Hi,
I have designed my experiment as a 25-1V fractional factorial design because I would like to investigate multiple repetition of each run. However, I am not able to read anything about repeated measurements and fractional factorial design.
Is it possible? Does it change anything? Does someone know course/book/paper on this?
Thank you
Yes, it is possible. It may change things, but it depends on the response and its inherent variability. Assuming that there is some uncertainty in the response, the mean response from multiple measurements can be used to get a more accurate measure of the factor effects.
Additionally, depending on how many measurements you are doing for each combination of factors, you could use other responses to see if there are any statistically significant main effects or interactions associated with the minimum, maximum, standard deviation, or even skewness or kurtosis of the distribution of measurement responses. This may give an indication of whether the uncertainty or distribution form of the response variable is changing with the factors in your (factorial) factorial design.
Hopefully the above strategy explains how the usual methodology can be used to analyze fractional factorial DOEs with multiple measurements. You might try Montgomery's 'Design of Experiments' book for further information. That is the textbook I would check first, at least.
Dear Yoann I concur with Mark’s comment but I would highlight his sentence “Assuming that there is some uncertainty in the response…” would be something new to me (in my field of work). In fact, according to my experience, if you are not able to see any variability between replicates (contributing therefore to the uncertainty in the response) it’s because you are not using the proper tool to measure the response.
Said that and taking into consideration your approach I guess you are facing a non-negligible variability (when compared to the change in the response) in order to justify the replication/repetition of a 5 factor design. Even if performing “only” duplicates you will be performing 16 experiments. Do you actually need to replicate (duplicate, triplicate) the whole fractional design? Can you afford it (money, time, materials, etc)?
A last though, it’s wiser and better to identify and control the sources of uncertainty. However, sometimes (too many) it is not possible and therefore repetition or replication is the only way left to tackle the issue. I also agree with Mark’s advice on the Montgomery’s book. Good luck. Regards.
Regarding the assumptions for statistical models and tests have to be satisfied before developing the statistical models and tests. Please refer to:
1. Landau, S. and Everitt, B. S.(2004). A Handbook of Statistical analyses using SPSS.
2.Howitt, D. and Cramer, D.(2008). Introduction to SPSS.
Regards,
Zuhair
re Spss I'd recommend the much more entertaining and discursive
Discovering statistics using SPSS by Andy Field.
His youtube channel shows his lectures re various aspects of statistical analysis https://www.youtube.com/channel/UCakigkjm3vBzEHpFzECDXQQ
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