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

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#### Felix_xx

Hallo all together!

I did set up an experimental design and made six repeated measurements for each combination of factors. Now I would like to analyses it with minitab starting with an ANOVA. The point is that I don’t know how to insert repeated measurements. I can only find explanations for replicates.

Can somebody help me out? Up to now I only manage to just use the average of the six repeated measurements or act as if they are replicates but that’s kind of wrong because I have “repeated measurements”.

In case somebody wants to look up the difference between a replicates and repeats you can just google: “minitab Replicates and repeats in designed experiments” (I am too new to post a link)

I am running out of time and can't believe that minitab is not able to analyze repeated measurements. Do you have a hint? Thanks a lot for your help!

Felix

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#### Felix_xx

Hallo Miner,

I didn't expect to get an answer that fast. Thanks a lot!

While trying to get the procedure right and running my own analysis I got two more questions. Could you please help me out?

1.
So if I get it right the only difference between “repeats” and “replicates” for minitab is that you insert an experimental block. In this example the experimental block is called “dial”. Is that right?

2.
When you have replicates the degrees of freedom increase a lot because you made “truly separate” runs. Now I wonder that the degrees of freedom also increase that much if I have repeats. I didn’t expect them to increase. I read in a book and on the side of minitab that for replicates you add new rows (so I assumed that you get more degrees of freedom) and for repeats you add new columns and write the results in the same rows (so I assumed that the degrees of freedom stay the same and only the total sum of squares (TSS), the sum of squares between groups (SSB) and the sum of squares within groups (SSW) change). Now I wonder that the degrees of freedom change the same way. Why do the degrees of freedom also increase that much for repeats? If the degrees of freedom also increase for repeats what’s the difference between repeats and replicates? The block doesn’t make that much of a change.

Felix

#### Miner

##### Forum Moderator
I think you are getting confused between the typical definition of repeats vs replicates, the repeats in repeated measures and the data entry structure used by Minitab to analyze repeated measures. In your first post, you have the correct sense of the difference between repeats and replicates under normal experiments. Replicates see more chance for variation than repeats because replicates include setup variation and time variation which repeats do not see. You are also correct that in normal designs, Minitab places replicates in additional rows and repeats in additional columns.

Repeats in a repeated measures design are different than repeats in the normal sense. At a minimum, these repeats include a time element of variation, and in a crossover design also include setup variation. In the strict sense they are really replicates. Unfortunately, the name repeated measures was given long ago and cannot be changed now.

The analysis of a repeated measures design is similar to that of a split plot design. Just as there is a difference in the error structure between the whole plot and the subplot, there is a difference in the error structure between subjects and within subjects. The "trick" Minitab uses with blocks allows Minitab to recreate that different error structures because the math behind the analysis happens to work the same as with blocks.

A screenshot of the partial datasheet that Minitab used in the example shows that the repeated measures were added in rows, not columns. This provides 53 degrees of freedom.

#### Attachments

• Repeated Measures data.jpg
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#### Felix_xx

Ok I think I got the difference between repeats and replicates. Makes sense to me. But I am still a little confused on how we are handling it in Minitab.

First I have to ask again (sorry for going on your nerves) weather I got it right that in the example the factor “dial” creates the block we need to “explain” to Minitab that we have repeats. Right? So this column is from the minitab point of view the only difference between repeats and replicates.

The other point I have problems with is:
Scenario 1:
I have a design with repeats and make an ANOVA where I kick out the factor of the block (because of low probability).
Scenario 2:
I have a design with replicates and make an ANOVA

The data (ANOVA and everything) I get from Scenario 1 and Scenario 2 looks the same. How can that be? From my understanding there has to stay a difference, no? It has to make a difference whether we use repeats or replicates!

Thanks a lot for your help!

#### Miner

##### Forum Moderator
Ok I think I got the difference between repeats and replicates. Makes sense to me. But I am still a little confused on how we are handling it in Minitab.

First I have to ask again (sorry for going on your nerves) weather I got it right that in the example the factor “dial” creates the block we need to “explain” to Minitab that we have repeats. Right? So this column is from the minitab point of view the only difference between repeats and replicates.

ETime stands for Elapsed Time. The levels of elapsed time are the points in time where the repeated measurements of the Subject are taken. Dial is one of the other factors.

The other point I have problems with is:
Scenario 1:
I have a design with repeats and make an ANOVA where I kick out the factor of the block (because of low probability).

Please clarify. You state (because of low probability). Do you mean a small p-value?

Scenario 2:
I have a design with replicates and make an ANOVA

The data (ANOVA and everything) I get from Scenario 1 and Scenario 2 looks the same. How can that be? From my understanding there has to stay a difference, no? It has to make a difference whether we use repeats or replicates!

It depends. Can you attach your file? Without seeing specific details, it is almost impossible to speculate.

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#### Felix_xx

Hallo!

I attached:
"Replicates" in there I analyzed the data as if I have replicates (without the column “Repeats”)
"Repeats" in there I analyzed the data as if I have repeats (so I added a column with "Repeats")

The first ANOVA of the Repeats-File includes the repeats-factor. In the next step I set the Alpha to remove = 0,7 (just as an example). In this ANOVA it removes the repeats-factor. The ANOVA we get now looks 100% the same as the one I got in the replicates-file (without the repeats-factor).

That means to me if I set a “low” alpha to remove some not that significant factors then the analysis of a design with repeats and replicates will give me the same ANOVA. Does that make sense? I don’t think so. Think I am a bit stuck :-/

Thanks for the grate discussion!

Greeting

#### Attachments

• Replicates_2.MPJ
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• Repli_Session_Wi.pdf
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• Repeats_03_Session_Wi.pdf
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• Repeats_03.MPJ
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#### Miner

##### Forum Moderator
Sorry for the delay. I was traveling this weekend then out sick.

Your approach to analyzing the replicates appears to be correct. The data are structured correctly and appears to have been set up correctly in the analysis. Side note: I am curious why you did not consider interactions in your analysis.

Regarding your set up for the repeats, I do have questions. The normal approach for repeats is to create a column for each repeat. Therefore, you would have had 6 columns of data. You would then create another column using Calc > Row Statistics > Mean in which to store the row means of these six columns. In the analysis, you would then analyze this new column. Did you see the method which you used somewhere? If so, please reference the source, so I can study it.

Your other questions are moot until we resolve the repeat analysis questions.

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#### Felix_xx

Hallo Miner,

I am curious why you did not consider interactions in your Analysis.
I would insert interaction later on. Was just a first try.

Did you see the method which you used somewhere?
I thought what I did is exactly what they did in the example (the one you send me). They just called the repeats “ETime” (Elapsed Time) and I called them “repeats”. Did I get it wrong?

Therefore, you would have had 6 columns of data. You would then create another column using Calc > Row Statistics > Mean in which to store the row means of these six columns. In the analysis, you would then analyze this new column.
If I follow your instructions it works (see attached files). Did they explain this procedure in the example?
I thought if I use the mean as an input I loos information. The software does not know that I made many repeats. It looks like a “normal” ANOVA without repeats / replicates. I thought that I am not supposed to use the mean but somehow insert every single measurement.

Greetings

#### Attachments

• Repeats_04.MPJ
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• Repeats_04.pdf
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