# Minitab Fractional Factorial Data Entry Help

R

#### rclukey

Dear Forum,
I'm new to the forum, minitab, and DoE...

I have a question about data entry / setup for Fractional Factorial designs that I was hoping someone could help me with. I haven't run the experiment yet, I'm still designing it...

I'm not sure how to enter data representing measurements from multiple participants for each of the 16 experimental conditions of my FF design.

For each experimental run, I recorded the subjective reaction from each participant. So, do I compute the simple average and enter it in my DV column?

And, can I use the same 8 participants for each of the 16 experimental conditions of the FF design? Is that essentially a repeated measures design?

Thanks
Ryan

#### Stijloor

Super Moderator
A Quick Bump!

Can someone help Ryan?

Thank you very much!

Stijloor.

#### Miner

##### Forum Moderator
You have asked several questions in this post, so without seeing the details my response may be incomplete.

1. Multiple responses: Enter each response in a separate column.
1. Each response is a separate Y variable: Analyze separately, and use Response Optimizer to jointly optimize settings if applicable.
2. Each response is a repeat under different noise conditions: Use Preprocess for Analyze Variability, then use Analyze Variability on standard deviations. Analyze means as usual DOE.
2. Using same participants:
1. Participants are noise factors: Analyze as in 1.2 above.
2. Participants over time is purpose of study: Treat as a Repeated Measures design.

R

#### rclukey

Hi Miner,

Thank you for your prompt reply. Please allow me ask a couple of follow-up questions. I'm struggling to understand the concept as it differs from regular ANOVA and GLM; most of my work has been running participants in small behavioral studies for psychological evaluations, not manufacturing process improvement and optimization. So, I'm used to collecting data from a sample of participants where there are only 1 or 2 independent variables, and the other variables are covariates.

Normally, when comparing means (e.g between men and women), you calculate the mean for each group, which has a corresponding Std Dev; so the mean has variance within each cell. Thus, in each experimental condition you have multiple subjects contributing to the mean. However, in DOE, it seems that you have 1 subject for each condition (run) - so where does the variance come from? (you see how I'm looking at this?)

Here's the actual problem:

I have a product design element (e.g. a button) which has 5 parameters that could be adjusted in a binary manner (e.g. low / high). Each of these parameters is believed to affect the user's perception of the quality of the product / experience (in this case the quality is really really important as there are both ergonomic and manufacturing costs associated with these decisions).

We need to know which variables affect the user's perception of quality, how what the optimal level setting is for each parameter - seems like a DoE experiment? The only problem is that, as with all psychological studies, we don't sample 1 subject(participant) per condition (run?) - we sample a group of participants (e.g. N= 10) in order to get a more realistic estimate of the actual mean and to generalize to some population. So, perhaps I'm trying to fit a square peg in a round hole, but really, I'm not entirely sure how I should go about this at all.

Right, so my brain is stuck on t-tests, and simple repeated measures experiments, and at most MANOVA, but from a behavioral sciences perspective. I appreciate your assistance, and could benefit from a little hand-holding in this case.

Thank you very very much for you willingness to share your expertise and knowledge on this topic.

Ryan

#### Miner

##### Forum Moderator
Hi Miner,

Thank you for your prompt reply. Please allow me ask a couple of follow-up questions. I'm struggling to understand the concept as it differs from regular ANOVA and GLM; most of my work has been running participants in small behavioral studies for psychological evaluations, not manufacturing process improvement and optimization. So, I'm used to collecting data from a sample of participants where there are only 1 or 2 independent variables, and the other variables are covariates.
DOEs are typically analyzed using a k-way ANOVA vs. the 1-way ANOVA used for a single factor. Each factor in the experiment has a line item in the ANOVA table, so the principle is the same.

Normally, when comparing means (e.g between men and women), you calculate the mean for each group, which has a corresponding Std Dev; so the mean has variance within each cell. Thus, in each experimental condition you have multiple subjects contributing to the mean. However, in DOE, it seems that you have 1 subject for each condition (run) - so where does the variance come from? (you see how I'm looking at this?)
You can have four different scenarios in a DOE:
1. Unreplicated: An unreplicated experiment will not have an error term with which to calculate an F-ratio. Standard practice in industry is to pool high order interactions (i.e., 3 and higher) to provide a pseudo-error term. Pooling non-significant 2nd order interactions and main effects is used as the next step. Refer to Statistics for Experimenter's by Box, Hunter and Hunter.
2. Replicated: A replicated experiment means the entire experiment was run multiple times. The replicates provide the error term. Replication includes setup to setup variation in the error term.
3. Unreplicated with Repeats: Handle the same as an unreplicated experiment. The advantage of repeats is that you can analyze the mean and the standard deviation separately and identify factors that may be used to reduce variation. Refer to Taguchi Parameter Design.
4. Replicated with Repeats: Same as Replicated plus ability to analyze mean and standard deviation separately.
Here's the actual problem:

I have a product design element (e.g. a button) which has 5 parameters that could be adjusted in a binary manner (e.g. low / high). Each of these parameters is believed to affect the user's perception of the quality of the product / experience (in this case the quality is really really important as there are both ergonomic and manufacturing costs associated with these decisions).

We need to know which variables affect the user's perception of quality, how what the optimal level setting is for each parameter - seems like a DoE experiment? The only problem is that, as with all psychological studies, we don't sample 1 subject(participant) per condition (run?) - we sample a group of participants (e.g. N= 10) in order to get a more realistic estimate of the actual mean and to generalize to some population. So, perhaps I'm trying to fit a square peg in a round hole, but really, I'm not entirely sure how I should go about this at all.
You are on the right track. A DOE is the correct approach and you are correctly identifying the right questions that must be asked.
• If you perform 10 complete setups of your experimental design and randomly assign the resulting product to the participants, you would be performing a replicated (10x) experiment. Design your experiment for 10 replicates. The analysis is straightforward in Minitab.
• If you perform 1 setup of your experimental design and create 10 units for each condition and randomly assign these to the 10 participants, you would be performing an unreplicated experiment with 10 Repeats. Calculate the means for each condition and analyze using the means. You will have to pool the high order interactions to create a pseudo-error term.
Right, so my brain is stuck on t-tests, and simple repeated measures experiments, and at most MANOVA, but from a behavioral sciences perspective. I appreciate your assistance, and could benefit from a little hand-holding in this case.

Thank you very very much for you willingness to share your expertise and knowledge on this topic.

Ryan
If you randomized the experimental units across the participants and randomize the order within each participant, you will avoid the complexity of a repeated measures experiment. You are not trying to determine a time effect for each participant.

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