[R] Basic question about confidence intervals

[David Winsemius]

On Jun 7, 2012, at 7:30 AM, Mohan Radhakrishnan wrote:

> Hi,
>
>         I am again asking a generic question and the general  
> response for such questions is cold. I am a beginner but use and  
> write simple R scripts.

Have you read the Posting Guide?

"If the question is well-asked and of interest to someone on the list,  
it may elicit an informative up-to-date answer. See also the Usenet  
groups sci.stat.consult (applied statistics and consulting) and  
sci.stat.math (mathematical stat and probability).
Basic statistics and classroom homework: R-help is not intended for  
these.  "



There are other forums online for such questions:

stats.exchange.com is one such. (And I would have to say that the  
Usenet group advice is seriously outdated.)


>         I am looking for some ideas to calculate the confidence  
> intervals based on this excerpt from the paper. Moreover it would  
> help if someone points to material to read about degrees of freedom  
> and any related concepts.

Now that last one is surely a sign of "failure to google".

-- 
David.
>
>
>
>
>
> Thanks,
>
> Mohan
>
>
>
>
>
> Cutting Corners: Workbench Automation
>
> for Server Benchmarking
>
>
>
> APPENDIX: Confidence Intervals
>
> Given N observations of response time from N runs at
>
> given arrival rate λ, the confidence interval for the response
>
> time at that λ with a desired confidence level, c%,
>
> is computed as follows:
>
> • Compute the mean server response time: μ =
>
> PN
>
> i=1 Ri/N, where Ri is the server response time
>
> for the ith run.
>
> • Compute the standard deviation for the server response
>
> time: σ = qPN
>
> i=1(Ri − μ)2/(N − 1).
>
> • Confidence interval for the response time at confidence
>
> 100c% is given as: [μ − zpσ/√N, μ +
>
> zpσ/pN], where p = (1 + c)/2, and zp is the quantile
>
> of the unit normal distribution at p.
>
> If N <= 30, we replace zp by tp;n−1, which is the pquantile
>
> of a t-variate with n−1 degrees of freedom,
>
> assuming that the response time values from N runs
>
> come from a normal distribution. We verified that
>
> response times do come from a normal distribution
>
> using a normal proability plot.
>
>
>
> DISCLAIMER:\ ===============...{{dropped:31}}
>
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.

David Winsemius, MD
West Hartford, CT