How to Include Repeats in DOE Response Data

[#1]

Good afternoon. I created a fractional factorial DOE with 6 factors and 2 levels. There are 8 response variables. The data table created for this DOE only has columns for 1 measurement for each response variable. However, each experimental code has 2 repeats for all 8 response variables. The data table does not have columns for the repeats. How do I get the repeats included in the data table so that I am able to complete ANOVA analysis?

[#2 · Accepted solution]

First, welcome to the community.

Just have 2 columns for each response variable in sequence (see attached)  When the data is collected, stack each of those 2 columns (Tables>Stack and run multiple series stack 8 is the number of series and check the Contiguous box). Run a simple range chart to look for the variability within treatment If satisfied with the range chart, Do Tables>Summary and summarize the 2 repeated data points (You may average and calculate the variance of those 2 repeated data points to use as response variables.)

[#3]

Hi @BILPE,

Welcome in the Community !

To add a complementary option to the one proposed by @statman, you could also leverage your repeats in the modeling part, by stacking your data under a new column like "repetition" (with two levels, 1 and 2 since you have two measurements per condition/run), and using this factor as a random effect : 

Then, using a Mixed model approach, you would have an estimate of the variance explained by this random effect "repetition" (you can also assess the variability importance visually with the actual by predicted plot and residuals visualization) and have more information about the comparison between effect’s estimated variance and model’s estimated error variance (see : Restricted Maximum Likelihood (REML) Method) :

Doing so would also enable more precise estimation of the other fixed effect terms.

Please find attached the datatable with data used for demonstration.

[#4]

Victor, you are allocating DFs to the repeats.  The repeats are not independent events and therefore should not be allocated DFs.  This would be appropriate if the data points were replicates, not repeats.

[#5]

You're right, sorry I answered too quickly.
I'm wondering if it couldn't be appropriate to fit a Repeated Measures mixed model, using the "Pattern" (treatment) as "Subject" role and "Repetition" as "Repeated" role ? The hardest part would be to figure out and assume the correct covariances structure.

[#6]

I don't think that would be "correct" (I'm not sure correct matters???).  There is no random variable, so the model is completely fixed effects (i.e., no mixed model). The DFs from the treatments are assigned to the model terms.  The repeats are within treatment.  The variation within treatment can't be due to the model effects as they are constant when the repeated measures are collected.  They must be due to the noise changing within treatment.  That noise can't be assigned when using repeats, however, it can be quantified with the use of standard deviation or variance as a response.  When you average the repeated measures it has the interesting impact of reducing the effect of the within treatment noise and thus increasing the precision of the experiment.