Metadata
- Author: Allen Downey
- Full Title:: What Does a Confidence Interval Mean?
- Category:: 🗞️Articles
- Document Tags:: Hypothesis testing,
- URL:: https://allendowney.substack.com/p/what-does-a-confidence-interval-mean
- Finished date:: 2024-04-18
Highlights
Under most reasonable interpretations of probability, you can say that a specific 90% CI has a 90% chance of containing the true parameter. There is no real philosophical problem with that. But there might be practical problems. Practical problems¶ The process we use to construct a CI takes into account variability due to random sampling, but it does not take into account other problems, like measurement error and non-representative sampling (View Highlight)
when the sample size is large, variability due to random sampling is small, which means that other sources of error are likely to be bigger. So as sample size increases, the probability decreases that the CI contains the true value. (View Highlight)
If you want to say that a 90% CI has a 90% chance of containing the true value, there is nothing wrong with that, philosophically. I think it is a meaningful and useful probabilistic claim. However, it is only true if other sources of error — like sampling bias and measurement error — are small compared to variability due to random sampling (View Highlight)