In case you aren't familiar, here's the wikipedia entry on confidence intervals.

#### Demonstrated interpretation

*If you repeat the procedure N times, the percent of calculated 90% confidence intervals that contain the true population parameter would tend toward 90%.*

I attempted to visualize this one. The animation below generates 100 random numbers from a normal distribution centered at 0 (0 is the true population parameter here). It then calculates the confidence interval. It does this hundreds of times and calculates the percentage of confidence intervals that contained 0. For an 80% confidence interval, that should be ~80%. For an 85% one, that should be 85%...

You can select the confidence interval to change it.

You can select the confidence interval to change it.

#### Bad interpretations that this demo clears up

- It is clear from the visualization that the X% confidence interval does not contain X% of the points.
- It is clear from the visualization that the X% confidence interval is not the entire range of plausible values. The fact that some of the calculated confidence intervals do not contain 0 shows this pretty conclusively.

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