two-way ANOVA with unbalanced data

[#1]

hello,

I can't find anything about the recommended way to treat unbalanced data in JMP (v15) in the help menu. If you do a search in these forums, there are lots of previous questions about this, but it's not clear to me which, if any, is considered the best option! So, apologies for raising what may be a frequent question, but if anyone can point me to a previous answer that is helpful I would be very grateful, thank you.

[#2]

There is no one way to treat unbalanced data or data at all. Treatment depends on what you want to compare/know (mean, spread, ...).

I think, best method is to first plot data, its all about the distribution. Depending on distribution of data and what you need to get, there are some options to figure out. Most methods have some prerequisites, some have no.

An example would be helpful.

[#3]

Thanks for the response. The data are from a designed two-factor experiment, which started out with 10 replicates per combination, but quite a number of samples have been lost along the way, such that we now have between 4 and 9 replicates per level.

[#4]

Balanced is not required for ANOVA. Unbalanced data will not bias the estimates. What is your concern about using ANOVA in this case?

[#5]

Thanks for the response. I have had people express very strongly to me that unbalanced data were unacceptable for an ANOVA model (although, admittedly, this was in the context of a repeated-measures ANOVA), and I was trying to be as principled as I could be when it comes to analysing my own data: I didn't want to be making unreliable inferences. As I said, I did try a search of these forums first, and I didn't find any conclusive answers. 

[#6]

There won't be any "conclusive" answers to your query.  Just to clarify, you have replicates or repeats?  (are the multiple samples per treatment independently acquired in relation to the treatment combinations or did you set up the treatment combination and get multiple samples (repeats)?). If these are truly replicates and they are randomly acquired, then they are going to be used to quantify the mean square error...balance won't be a significant issue. 

Of course it might be worthwhile to understand why the samples were "lost".

[#7]

I suspect that these comments come from people without an education in statistics. Ask them for the basis of their concern. Why is balance important? it used to be when ANOVA was invented a century ago. The calculations were obtained using computers, but that was a job title for a human. The calculations simplify when the data are balanced, but that is not a requirement of ANOVA itself. It is a requirement of the computers a century ago.