|
Tags: Blanking Manual revert |
Line 1: |
Line 1: |
| Proportion estimation is another common task for sample statistics.
| |
|
| |
|
| We have sample proportion
| |
|
| |
| <math>
| |
| \hat{p} = \frac{y}{n}
| |
| </math>
| |
|
| |
| where <math>y</math> is the number of subjects in the sample with a
| |
| particular trait, and <math>n</math> is the sample size.
| |
|
| |
| We have
| |
|
| |
| <math>
| |
| \mu_\hat{p} = p, \sigma_\hat{p} = \sqrt{\frac{p (1 - p)}{n}}
| |
| </math>
| |
|
| |
| and standard error
| |
|
| |
| <math>
| |
| SE = \sqrt{\frac{\hat{p} (1 - \hat{p})}{n}}
| |
| </math>
| |
|
| |
| = Wilson-Adjusted CI for p =
| |
|
| |
| ''Correcting'' the sample proportion narrows the confidence interval. We
| |
| do this with the '''Wilson-Adjusted estimate''' for <math>p</math>
| |
|
| |
| <math>
| |
| \widetilde{p}
| |
| </math>
| |
|
| |
| [[Category:Sample Statistics]]
| |