Confirmation a Black Widow Spider ID? (central New Jersey)

When collecting near the Cimmaron river in Oklahoma, I encountered under rocks in a 100x100 meter area the same spiders but with the lines and patterns of red all different - no hourglass shape, red line only, etc. It was very interestiong to see a small area with such pattern diversity. I also saw in Florida, a male Fiddler crab silked up in a black widow web. He was certainly dying but I was impressed that a little spider was able to tackle something ten times its size.

The shiny abdomen and legs as well as the shape cause me to think this is a female widow.