# HP Forums

Full Version: Pooling Standard Deviation
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I am looking into getting a Prime and am currently playing around with the simulator. (I currently have an HP71B which which has a flaky keyboard - after 30 years or so, not bad!)

Anyway, I was trying my favorite function: Calculating the confidence interval of the mean. I had no problem calculating the interval from some sample data, and it agreed with my reference.

However, my reference is for a DOE class and they apply the formula using the "pooled" standard deviation. If you have a bunch of replicants of a response surface, you use all the points to calculate the standard deviation, while you use only the number of samples in your mean calculation (one portion of the response surface) for N.

So for example the example in the course, you have 11 degrees of freedom for the standard deviation and only 3 points for N. This tightens the interval considerably.

So is there any way to use a pooled standard deviation with more degrees of freedom than you might have points that calculated the mean?
The 'pooled standard deviation' is the 'root mean square error' estimate from a regression analysis of the DOE data. It is based on the correct degrees of freedom. If it is not reported directly then it is the square root of the mean squared error in the analysis of variance results.
Search for a HP Prime app or program that suits your data. If you have a single categorical factor, then use one-way ANOVA in the Inference app. If you have a single continuous factor, then use regression in the Stats 2Var app. You will need a program for a DOE with more than one factor.
Thanks, but what I want is a way to unlink the degrees of freedom of the std deviation estimate from the number of points used to calculate the mean.

For example, lets say I am manufacturing batches of widgets:
I have made several batches, so I know my standard deviation with pretty good accuracy. I make a new batch of 5 widgets.

I would like to be able to specify that my standard deviation is associated with a number of degrees of freedom much larger than 5 to greatly improve my estimate, but I can't with the current inference App.

It would be nice if the degrees of freedom for the std dev would be specified separately, but default to 1-the number used to calculate the mean.
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