# Sample Size Determination for Variance Reduction

Six Sigma – iSixSigma Forums Old Forums General Sample Size Determination for Variance Reduction

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• #52348

Travis
Member

Im trying to locate a formula that can be used to determine the sample size requirements to detect a reduction in variance.  All literature and discussion threads Ive found only discuss sample size determinations for differences in the mean.

Basically, I want to determine how many samples must be tested in order to detect a 10% reduction in variance at 95% confidence.  The current sample standard deviation is 0.0008.

I would greatly appreciate any feedback.

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#184091

annon
Participant

Cant you use the Power and Sample Size function on MTB to accomplish this?

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#184110

Allard Munters
Participant

No, Minitab’s power and sample size calculation does not support test for equal variance…

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#184115

Asleeper
Participant

Yes, Travis, there is a simple formula. If I interpret your question correctly, this is a
one-sample test, that is, you will take one sample
of parts and test them to see if the population
standard deviation has changed from a previous
valueAlso, this is a one-sided test. That is, you are
not looking for an increase, only a decrease.In this case, here is the sample size formula,
given as an Excel formula:=1+0.5*(((NORMSINV(Alpha)*Sigma0+NORMSINV(Beta)*Sig
maBeta)/(Sigma0-SigmaBeta))^2)Where Alpha is the risk of a Type 1 error (0.05?)
Beta is the risk of a Type 2 error (0.05 to give
95% confidence of detecting a shift)
Sigma0 is the old std. dev. (0.0008)
SigmaBeta is the new std. dev. to be detected
(0.00072 in your case)With these values, the sample size is 490, after
rounding up the results of the calculation.This is from p. 413 of my book, Design For Six
Sigma StatisticsI hope this helps!

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#184117

Cone
Participant

Your book is wrong.You might want to try a book where the people have an
appropriate background.Look at the formulas for confidence interval of the standard
deviation, it is based on a chi squared distribution. You can decide
how big of a variance reduction you desire to be able to detect and
solve for n in the equation. The solution is iterative, that’s why
most stats book stay away from it.There are also graphs in the back of Juran’s Quality Handbook, at
leas since the second edition that will help you quickly know the
right answer. The graphs are based on the chi squared distribution.

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#184119

Cone
Participant

messageID=156786

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#184120

Asleeper
Participant

The formula I offered uses a normal approximation
to the chi-squared distribution, which is
reasonably good for large sample sizes. I stand by the formula as being a useful
approximation.

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#184133

Cone
Participant

Sloppy stats and it way overestimates the sample size needed.
Do some simulations using the sample size you have suggested and you will see.

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