Paired T-Test with 3 Processes and Multiple Response

tnorthen

Hi Everybody, 

 

I ran an experiment where the goal was to compare whether three separate processes produced similar results. I made 6 different products (with different specifications) on each of the three processes (6 products x 3 processes = 18 total). Additionally, I have at least two different responses I want to compare the output of. I am almost certain this data is paired, but I don't know if I can run a paired T-test or Anova on these. 

 

On idea I had was to subtract the differences from each permutation and then do an Anova. Alternatively, I could run 3 different paired T-tests as well, but I'm not sure if this is the correct way to do it. 

 

Thanks for the help!

gzmorgan0

Hi @tnorthen,

A paired t-test is a comparison of two treatments on blocks (products). When there are more than two treatments, this is typically run and analyzed as "randomized block" design. If I understand your question correctly your data is this type of design. This type of design can be analyzed with Fit Y by X with Product as a block factor and Process as a treatment (x) factor. If the ANOVA test (comparison of between treatments is larger than expected random product effects (within treatment group) then a multiple comparison test (I like Tukey-Kramer HSD) is run to estimate/quantify the differences in the treatments.  

 

This is a high level description that hopefully gives you some leads to investigate.  I have attached a tricked up test table. The table has the analysis script embedded.  Note there are many ways the analysis can be biased in the way the data was generated. For example, suppose each process involves different equipment. This begs the question whether any observed differences are due to the process or due to the equipment? If the same equipment was used, were the processes run in random order over the different products?  Without going into details, process order, cross contamination, etc could influence results.  I suggest if possible find someone in your org that might be familiar with these methods to work thru the analyses and details of your data collection.

 

TestRandomizedBlock.jmp