memorial Hermann
Setting the Stage: About Me
Setting the Stage: Pennsylvania Polling
Setting the Stage: Pennsylvania Polling
Recreating Results
Recreating Results
Recreating Results
| group | group_mean | population | p_respond |
|---|---|---|---|
| A | 400 | 60% | 10% |
| B | 800 | 20% | 5% |
| C | 700 | 10% | 3% |
| D | 600 | 10% | 1% |
- True population mean: 530
- Responses sampled from \(\mathcal{N}(\mu_g,50)\)
- Simple population weighting strategy: \(w_g = \frac{P_g}{\left(\frac{N_g}{\sum_g N_g} \right)}\)
Recreating Results
Extending the Example
Extending the Example
- Little and Vartivarian demonstrate the effect of weighting with a continuous outcome.
- A broad class of survey results are discrete outcomes.
- How do these effects hold up in the discrete case?
Extending the Example
| group | group_mean | population | p_respond |
|---|---|---|---|
| A | 3% | 50% | 5% |
| B | 97% | 50% | 7% |
- True population mean: 50%
- Responses sampled from \(\text{Bernoulli}(\theta_g)\)
- Simple population weighting strategy: \(w_g = \frac{P_g}{\left(\frac{N_g}{\sum_g N_g} \right)}\)