# Overall and Within/Between STDEV - Why not the same?

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#### puck1263

So, I understand the concept of WITHIN (subgroup) standard deviation and BETWEEN (subgroup) standard deviation. Also that BETWEEN/WITHIN is root(within^2+between^2).
OVERALL is stdev of all measures.

Question 1:
Why is Overall stdev not equal to between/within? I don't understand.

Question 2:
I have a process improvement where WITHIN, BETWEEN, and WITHIN/BETWEEN stdev all went down (by quite a bit), but OVERALL went up. How can this be? Perhaps related to question 1.

#### Bev D

##### Heretical Statistician
Super Moderator
not sure I'm following you. could you post your data showing the calculations?

in general: Stotal = sqrt(Swithin^2+Sbetween^2) of course depending on the sampling the two numbers won't be exactly the same .

not sure what you mean by between/within - or within/between - what do you think that is?

P

#### puck1263

Sure -
Attached are jpg graphs created in Minitab.
One is process capabilty prior to an improvement, and one is post improvement.

#### Attachments

• Within Capability of CH ww18-ww25.jpg
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• Within Capability of Compressed_height_(um)PDC_ww17.jpg
43.1 KB · Views: 535
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#### Darius

I am not sure of
Stotal = sqrt(Swithin^2+Sbetween^2)

But, the reason of:

why you can reduce between and within variation and not total variation?

The answer is not in your distribution, but your data..., the missing part of within and between variation estimates is the trend component of your data. You can have a very small between and within variation, but a large total variation if your data shows a trend. So the different variation estimates by themselves don't tell all the story, but if you analyse the 3 as a group gives you the required understanding of your process (if your subgroup strategy is the right one for your goal).

#### Bev D

##### Heretical Statistician
Super Moderator
please post your raw data with subgrouping and timeseries labels. this is the only way to understand what is going on.

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#### puck1263

Attached is spreadsheet with raw data.

Data subgrouping is by row. Each sample has a subgroup of 15

The two worksheets are before and after a process change. After the change, BETWEEN, WITHIN, and BETWEEN/WITHIN all go down, but OVERALL goes up. How does this work?

#### Attachments

• Process_capabilty_data.xls
20.5 KB · Views: 479

#### Bev D

##### Heretical Statistician
Super Moderator
Several very wise men have said: "first plot your data in time series"

Take a look at that first.

by the way - I don't see much improvement...

#### Attachments

• Elsmar Process Capability.xls
31 KB · Views: 622

#### Miner

##### Forum Moderator
Attached is spreadsheet with raw data.

Data subgrouping is by row. Each sample has a subgroup of 15

The two worksheets are before and after a process change. After the change, BETWEEN, WITHIN, and BETWEEN/WITHIN all go down, but OVERALL goes up. How does this work?
I checked the (broken link removed) knowledge base. It essentially states what you wrote in your original post.

The answer that you are looking for lies in the way each is calculated and to what each is sensitive.

Take an example where your process is running consistently at a given level, then shifts 1 StdDev where it again runs consistently. In a histogram of the individual points, this will appear bimodal and will drastically inflate the overall variation since it is calculated as one group. However, the between subgroup variation will be little affected because the shift of 1 StdDev will be one single data point among the rest. It will appear on a between subgroup histogram as a single outlier and will not have much effect on the between subgroup variation.

#### Statistical Steven

##### Statistician
Super Moderator
I checked the (broken link removed) knowledge base. It essentially states what you wrote in your original post.

The answer that you are looking for lies in the way each is calculated and to what each is sensitive.

Take an example where your process is running consistently at a given level, then shifts 1 StdDev where it again runs consistently. In a histogram of the individual points, this will appear bimodal and will drastically inflate the overall variation since it is calculated as one group. However, the between subgroup variation will be little affected because the shift of 1 StdDev will be one single data point among the rest. It will appear on a between subgroup histogram as a single outlier and will not have much effect on the between subgroup variation.

I take a slightly different approach. Assume that the within variation is a single lot and the between variation is lot to lot. Within lot consistency could be excellent, though lot to lot could be awful, leading to overall or total variability is awful. Cpk/Cp are great, Pp/PpK is awful.

#### Bev D

##### Heretical Statistician
Super Moderator
So, I understand the concept of WITHIN (subgroup) standard deviation and BETWEEN (subgroup) standard deviation. Also that BETWEEN/WITHIN is root(within^2+between^2).
OVERALL is stdev of all measures.

Question 1:
Why is Overall stdev not equal to between/within? I don't understand.

Question 2:
I have a process improvement where WITHIN, BETWEEN, and WITHIN/BETWEEN stdev all went down (by quite a bit), but OVERALL went up. How can this be? Perhaps related to question 1.

well, I'm confused. I've looked at the raw data that was posted and maybe I've misinterpreted the structure of the data. I certainly don't know what Within/Between means???

I looked at the befroe data and the after data. There is a slight centering of the after data that may or may not be due to your "improvement". The data is not very compelling at this point as the centering shift is small and not coincident with your stated change point...

I have attached my results. (I dont' have minitab; I use JMP or just excel)
the after between and total SDs went down. and the Ppk got better, just a little bit but it all makes sense.

I don't see the Problem as you describe it

#### Attachments

• Elsmar Process Capability.xls
31.5 KB · Views: 392