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I did an experiment with a Mass spectrometer and want to compare the different treatments.

Control: Week 0: Immediate measurement of specimens (n=200) after taking the sample.

Treatment 1: Specimens (appx. n=120) taken from samples stored at -25°C in 100% ethanol. Sample measured after 1, 2, 3, 5, 7 and 12 weeks of storage.

Treatment 2: Specimens (appx. n=120) taken from samples stored at -25°C in 70% ethanol. Sample measured after 1, 2, 3, 5, 7 and 12 weeks of storage.

Treatment 3: Specimens (appx. n=120) taken from samples stored at Room Temperature in 70% ethanol. Sample measured after 1, 2, 3, 5, 7 and 12 weeks of storage.

My questions are: 1) Are the treatments different from the control? 2) Are the treatments different from each other? 3) What are the factors responsible for the difference?

The idea is, that the storage temperature has a strong negative influence on the number of peaks measured. This is also obvious in the following plot:

enter image description here

Dependent variable (response): Peaks

Independent variables:Temperature (categorical); Ethanol concentration (categorical); Time (is it categorical in this case?)

I was told to carry out an ANCOVA but: My residuals were not normally distributed when using a linear model. So I wanted to try GLM in which I had to specify, what distribution my data has. I tested for distributions and found, that a beta distribution was found to fit my data best. The problem is, that it is apparently not possibly to fit a beta regression on the data and use it for an ANCOVA. I found that using quasi-binomial distribution with a logit link could be used as a model in this case. This again lead to not normally distributed residuals. I mean the tests always showed my time as well as temperature had a significant influence on the response, but I cannot use this result since the test is not valid because of the distribution of the residuals.

Am I using the wrong test? Should I just carry out a U Test and compare the treatments to the control? And if so - how can I statistically show that temperature is responsible for the difference?

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A couple of thoughts. First, you seem to be testing the questions: 1) does temperature affect the sample result over time, and 2) does the ethanol concentration affect the sample result over time. However, you can only test question #1 on "treatment groups" control, 2, and 3 and you can test question #2 on treatment groups control, 1, and 2. I think these need to be separate tests you perform. Ideally if you had not carried out this test yet I would suggest adding another treatment group stored at room temperature in 100% ethanol.

Secondly, it seems to me that you are ignoring the correlation within samples over time in your data. A repeated measures model would account for the correlation in your data (i.e., the value of Sample A at time 0 should be fairly similar to the value of Sample A at times 1, 2, and 3).

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  • $\begingroup$ Thanks for your answer. About the first part: Yes I am well aware of that, and that is just the way I designed the study. There was not enough time to include another treatment, which is why I had do exclude one. Based on literature I chose to drop the treatment you mentioned. Secondly I need to admit, that I do not understand the second part of your answer. :/ Why should the number of peaks in week 0 be the same as in week 1,2 and 3 if I can clearly see differences? I think I just don't understand you right here. $\endgroup$
    – S.R.
    Commented Aug 1, 2017 at 6:32
  • $\begingroup$ Regarding the repeated measures mixed model, I apologize if I'm not explaining it clearly, it's a complex topic. I wasn't suggesting that the number of peaks would be the same over the weeks, I am suggesting that there is a correlation among the samples over time that should be accounted for. Try reading a bit about it. This is a good web page explaining some of the advantages of using it for situations like yours where you are repeatedly sampling from the same thing over time. uvm.edu/~dhowell/StatPages/More_Stuff/Mixed-Models-Repeated/… $\endgroup$
    – Bosley
    Commented Aug 1, 2017 at 12:16
  • $\begingroup$ However, if you don't want to go down the repeated measures mixed model road, there is some evidence that non-normal residuals might not be such a big deal. blog.minitab.com/blog/adventures-in-statistics-2/… stats.stackexchange.com/questions/163642/… $\endgroup$
    – Bosley
    Commented Aug 1, 2017 at 12:17

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