I am new to the board and tried to search for Hotelling's T but could not find an answer to my problem (the appropriate test statistic). I'm not sure if Hotelling's is the correct stat, or if one exists.

Setup: I have two samples of different sizes, A and B, drawn from different populations based on complex survey design. For each sample I have 12 variables reflecting some aspect of `quality' (which are actually calculated as weighted ratios of each of the 12 variables to 1 common `13th' variable...I hope that makes sense: [A1/A13 ... A12/A13] [B1/B13 ... B12/B13]). An estimate of "overall quality index"

*for each of the populations*is defined as the sum of the 12 estimated mean sub-qualities.

How would one test if `overall quality index' is significantly different for the two samples? Should I test each individual quality separately using t-test? Use Hotelling's? Any other suggestions?