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Brian_Pimentel
Level II

Interval Explorer for One Sample Variance

I don't understand what the interval, lower and upper bound outputs for this explorer tool are - they don't seem to match the traditional chi^2 math you would do to calculate the CI of a stdev. "Interval" doesn't even seem to match the range between the upper and lower bound....

What are the units of interval width?

Are they dependent on the value of the standard deviation?

Is it a half width or a full width?

How do I use this to calculate a CI? I know it's not supposed to be symmetrical...

 

Please and thank you,

 

Brian_Pimentel_0-1724110672641.png

 

1 REPLY 1
MRB3855
Super User

Re: Interval Explorer for One Sample Variance

Hi @Brian_Pimentel : You can find that information here (click on help button).

https://www.jmp.com/support/help/en/18.0/#page/jmp/margin-of-error-for-one-sample-variance.shtml#

 

There it says the width (full width since you chose the Interval option) as shown is the same as you expect with the assumption that the sample variance =1 (this makes sense because you haven't collected the data yet). So, in your case, if you then take a sample of size 27, the width  of the 95% CI for the Population Variance will be 1.258*Sample Variance. 

 

Your other questions:

1. What are the units of interval width? Unitless.

2. Are they dependent on the value of the standard deviation? No.

3. Is it a half width or a full width? Answered above.

4. How do I use this to calculate a CI? This is not a tool to make any calculation of a CI. It is a tool to assess what sample size you want based on the desired width as a function of sample size. Width is a measure of the precision that the Sample Standard Deviation has as an estimate of the Population Standard Deviation. As you a see from the plot, as your sample size increases, the gain in precision diminishes.  For example, width =   7.898 when n=5 and 2.86 when n=10. So, by increasing your sample size from 5 to 10 you get a big increase (7.898 to 2.86) in precision.  But, going from 10 to 15 (increasing by 5 again) you get a width of 1.951. So, the increase in precision is smaller (2.86 to 1.951) for the same increase in sample size. So, you get diminishing returns in precision as your sample size increases (as indicated by the plot getting flatter and flatter as sample size gets larger).  It is left to you to decide the trade-off between precision and sample size.

 

Once you’ve collected the data, you can use the Distribution platform to calculate the confidence interval. 

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