Understanding the Standard Error in Political Polls: A Guide with Trump vs. Harris Polls Example

Written by

Political polls are a staple of election season, providing insight into which candidate holds a lead. However, it’s crucial to interpret these polls carefully, especially when it comes to the standard error (SE) — a key statistic that indicates how much the poll results might vary from the true population sentiment.

What is Standard Error?

The standard error represents the margin of error in the poll’s results. It reflects the variability of the sample, and its size is influenced by both the sample size and the degree of variability in responses. A lower SE suggests more confidence that the poll reflects the actual views of the population, while a higher SE implies less certainty.

SE is important because it helps us assess how reliable the polling numbers are. In political polling, the reported “margin of error” (MOE) is typically based on the standard error, with most polls using a 95% confidence interval. This means that if we repeated the poll multiple times, we’d expect the true population result to fall within the margin of error 95% of the time.

Example: Trump vs. Harris General Election Polls

Let’s look at an example from recent Trump vs. Harris general election polls in Georgia.  The poll, conducted by Pollster YouGov and sponsored by CBS News was conducted September 20-24 and showed the following results:

  • Trump: 51%
  • Harris: 49%
  • Sample size (n): 1,441 Likely Voters (LVs)
  • Margin of Error (MOE): ±3.5 percentage points

With a 3.5% margin of error, this means Trump’s true support could be as low as 47.5% or as high as 54.5%, and Harris’s support could range between 45.5% and 52.5%.

Why the Standard Error Matters

In this example, the 2-point lead that Trump holds over Harris is within the poll’s margin of error, meaning it’s not statistically significant. The race is essentially a toss-up, as the poll results are too close to draw firm conclusions. This is why understanding the standard error and margin of error is crucial — even when one candidate appears to be ahead, the lead may not be as solid as it seems.

Takeaway

When interpreting political polls, always consider the standard error and the margin of error. A lead within the margin means the race could go either way, and polls should be viewed as a snapshot of current sentiment, not a guarantee of the final outcome.

As the Trump vs. Harris example shows, even small leads should be treated with caution when the standard error is factored in.

Traditional Methods Versus Monte Carlo Simulation in Epidemiological Analyses

Written by

Working to build infectious disease outbreak models can be daunting especially for new students in epidemiology. Typically their first approach is to build compartment models after learning the basics of traditional statistical analyses. While compartmental models certainly have their place in epidemiology, I think it’s instructive for new students to learn and understand principles of Monte Carlo Simulation (especially Markov Chain Monte Carlo or MCMC), but sadly this material seems rarely to be covered in Masters level epidemiology courses. As I was mentoring and providing some guidance to a student today on a practicum, I was asked an excellent question: “What is the advantage of a MCMC simulation over a compartmental model?” After thinking through this a bit, I provided the following, which I think are effective guidelines to be used when considering when to select a MCMC model for an analysis, so I’d thought I’d share:

Flexibility
Monte Carlo models provide greater flexibility in modeling complex and dynamic systems. They allow for more intricate representations of real-world scenarios, including variations in individual behavior, social interactions, and other stochastic factors. Their flexibility is especially useful when dealing with heterogeneous populations or when the assumptions of compartmental models do not hold.

Incorporation of uncertainty
Monte Carlo models naturally account for uncertainty and randomness. They can include probabilistic distributions to represent uncertainty in various parameters such as transmission rates, incubation periods, or contact patterns. This allows for the exploration of a wide range of possible outcomes and the estimation of confidence intervals.

Individual-level simulations
Monte Carlo models operate at the individual level, simulating the behavior and interactions of each person in the population. This level of granularity allows for the consideration of individual variations, such as susceptibility, contact patterns, and compliance with interventions. It can capture the impact of heterogeneity on disease spread more accurately than compartmental models.

Simulation of interventions
Monte Carlo models are well-suited for simulating and evaluating the effects of different interventions and control strategies. By simulating a large number of scenarios, researchers can estimate the effectiveness of various measures, such as social distancing, vaccination campaigns, or contact tracing, and assess their impact on disease transmission.

Exploration of complex scenarios
Monte Carlo models can handle complex and multiple interacting factors. They can simulate the effects of changes in population demographics, travel patterns, or behavior modifications, allowing for a better understanding of the outcomes and the identification of critical factors driving the spread of the disease.

Other advantages exist, but I think these are perhaps the most relevant. I welcome and encourage others.