# Describing Differences between Two Inferred Populations

I am interested in the size of an animal in two populations, and found reliable estimates of the population provided by NOAA. The data was in the form of estimated total population within discrete size intervals, presented like so:

Size    Pop1     Pop1_Norm   Pop1_Cumul  Pop2    Pop2_Norm   Pop2_Cumul
21      584.14   1.15E-06    1.15E-06    5092.75 9.28E-05    9.28E-05
22      98365.15 0.000194238 0.000195391 503.38  9.18E-06    0.000102018
23      41899.32 8.27E-05    0.000278128 5723.3  0.000104337 0.000206355
...


Pop1 and 2 represent the number of individuals at a given size, the Norm columns represent the fraction of the total population, and the Cumul columns the cumulative proportion of individuals at or below the given size class. Unfortunately, I don't have access to the raw sample data, and so understand I can't do any inference myself.

However I'd still like to quantify the difference in the population distributions. What are the best methods for describing differences between two populations? Should I just take the difference of the means? What methodological problems do I face working with an estimate of the true population distribution?

I have graphed the cumulative size distributions of these populations, now how can I describe the difference?

• Could you edit your post to give any details about the table columns? – Stephan Kolassa Mar 30 '15 at 9:24
• Done, sorry for the ambiguity – Mike Rhodes Mar 30 '15 at 20:50