# Pooled Standard Deviation

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- This topic has 6 replies, 6 voices, and was last updated 12 years, 6 months ago by Jim Ace.

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- July 16, 2007 at 2:36 pm #47575

Kiran VarriParticipant@Kiran-Varri**Include @Kiran-Varri in your post and this person will**

be notified via email.Hi Guys,

Can some one offer an example for calculating Pooled Standard Deviation.

Thank you.

Kiran Varri0July 18, 2007 at 5:07 pm #158814

David O’ CParticipant@David-O'-C**Include @David-O'-C in your post and this person will**

be notified via email.COuld someone show the pooled Standard Deviation for this set of data,56.5256.5356.5856.5356.5356.5756.5556.5556.5856.5756.5756.55Thanks, David.

0July 18, 2007 at 6:24 pm #158815You have not given enough information. If the data falls into one group, there is no need to pool the standard deviation.

0July 18, 2007 at 8:40 pm #158817HACL,

Can you simply take the average of your subgroup std dev or is it necessary to break it down accordingly into SOS and DOF componennts as shown in the Dictionary definition on this site?

THANKS0July 18, 2007 at 10:43 pm #158819Don’t average, but pool as follows:

s2p = [(n1 1) s12 + (n2 1) s22] / (n1 + n2 -2)

0July 28, 2007 at 2:39 pm #159235do you know any online programs that will calculate the pooled standard deviation? ive been searching for one but cant find it.

0July 28, 2007 at 7:00 pm #159247

Jim AceParticipant@Jim-Ace**Include @Jim-Ace in your post and this person will**

be notified via email.May, your question is a good one! The pooled standard deviation can be estimated by the equation:

Spooled = sqrt[SSwithin / g(n-1)]

Notice that Spooled assumes your data is organized into groups (g = the number of groups and n = the number of replicates within each group). Also notice that this equation requires the same sample size for each group. You can also estimate the pooled standard deviation using Rbar/d2. There are several other minor theoretical considerations that can be argued, but overall, you are safe with this method of analysis.

Extra Insight: See ANOVA SStotal = SSwithin + SSbetween

For a more complete understanding of the pooled standard deviation you should look at the Minitab help menu. Several of the computational methods in Minitab relies on the pooled standard deviation and gives you some good options on how it can be computed, like when you are attempting to estimate process capability.

Jim Ace0 - AuthorPosts

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