# ExpandProbs

##### Calculate modified probabilities for more accurate confidence intervals

Compute modified quantiles levels, for more accurate confidence intervals. Using these levels gives sider intervals, with closer to desired coverage.

- Keywords
- htest, nonparametric

##### Usage

`ExpandProbs(probs, n)`

##### Arguments

- probs
- vector of numerical values between 0 and 1.
- n
- number of observations.

##### Details

Bootstrap percentile confidence interval for a sample mean correspond roughly to $$\bar x \pm z_\alpha \hat\sigma$$ instead of $$\bar x \pm t_{\alpha,n-1} s$$ where $$\hat\sigma = \sqrt{(n-1)/n s}$$ is like s but computed using a divisor of n instead of n-1. Similarly for other statistics, the bootstrap percentile interval is too narrow, typically by roughly the same proportion.

This function finds modified probability levels probs2, such that $$z_{\mbox{probs2}} \sqrt{(n-1)/n} = t_{\mbox{probs}, n-1}$$ {z_probs2 sqrt((n-1)/n) = t_probs,n-1} so that for symmetric data, the bootstrap percentile interval approximately matches the usual $t$ confidence interval.

##### Value

- A vector like
`probs`

, but with values closer to 0 and 1.

##### References

This discusses the expanded percentile interval:
Hesterberg, Tim (2014), What Teachers Should Know about the
Bootstrap: Resampling in the Undergraduate Statistics Curriculum,

##### See Also

##### Examples

```
probs <- c(0.025, 0.975)
n <- c(5, 10, 20, 40, 100, 200, 1000)
outer(probs, n, ExpandProbs)
```

*Documentation reproduced from package resample, version 0.4, License: BSD_3_clause + file LICENSE*