# Sample Size Determination for Variance Reduction

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- This topic has 7 replies, 5 voices, and was last updated 10 years, 7 months ago by Cone.

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- May 13, 2009 at 6:14 pm #52348
Im 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 Ive 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.0May 13, 2009 at 6:32 pm #184091Cant you use the Power and Sample Size function on MTB to accomplish this?

0May 14, 2009 at 8:19 am #184110

Allard MuntersParticipant@Allard-Munters**Include @Allard-Munters in your post and this person will**

be notified via email.No, Minitab’s power and sample size calculation does not support test for equal variance…

0May 14, 2009 at 12:38 pm #184115

AsleeperParticipant@Asleeper**Include @Asleeper in your post and this person will**

be notified via email.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!0May 14, 2009 at 1:15 pm #184117Your 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.0May 14, 2009 at 1:54 pm #184119This is also helpful.https://www.isixsigma.com/forum/showmessage.asp?

messageID=1567860May 14, 2009 at 3:16 pm #184120

AsleeperParticipant@Asleeper**Include @Asleeper in your post and this person will**

be notified via email.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.0May 14, 2009 at 5:22 pm #184133Sloppy stats and it way overestimates the sample size needed.

Do some simulations using the sample size you have suggested and you will see.0 - AuthorPosts

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