Calculating Percentage Contribution Ratio (PCR) in Minitab

C

christianos

#1
Hi,

I am wondering how to calculate this in Minitab. As far as I know other software for statistics sometimes can present that contribution in a graph and give a real %.

I was trying to find it in Minitab and I am confused.

Basically, the standard formula for this is:

p% (PCR) = [Variance (F) x mean square variance error] / total sum of squares x 100%

It seems I cannot get all of the components to calculate it.

Am I doing something wrong?

I can rely on Pareto charts to see which factor has an impact but it's not giving me any "numbers"

Also, as it is seen below, Main Effects are showed together. Is there any way to see these calculations for each factor?

Analysis of Variance for Option 1 (coded units)

Source DF Seq SS Adj SS Adj MS F P
Main Effects 4 1,1104 1,1575 0,2894 1,72 0,201
2-Way Interactions 6 1,4564 1,2768 0,2128 1,27 0,333
3-Way Interactions 4 1,1022 1,1087 0,2772 1,65 0,217
4-Way Interactions 1 0,2175 0,2175 0,2175 1,29 0,274
Residual Error 14 2,3516 2,3516 0,1680
Pure Error 14 2,3516 2,3516 0,1680
Total 29 6,2382
 
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Miner

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#2
Many of Minitab's ANOVA routines have a Results button. The Results submenu should have a box you may select that states "Display expected mean squares and variance components" That will provide the information for which you are searching.
 
C

christianos

#3
Many of Minitab's ANOVA routines have a Results button. The Results submenu should have a box you may select that states "Display expected mean squares and variance components" That will provide the information for which you are searching.
I chose Full Table and still cannot find which number express a Contribution Ratio in %.

Maybe the only way to do that is by calculating it using the formula which I put in my 1st post? However, I am looking for a faster solution.
 
S

steelejc15425

#4
To my knowledge, the only place that percent contribution is in the output in Minitab is in the Gage R&R studies. Are you doing one of those? The most common one in Minitab is Stat > Quality Tools > Gage Study > Gage R&R Study Crossed.

If you're not doing a Gage R&R study, but you have two or more factors, you can probably still get percent contribution from the Gage R&R analysis tools. You'll just have to know which factor is accounting for reproducibility and which is for repeatability in the output. If you have two factors, you can use Minitab 15. If you have 3 or more factors, you'll need Minitab 16 so that you can use the new Gage R&R (Expanded) tool.


I don't have enough posts to add a link, but if you don't have Minitab 16 you can download a free trial from the Minitab website.

Is that what you were looking for?
 

Miner

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Leader
Admin
#5
I chose Full Table and still cannot find which number express a Contribution Ratio in %.

Maybe the only way to do that is by calculating it using the formula which I put in my 1st post? However, I am looking for a faster solution.
Minitab does not express it in terms of a contribution ratio (other than in the Gage R&R routine). You can use the variance components table and the formula that you posted previously to manually calculate the ratio.
 
C

christianos

#7
Minitab does not express it in terms of a contribution ratio (other than in the Gage R&R routine). You can use the variance components table and the formula that you posted previously to manually calculate the ratio.
I tried to calculate it using my formula from the 1st post. As it is visible I have F value (Variance). I am not sure what should I treat as a Mean value: Seq SS or Adj SS and what treat as a MEAN Square variance error and as Total sum of squares?

However, If I know that information still I do not know how to calculate contribution of each factor using that formula. The Analysis of Variance for AVERAGE Option 1 (coded units) presents only values for Main effects and interactions. I would like to know what is the contribution of each factor.

Just to make it clear I was doing L16 Full factorial design replicated two times, using two blocks. However, I've found those blocks irrelevant as a p-value was very high around 0.800



Factorial Fit: AVERAGE Option 1 versus SPEED; FEED; OPt1; OPt2

Estimated Effects and Coefficients for AVERAGE Option 1 (coded units)

Term Effect Coef SE Coef T P
Constant 6,88843 0,01274 540,78 0,000
A -0,06805 -0,03402 0,01274 -2,67 0,018
B -0,04431 -0,02215 0,01274 -1,74 0,104
C -0,09201 -0,04600 0,01274 -3,61 0,003
D -0,10069 -0,05034 0,01274 -3,95 0,001
AB 0,07706 0,03853 0,01274 3,02 0,009
AD -0,05281 -0,02641 0,01274 -2,07 0,057
AC -0,01113 -0,00556 0,01274 -0,44 0,669
BC 0,00368 0,00184 0,01274 0,14 0,887
BD -0,06132 -0,03066 0,01274 -2,41 0,030
CD 0,06673 0,03336 0,01274 2,62 0,020
ABC -0,00120 -0,00060 0,01274 -0,05 0,963
ABD 0,05989 0,02994 0,01274 2,35 0,034
BCD 0,05646 0,02823 0,01274 2,22 0,044
ACD -0,02617 -0,01309 0,01274 -1,03 0,322
ABCD -0,03578 -0,01789 0,01274 -1,40 0,182


S = 0,0679362 PRESS = *
R-Sq = 85,34% R-Sq(pred) = *% R-Sq(adj) = 69,63%


Analysis of Variance for AVERAGE Option 1 (coded units)

Source DF Seq SS Adj SS Adj MS F P
Main Effects 4 0,184235 0,161772 0,040443 8,76 0,001
2-Way Interactions 6 0,129173 0,110231 0,018372 3,98 0,016
3-Way Interactions 4 0,053604 0,056200 0,014050 3,04 0,053
4-Way Interactions 1 0,009103 0,009103 0,009103 1,97 0,182
Residual Error 14 0,064615 0,064615 0,004615
Pure Error 14 0,064615 0,064615 0,004615
Total 29 0,440729
 
C

christianos

#8
To my knowledge, the only place that percent contribution is in the output in Minitab is in the Gage R&R studies. Are you doing one of those? The most common one in Minitab is Stat > Quality Tools > Gage Study > Gage R&R Study Crossed.

If you're not doing a Gage R&R study, but you have two or more factors, you can probably still get percent contribution from the Gage R&R analysis tools. You'll just have to know which factor is accounting for reproducibility and which is for repeatability in the output. If you have two factors, you can use Minitab 15. If you have 3 or more factors, you'll need Minitab 16 so that you can use the new Gage R&R (Expanded) tool.


I don't have enough posts to add a link, but if you don't have Minitab 16 you can download a free trial from the Minitab website.

Is that what you were looking for?

Rather it is not I am looking for. I am doing analysis of a full factorial design. Unfortunately, I have only Minitab 15 and 4 factors in total ;/

But thank you anyway. That information might be useful in the future.
 

Miner

Forum Moderator
Leader
Admin
#9
Strictly speaking a factor should be random to be able to calculate a
%contribution.

Or am I wrong on that?
No. You are not wrong, but it all depends on what use you want to make of the % Contribution.

If you want the % Contribution to be repeatable in future studies, the factors should be random. However, if you only want to assess the relative magnitude of effects for this specific study, they do not have to be random.
 

Miner

Forum Moderator
Leader
Admin
#10
I tried to calculate it using my formula from the 1st post. As it is visible I have F value (Variance). I am not sure what should I treat as a Mean value: Seq SS or Adj SS and what treat as a MEAN Square variance error and as Total sum of squares?

However, If I know that information still I do not know how to calculate contribution of each factor using that formula. The Analysis of Variance for AVERAGE Option 1 (coded units) presents only values for Main effects and interactions. I would like to know what is the contribution of each factor.

Just to make it clear I was doing L16 Full factorial design replicated two times, using two blocks. However, I've found those blocks irrelevant as a p-value was very high around 0.800



Factorial Fit: AVERAGE Option 1 versus SPEED; FEED; OPt1; OPt2

Estimated Effects and Coefficients for AVERAGE Option 1 (coded units)

Term Effect Coef SE Coef T P
Constant 6,88843 0,01274 540,78 0,000
A -0,06805 -0,03402 0,01274 -2,67 0,018
B -0,04431 -0,02215 0,01274 -1,74 0,104
C -0,09201 -0,04600 0,01274 -3,61 0,003
D -0,10069 -0,05034 0,01274 -3,95 0,001
AB 0,07706 0,03853 0,01274 3,02 0,009
AD -0,05281 -0,02641 0,01274 -2,07 0,057
AC -0,01113 -0,00556 0,01274 -0,44 0,669
BC 0,00368 0,00184 0,01274 0,14 0,887
BD -0,06132 -0,03066 0,01274 -2,41 0,030
CD 0,06673 0,03336 0,01274 2,62 0,020
ABC -0,00120 -0,00060 0,01274 -0,05 0,963
ABD 0,05989 0,02994 0,01274 2,35 0,034
BCD 0,05646 0,02823 0,01274 2,22 0,044
ACD -0,02617 -0,01309 0,01274 -1,03 0,322
ABCD -0,03578 -0,01789 0,01274 -1,40 0,182


S = 0,0679362 PRESS = *
R-Sq = 85,34% R-Sq(pred) = *% R-Sq(adj) = 69,63%


Analysis of Variance for AVERAGE Option 1 (coded units)

Source DF Seq SS Adj SS Adj MS F P
Main Effects 4 0,184235 0,161772 0,040443 8,76 0,001
2-Way Interactions 6 0,129173 0,110231 0,018372 3,98 0,016
3-Way Interactions 4 0,053604 0,056200 0,014050 3,04 0,053
4-Way Interactions 1 0,009103 0,009103 0,009103 1,97 0,182
Residual Error 14 0,064615 0,064615 0,004615
Pure Error 14 0,064615 0,064615 0,004615
Total 29 0,440729
This printout does not provide the information that you need. Did you analyze this as a Taguchi experiment? The components of variation may not be an option for Taguchi. I cannot remember. You might try using GLM to obtain the components of variation.
 
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