Concentrations of 50 proteins were measured in 50 normal persons and 150 patients. I am just wondering what kind of analysis will be most appropriate to finding out which protein concentration is most different.
I think that your problem could be analysed thought a multivariate approach. It is a shame that the n are inequal. Permanova (permutational ANOVA) is a powerful tool design for mutivariate analysis though permutation techniques (www.stat.auckland.ac.nz/~mja/Programs.htm) there are extensive manuals on that web site.
I would conduct a one-way permanova (on eucledian distances - on 50 dv (proteins), and if you find statistical diferences between those two group, i will follow analysis of which variable/s are responsables for the major differences. These techniques are very studied in ecological situations (replace proteins type by species; and then it is always important to know which species (or proteins) are responsable of the differences between sites (or groups)), i will search for IndVal techniques or SIMPER rutine. please excuse my english!
I would suggest the following approach:
First run unpaired t tests on each of the 50 proteins. Record the P value from each comparison, but ignore any statements about statistical significance.
You next will divide the 50 proteins into two groups, those where you suspect the difference is real ("discoveries") and those where you suspect the difference is a coincidence. To decide where to draw the line, you need to choose the maximum false discovery rate (FDR) you feel comfortable with. This is the probability that a protein that you think shows a real difference is in fact a coincidence of random sampling, a false discovery.
Once you have decided on your desired maximum FDR (a fraction between 0 and 1, usually abbreviated Q), you can easily divide your 50 proteins into "discoveries" and "not discoveries" using the method of Benjamini and Hochberg. Briefly, the method first sorts the P values from high to low. The comparison with the largest P value is considered to be a "discovery" if it is less than Q. The second largest is a discovery if the P value is less than Q*(24/25), ... and the comparison with the smallest P value is a discovery if it is less than Q/25. (Why 25? Because there are 25 comparisons in your example). Once you find a comparison to be a "discovery", also call all other comparisons with smaller P values to be discoveries (without doing more calculations).
Note that the term "significant" is not used with this FDR method.
GraphPad Prism 6 can do all this with its multiple t test analysis. But so can lots of programs. It also wouldn't be hard to do it all with Excel.