If you want to compare two populations (say X and Y) with the same sample size N, you can do the following:

1. for i from 1 to N calculate z[i]= x[i]-y[i]

2. test z[i] against zero.

Even if x[i] and y[i] are skewed, it is likely that z[i] will not be skewed.

But I am still not sure about what your research question is. Please formulate it more clearly: do you want to compare the means of distributions?

How is size being measured?

Thank you Andrey and Mr. Bruce. I would love to explain a bit about the data so that you can know better which statistical method I can apply.

I conducted the experiments about feed management for Pacific White Shrimp. I evaluated 4 feeding protocols to see how different feed allowances affect to the growth of shrimp under ponds conditions. The study was done in sixteen 0.1 ha-ponds (4 replicates/ 4 feeding protocols for each treatments). At harvest, I weighed individually 150 shrimps for each ponds  to see the size distribution of each pond. I made the count frequency for each ponds, then average for each treatment. For example: Treatment 1 shows that size I: 10-15 shrimp/lb accounted for 20%, size  II:15-20 shrimp/lb accounted 50%, size III:20-25 shrimp/lb accounted for 10%, size IV:e 25-30 shrimp/lb accounted 5%, size V: 30-35 shrimp/lb 4%, etc. As the size of shrimp (how big the shrimp is) is the major factor determining the its value, then I go further with economic evaluation. Therefore, I want to see 2 things: 1/ compare the mean distribution among 4 treatments. 2/ Wondering that if it is possible to see the difference at each size group, for instance: size I: 10-15 shrimp is 20% for Treatment 1 but 22% for treatment 2, or 23% for treatment 3, etc.

Thank you in advance for discussion and sound suggestion.