# ExpandProbs

0th

Percentile

##### 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, http://arxiv.org/abs/1411.5279.

CI.percentile, CI.bca,

• ExpandProbs
##### 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

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