Well, I am assuming I have to use an nonparametric test. My data is interval in nature, but the series used to get that data were not randomly selected. Allow me to explain.

I started with a data set from another researcher consisting of 88 series of crimes. Each series consists of the lat/lon coordinates for a number of crime scenes; the number of scenes varies from series to series. Each series also contains the lat/lon coordinates of the criminal's home residence. I am not exactly sure how these cases were chosen for the set, but they were most likely selected based on their status as solved cases committed by a single criminal living at one location for the duration of the series.

I then selected 55 series from the set of 88 based on criteria recommended by researchers for conducting my type of research. This basically consisted of eliminating series where the home residence is significantly outside the convex hull of the crime scenes.

The actual data I am testing consists of an accuracy measure called the "search cost". Basically, it is the percentage of the map each program has to search before finding the actual home residence.

Am I limited to nonparametric tests because of the way I selected certain series to be included in the research? Or can I employ parametric tests because I did not select the series based on the the actual data I am analyzing (search costs) and had no idea what those would be while building the data set?

I apologize for the continuing and lengthy treatise on my problem, but I greatly appreciate all of your help!

**UPDATE:** I did a normality test for my data and found it is far from normal. So I guess I'm limited to nonparametric tests after all. However, if anyone has parametric data and needs to test for equivalence, you may find this link very helpful:

http://www.graphpad.com/library/BiostatsSpecial/article_182.htm