ANOVA with repeated measures

[#1]

Hi I set up a "DoE" with 5 factors, four of them have continuous values on 2 levels and last factor discrete numeric(K) also on 2 levels. I have 17 samples, each tested twice. In total we have 34 attempts. I want to perform for the ANOVA with repetition.

I have attached the file, can you take a look and give me a timely response.

Thanks in advance

[#2]

Hi,

What is the nature of the repeats? "Repeated measures" usually refers to a situation where measures are taken over time to understand how a response is changing with time. I don't think that is the case here. 

Is there any reason why you can't just take the average of the 2 repeats and analyse that as your response? You can create an average column by selecting the 2 columns (click and drag on the column headers), then right-click > New Formula Column > Combine > Average.

What is the objective of the experiment? The goal is important in understanding the appropriate analysis as different models are possible. It looks like it was probably designed to test a model with all main effects and 2-factor interactions. You would do that using Fit Model from the Analyze menu like this:

I am a bit confused why you have supplied the table as an Excel file. Was the experiment designed in JMP?

[#3]

It might be a good idea to look at the correlation between the 2 repeats. For the most part they correlate well, but there is at least one (BV_11) where there is a bigger difference between repeats.

[#4 · Accepted solution]

View more...

Sam, it would be helpful if you could attach JMP files vs. excel.  Here are my thoughts/comments/questions:

If I understand your situation, you have 1 experimental unit (sample) for each treatment.  16 Degrees of freedom.  The two "data points" for each experimental unit are acquired by measuring the sample twice.  The reason why those two data points would vary is due to the measurement process (and possibly within sample variation).  I also assume the measurement system is not destructive, is  that correct?

If this is the case, then I would plot the ranges on a range chart to estimate the stability of the measurement process.  If it is stable, certainly you can average those 2 value (which has the effect of reducing the measurement system variation (S^2/n)) and thus increasing the precision of the experiment.  If those 2 data points also capture other components of variation (e.g., within sample variation), you could also use the variance of the 2 data points as a response variable to see if the x's in your experiment causally relate. And yes, it would be a good idea to look at the correlation of the mean and range.

Sam, I have attached 2 JMP files.  

RauheitStack is stacking the 2 data points for analysis.  I added two script to analyze the data.

RauheitSum is the summary statistics for the 2 data points (keep in mind I did not remove or replace the unusual data points from sample 13.  I also added a multivariate and a fit model script.

Now to properly analyze the data set, before you do any statistics, you need to determine if the amount of variation created in the experiment is of any practical value.  Did the response change enough?  If so proceed with analysis.  If not, why?