Statistical Analysis Question: Confidence Intervals

[jpenmech]

Hi all,

I have 26 data points I'd like to form a confidence interval around (i.e. points to bound the sample data and possibly the population data).

I can use a t-distribution type: mean +/- [sample/root(# data points)]*t_%5, but it doesn't fully capture the data points.

OR

I can use: mean +/- 3sigma, which does capture the data.

So I'm confused about the difference between the first and the second method.

I'd appreciate some help explaining this.

Cheers

 

[btrueblood]

To start with, a t_5% distribution is supposed to capture 95% of the data, while 3-sigma gaussian should capture 99.8% of the data. A 2-sigma deviation would be closer to a t_5%.

 

[jpenmech]

Yeah that makes sense.

Something I'm realizing the more I read about CI, is they don't bound individual data points of a sample, but rather bound the mean of a sample.

So I want to bound data points of any sample.

 

[IRstuff]

a normal distribution is a t-distribution with infinite degrees of freedom.

I suggest you read the Wikipedia articles on the subject:

http://en.wikipedia.org/wiki/Student's_t-distribution

http://en.wikipedia.org/wiki/Confidence_interval

TTFN
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[jpenmech]

Thanks, but I've already been through those articles and much Googling. The terminology used for statistics is a bit confusing.

A confidence interval or confidence bounds are not for individual data points of a sample.

The CI is for a samples mean only and says nothing with regard to the scatter range in a sample.

Maybe I need to look into sample variation (not variance) analysis......

 

[IRstuff]

"A confidence interval or confidence bounds are not for individual data points of a sample."

That's not strictly true. They bound the distribution of a PDF that best fits the data. Therefore, if your data is consistent with the PDF you are applying, then the CI will be consistent with those data points. When you calculate a standard deviation or variance, you make explicit assumptions about the data you are fitting, and if those assumptions are incorrect, then the variance could be drastically different than what it might be.

TTFN
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[Denial]

Confidence intervals can be formulated so that they apply to sample means, or they can be formulated to apply to an individual point.

 

[Dougt115]

Confidence levels are used all the time to set requirements.

Example: Your product will meet the 50% confidence interval with a tolerance of +-.001.

But after you have the data, post manufacturing, it is only used to describe the distribution.

Since you have your data points all you can do is use the confidence interval to describe the distribution to show it does or does not meet requirements.

 

[rb1957]

"So I want to bound data points of any sample." ... unless your data is truly limited by real constraints, can you bound "any" dataset ? why would you want to ? and bounding "any" dataset could be misleading in that you could be giving weight to out-lying points and to data that may be overly influenced by the data collection and recording process.

another day in paradise, or is paradise one day closer ?

 

[jpenmech]

@ Denial

That is what I ended up doing. Setting a t-CI specifically for the points around 3sigma from the sample mean.

 

[Dougt115]

So your confidence interval is 100%??? 3 sigma is 99.8% What is this good for? I really don't understand please explain.