How to make an ANOVA of a design with repeats (not replicates) in Minitab?

F

Felix_xx

#11
Hallo Miner,
I don’t understand your question. Can you please ask differently or make an example. Thanks
 
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Miner

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#12
Let's go back to the different types of repeats.

  1. Repeats in the typical experimental design sense: These are just multiple measurements taken under the same experimental conditions. For example, you run an experiment on injection molding. Under each experimental run, you collect and measure 10 parts. Each part is measured a single time.
  2. Repeats in a Repeated Measures design sense: Now we change the previous example slightly. We run the same experiment on injection molding. However, this time we collect a single part (i.e., the subject) then measure that part repeatedly. Once, hot out of the mold, then again at 30 minute intervals over a 4 hour period. The repeated measurements will help quantify the shrinkage of the part over time.

In the first example, the repeats are placed in multiple columns. The repeat values are averaged, then the averages are analyzed.

In the second example, the repeat measurements of each part (i.e., subject) are entered as in the example from Minitab. But we must associate every repeat with a specific subject and the time when it was measured.
 
F

Felix_xx

#13
Thanks for the detailed explanation! It helped a lot.

I think now that we dig deeper and deeper it makes sense that I explain more detailed what we actually did before I knew the difference between replicates and the two types of repeats. Sorry that I waited that long to explain all the details of our experiment but I thought it would be easier and all the details would just make it more difficult. Now I think that we need the details to discuss it correctly.

What we did:
1. Step: We mix a big batch of material. This recipe of this mixture depends on the factors D, E and F
2. Step: We run an experiment with the material we mixed. The conditions of this experiment depend on the factors A, B and C. Running this experiment we have three sensors that are measuring forces. So we get three measurements out of one run.
3. Step: We take the material we used in step two out of the test bench and fill it again with the material from our big batch (Step 1). We do not willingly change (or reset and set them on the same levels) the factors A, B and C. But there will be some variation in it because it is not the same run (B for example is a speed which will never be 100% the same). Running this experiment we get three more measurement.

Then we clean everything up and mix a new batch (different settings for D, E, F). Also the factors A,B and C change for the steps 2 and 3.

So what kind of replicates or the two types of repeats is that?
1. Way of thinking: We measured six times with the same factors but the sensors are independent and we didn’t just measure the same thing six times. => all six measurements are “repeats in the typical experimental design sense”
2. Way of thinking: The important factors for us are A, B and C. Even if we didn’t change them they will never be 100% the same in two following runs. => The first three measurements (out of the 2. Step) are “repeats in the typical experimental design sense”. Then we create a replicate by the 3. Step (ok maybe it is not a perfect replicate but the factors A, B and C naturally have to vary a little). This replicate consists out of the second three measurements.


What do you think? What do we have in this setting? :confused:
 
F

Felix_xx

#15
Looks perfect! That’s a very nice diagram!

Just one additional word to the three sensors: They don’t measure the very same thing. So if the sensors deliver different values it is because of the process and because of the sensors. We do not (!!) have the situation that the three sensors measure the very same thing and that the difference in measurement only comes from the error of the sensors.

I think that was maybe the last not that clear bit of our procedure.

What do you think?
 

Miner

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#16
I am fairly certain that I understand the setup, so I'll go ahead with an explanation.

I'll start with the bad news and get that out of the way. The way your experiment is constructed is an extremely complex design structure. In addition, the three sensors and the split batches are neither true repeats nor true replicates. The three sensors have sensor to sensor differences as well as positional differences included while the split batches have time differences and non-setup related variations. Normally, this type of experiment would be setup as a split plot or a least a blocked design. However, it is too late to do so now.

Now the good news: Both the split plot and blocked designs are intended to deal with large sources of noise variation and situations where the level of noise varies from whole plot to subplot. In your experiment, the variation from sensor to sensor, and from half batch to half batch is quite small. I replaced your repeat column with two columns; one for sensor location, the other for half batch. These were not even close to significance. While the following is technically a cheat, it is a very practical solution to your issue.

I would treat these as if they were true repeats. That is, set up six columns for the six results. Take the mean of the six values and put it in a seventh column then analyze that column as your response. If minimizing variation within a run is important, you can take it a step further and put the standard deviation of the six columns in an eighth column and analyze that in addition to the mean.
 
F

Felix_xx

#17
Hallo Miner!

I know that the plan is not perfect but as the quote beneath your post says some people learn from experience ;-)

I tried all the things you mention and would like to sum it up in my own words to see whether I got it right and we are on the same point.

1. Testing the split plot and the blocked design
“the three sensors and the split batches are neither true repeats nor true replicates”. We should have used a split plot or a blocked design. If we would have a “large sources of noise variation and situations where the level of noise varies from whole plot to subplot” then these effects could be eliminated by the split plot and the blocked design. If these effects have no significance then it is a practical solution to treat our six measurements as “Repeats in the typical experimental design sense”.
The files starting with “Test_sensor_batch” show:
- We have a p-Value for the factor “Sensor Location (1, 2, 3)” of 0,957.
- We have a p-Value for the factor “Half Of The Batch (1, 2)” of 0,649.
These p_Values are quite high so the influence of these effects is low. As mentioned it is “ok” to treat the six measurements from now on as “Repeats in the typical experimental design sense”

2. “Repeats in the typical experimental design sense”
“That is, set up six columns for the six results. Take the mean of the six values and put it in a seventh column then analyze that column as your response.” The files for that start with “Repeats” (I already uploaded a few of them in Post Number 9).

Is that right like that? Are we on the same page? :)

Greetings
Felix
 

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Miner

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#18
Yes. You duplicated my sensor/batch analysis and correctly set up the repeat columns and mean column.
 
F

Felix_xx

#19
ok thanks a lot for the discussions and your help! There are quite some things I will do differently next time :D
Have a nice weekend!
 
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