Statistical test on percentage data with replicates Imagine I am doing an experiment where I want to look at the cellular composition of tumour samples
I have 3 samples with phenotype A (e.g. metastasizing) and 3 samples with phenotype B (e.g. not metastasizing)
The samples with phenotype A consist of (respectively) 30%, 32% and 33% "green cells", 28%, 27% and 28% "blue cells" and 42%, 41% and 39% "red cells".
The samples with phenotype B consist of (respectively) 10, 9 and 11 "green cells", 50%, 49% and 47% "blue cells" and 40%, 42% and 42% "red cells".
How can I tell if there is a significantly different % of the different cell types between the different types tumours (e.g. between phenotypes)?
Normally it would require 3 t-tests. However because they are %s, I suppose that the assumptions of a t-test are not met. Is there an analogous test for %s?
 A: If I understand the problem description correctly, I would use a multinomial regression model with a binary indicator for whether the sample was from cells of type A or B. Because we would be interested in whether there were any difference in any proportion of cells of any type, we want to treat the outcome as fully categorical. The null hypothesis for the Wald test or maximum liklihood test for the parameter associated with the indicator is that there is no difference in proportion of cell types between metastasized and non-metastasized cell samples. This test is analogous to a Pearson chi-square test 2 by K for contingency tables, but accounts for the fact that a single replicate contributes some proportion to the K categorical outcomes. In this case, K is three.
It would be a useful secondary analysis to describe specifically what the distribution of cells are and how you would hope to make a biomarker or other useful diagnostic model for metastasis. 
A: Why not try resampling (with replacement)? 
Example: Combine your 6 samples into two. One sample for A with m data points, and one sample for B with n data points. Compute your percentages.
Now simulate a large number of samples with replacement, where you choose randomly from all (m+n) data points, and you again choose samples of size m and n. 
Count up the number of samples that produce test statistics that match or are more extreme than your observed value. 
The p-value is the ratio of the count in the previous step over the number of resamples. 
