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.
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.
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}}
Apology. The formulas are munged.
I am referring to 'APPENDIX: Confidence Intervals' in the paper at
http://www.cse.iitb.ac.in/~puru/courses/spring12/cs695/downloads/cuttingcorners.pdf
Mohan
-----Original Message-----
From: r-help-bounces at r-project.org [mailto:r-help-bounces at r-project.org]
On Behalf Of Mohan Radhakrishnan
Sent: Thursday, June 07, 2012 5:00 PM
To: r-help at r-project.org
Subject: [R] Basic question about confidence intervals
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.
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.
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 ??, the confidence interval for the response
time at that ?? with a desired confidence level, c%,
is computed as follows:
??? Compute the mean server response time: ??
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: ?? = qPN
i=1(Ri ??? ??)2/(N ??? 1).
??? Confidence interval for the response time at confidence
100c% is given as: [?? ??? zp??/???N, ?? +
zp??/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}}
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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 ?, the confidence interval for the response > > time at that ? with a desired confidence level, c%, > > is computed as follows: > > ? Compute the mean server response time: ? > > 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: ? = qPN > > i=1(Ri ? ?)2/(N ? 1). > > ? Confidence interval for the response time at confidence > > 100c% is given as: [? ? zp?/?N, ? + > > zp?/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