# Thread: Analysis of variance problem

1. ## Analysis of variance problem

Can anyone help me with the analysis of data for the problem below? Unfortuantely, I did not design the experiment so I have to work with the data provided.

Samples of a homogeneous powder were distributed to 6 laboratories (A-F) for analysis. Each laboratory determined the purity of powder by 6 sequential analyses on the same day. The powders were then analysed in duplicate, each day over a period of the next 6 working days (producing another 12 results for each laboratory). I want to compare the variances between results from each laboratory for samples run on the same day (I think can do this for the first set of results with a one-way analysis of variance). However, I want to see if there is any additional variance for samples run on different days (i.e. are the intruments stable over the 6 days or is there some additional error).

Can I combine the 2 sets of data and what would be the best way of processing the data in R? In particular I am not sure how to deal with the second set of results where there is a mixture of samples run on the same day and on different days.

Any help and suggestions would be much appreciated.

2. You have two levels of possible correlation.The only independent measures you really have are from each of the 6 laboratories.

My understanding of the way you presented your problem is that among the 6 labs:

Day 1: 6 measurements
Day 2-6: 2 measurements per day

So in total, you have 18 measurements from each lab, which totals 108 obs. Is that correct? If so, are you aware of GEE models?

3. Yes, there are 6 labs with measurements made on 7 different days, giving a total 108 observations:
Day 1: 6 measurements for each lab
Day 2-7: 2 measurements per day for each lab

Measurements made the same day are made consecutively in the analysis batch. Days 1 to 7 are different days and not necessary a regular time series. Intuitively, there should be less experimental error between samples run on the same day compared to samples run on different days.

I have not used GEE models, but I have looked at the geeglm function in the geepack library. There are a lot of parameters I don't understand so I am not sure how I would apply this function. Can I use something like the glm fuction? Also if I use a function with a formula to represent the model how should I include Day number in the formula?

4. If you have 6 days of subsequent measurements the total obs would be 6*(1) + 6*(2) = 18 measurements per lab, which totals 126 observations.

It looks like you have two levels of possible correlations. There is correlation among daily measurements and correlation among all the measurements from each lab.

I'm not familiar with R and so I cannot help you with the syntax. If you are interested in using GEE models though, here is a good link:

http://ehs.sph.berkeley.edu/hubbard/...pril_2006b.pdf

HTH

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