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I have a dataset of three groups of cells treated with 10 different compounds and am not sure how to check for significant differences between those treatments. Within each group the data is also paired.

I tried doing an two-way ANOVA; however, that doesn't work because of the unbalanced sample size. I then used GLM in SPSS, which at least gives me the correct means and standard deviations for each treatment, but it doesn't calculate correct p-values since it assumes equal variances.

Could somebody suggest the correct test in this case or knows how to modify the GLM accordingly?

Edit: So here is how my dataset looks like in priciple, I only have 8 more treatments: enter image description here

I now would like to compare the treatment conditions to each other, so for example 'is there a significant difference between the number of puncta in control and starvation conditions?'.

So far I used univariate GLM with the Puncta as dependent variable and group and treatment as independent factors.

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    $\begingroup$ Not enough detail here. What is your response (outcome) variable? Unequal group sizes (presumably what you mean) shouldn't derail ANOVA. What GLM did you use? Can you post the data? The answer may well be: use a GLM with appropriate family and link, but we can't possibly advise on what those are while being told nothing about the response. $\endgroup$
    – Nick Cox
    Commented Nov 15, 2013 at 9:51
  • $\begingroup$ Sorry, I'm quite new to this, but I'll try to give you more details. The output variable is the number of puncta within my cells - so basically a certain phenotype defined by a number of dots that appear within the cells. So I have this: Treatment: Control Starvation $\endgroup$
    – Laura
    Commented Nov 15, 2013 at 12:14
  • $\begingroup$ Sorry, its like this: Treatment: 10 different conditions, within each condition there are 3 groups and within the groups there are 5-10 values. I used univariate GLM and will try to post the data to give you a better overview... $\endgroup$
    – Laura
    Commented Nov 15, 2013 at 12:26
  • $\begingroup$ Number of puncta: sounds as if you should be checking out a Poisson model in the first instance. That fits under generalized linear model. You should specify which GLM you used (e.g. exact syntax used). $\endgroup$
    – Nick Cox
    Commented Nov 15, 2013 at 13:27
  • $\begingroup$ It would really help if you would in detail explain your experiment using non-biological terms. At the moment, the question is still extremely vague and it might generate wrong advices. @NickCox: I am 95% confident that "GLM" means "General linear model" here (resp. in SPSS), including repeated measures ANOVA. $\endgroup$
    – Michael M
    Commented Nov 15, 2013 at 14:03

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In the past I had a similar problem with the analysis of clinical data using 2-way ANOVA. What I did was to use the Anova function of the R package car and set the test type to III (type="III"). If you had posted more information, maybe I could provide also a code example. The results I got seemed reasonable.

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I see that the two factors(trt, grp) are crossed, which seems a two-way ANOVA problem with unequal cell sizes. A general way to do is to use linear mixed model procesure, so you can specify different variances for difference groups. To answer research questions, you can use contrasts to compare ctrl vs star within grp A for instance.

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