# Multiple Factor ANOVA with Count Data as Output

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• #52793

Lisa_Larae
Participant

I have a statistician who recently designed and ran an experiment where the response was a count of how many of the parts failed.
The experiment has 3 factors and their interactions, it was analyzed (incorrectly) using ANOVA.  What should he do with this data?  I can’t find anywhere where Minitab treats 3 factors and their interactions if the response data is not normal.  To add to the complexity, two of the factors are continuous and one is categorical.

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#186185

newbie
Participant

A couple ideas.  First, running an ANOVA on non-normal data isn’t necessarily an incorrect approach.  It is largely robust to this assumption, and depending on the number of distinct categories you find in your data set, an argument could be made for it being a valid approach.  If not, you could always investigate transforming the data (ie Box Cox) then running the analysis, or simply using a non-parametric test like a Moods Median Test for statistical difference.  If prediction is of interest, you could fit a regression model , which would give you both statistical significance of the 3 predictors as well as the magnitude and direction of their effects on the response.
What did the statistician tell  you as to why he chose that tool?  Why are you, a LSS person, overseeing the stat guy?  He isnt qualified to act as your statistical SME?

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#186186

Robert Butler
Participant

I’m not trying to be insulting nor am I trying to start a fight but if you really have an individual with a degree in statistics (BS,MS, PhD) then you need to tell him to address this problem.
The statement “I can’t find anywhere where Minitab treats 3 factors and their interactions if the response data is not normal” suggests (I hope) that he designed the experiment and someone else analyzed it.  I say this because any statistician could tell you the fact that your response isn’t normal isn’t an issue.
In order to offer a meaningful answer to your question you will need to tell us more about the data.  In particular, how were the results from each experiment recorded.
Did you set up an experiment, choose a fixed period of time, count the failures, record the result and move on to the next experiment after a making a single measure or did you take multiple measures over fixed periods of time for each experiment or did you do something else?  It would also be helpful if you could give us some idea of the range of counts across the design – minimum, maximum, and median.
If you can provide this information perhaps I or someone else could offer some suggestions.

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#186189

Lisa_Larae
Participant

The data is reported out simply as the number of failures per condition.  For example, condition #1 had 1 failure, condition #2 had 0 failures, condition #3 had 4 failures.   Values for the number of failures in the experiment were as follows:   1, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 2, 3, 0, 0.  His report doesn’t tell me the total number of samples that were examined at each condition for failure.

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#186198

Robert Butler
Participant

If I understand your posts correctly you have 3 factors and you have a design with 15 experiment where each experimental condition was run only once.  In addition, only one sample was taken for each condition.  You haven’t said anything about the amount of time for each condition but I’m hoping that your method consisted of lining out the process for each setting and then when everything was running smoothly at that condition you started the clock and counted failures for a specified period of time (by the way – we are assuming that failures could only be classed as a yes or a no – if this isn’t the case, for example if failure is something like number of flexes to stress failure then there may be other ways to address your problem).
3 variables in 15 experiments along with your comments concerning intereactions and your lack of comments concerning replication of experiments would suggest you ran a rotatable composite design with no replicates. I make this statement since this is the only design I can think of that would test 3 variables in 15 experiments ( 2**3 + 2*3 +1).
If this is the case then the best I can offer is a salvage operation.
Run the regression where the full model will consist of all main effects, all curvilinear effects, and all two way interactions and the Y response would just be the 15 values you cited in your earlier post and see what you get.  Run both backward and stepwise to see if the two methods agree and report what you find.  You may get lucky and get something but given the Y values you posted I rather doubt it.

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