Standard Error — Precision of Sample Statistics
Foundations of Statistics
Measuring the Reliability of Estimates
The standard error quantifies how precisely a sample statistic estimates the population parameter, forming the foundation for confidence intervals and hypothesis tests. It decreases with sample size, enabling better estimates with more data.
- Medical Research — Assessing precision of treatment effect estimates in clinical trials
- Polling — Reporting margins of error for survey estimates
- Economics — Evaluating precision of economic indicators and forecasts
The standard error tells you how much trust to place in your estimates.
Core Concepts
The standard error (SE) measures the precision of a sample statistic — it quantifies how much the statistic would vary across repeated samples.
Formal Derivation
SE for Proportions
How Sample Size Affects SE
Worked Example
A pharmaceutical company measures blood pressure reduction. From prior studies, mmHg.
| 95% CI half-width | ||
|---|---|---|
| 25 | ||
| 100 | ||
| 400 | ||
| 1600 |
Key observation: Going from to (4× the sample) halves the SE from 1.20 to 0.60. The cost of data collection must be weighed against this diminishing return.